%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN917+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:41:00 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN917+1 : TPTP v9.0.0. Released v3.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:05:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(p_type, type, (
% 0.19/0.39 p: $i > $o)).
% 0.19/0.39 tff(elem_25_type, type, (
% 0.19/0.39 elem_25: $i)).
% 0.19/0.39 tff(c_type, type, (
% 0.19/0.39 c: $o)).
% 0.19/0.39 tff(tptp_fun_X_18_type, type, (
% 0.19/0.39 tptp_fun_X_18: $i)).
% 0.19/0.39 tff(tptp_fun_X_11_type, type, (
% 0.19/0.39 tptp_fun_X_11: $i)).
% 0.19/0.39 tff(q_type, type, (
% 0.19/0.39 q: $i > $o)).
% 0.19/0.39 tff(tptp_fun_X_6_type, type, (
% 0.19/0.39 tptp_fun_X_6: $i)).
% 0.19/0.39 tff(tptp_fun_X_8_type, type, (
% 0.19/0.39 tptp_fun_X_8: $i)).
% 0.19/0.39 tff(tptp_fun_X_7_type, type, (
% 0.19/0.39 tptp_fun_X_7: $i)).
% 0.19/0.39 tff(tptp_fun_X_13_type, type, (
% 0.19/0.39 tptp_fun_X_13: $i)).
% 0.19/0.39 tff(tptp_fun_Y_14_type, type, (
% 0.19/0.39 tptp_fun_Y_14: $i)).
% 0.19/0.39 tff(tptp_fun_Y_15_type, type, (
% 0.19/0.39 tptp_fun_Y_15: $i)).
% 0.19/0.39 tff(tptp_fun_X_19_type, type, (
% 0.19/0.39 tptp_fun_X_19: $i)).
% 0.19/0.39 tff(tptp_fun_X_16_type, type, (
% 0.19/0.39 tptp_fun_X_16: $i)).
% 0.19/0.39 tff(tptp_fun_X_12_type, type, (
% 0.19/0.39 tptp_fun_X_12: $i)).
% 0.19/0.39 tff(tptp_fun_X_10_type, type, (
% 0.19/0.39 tptp_fun_X_10: $i)).
% 0.19/0.39 tff(tptp_fun_X_20_type, type, (
% 0.19/0.39 tptp_fun_X_20: $i)).
% 0.19/0.39 tff(tptp_fun_X_17_type, type, (
% 0.19/0.39 tptp_fun_X_17: $i)).
% 0.19/0.39 tff(tptp_fun_X_9_type, type, (
% 0.19/0.39 tptp_fun_X_9: $i)).
% 0.19/0.39 tff(f_type, type, (
% 0.19/0.39 f: $i > $o)).
% 0.19/0.39 tff(h_type, type, (
% 0.19/0.39 h: $i > $o)).
% 0.19/0.39 tff(g_type, type, (
% 0.19/0.39 g: $i > $o)).
% 0.19/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.39 tptp_fun_Y_0: $i)).
% 0.19/0.39 tff(tptp_fun_X_4_type, type, (
% 0.19/0.39 tptp_fun_X_4: $i)).
% 0.19/0.39 tff(r_type, type, (
% 0.19/0.39 r: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_X_2_type, type, (
% 0.19/0.39 tptp_fun_X_2: $i)).
% 0.19/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.39 tptp_fun_Y_1: $i)).
% 0.19/0.39 tff(tptp_fun_Y_5_type, type, (
% 0.19/0.39 tptp_fun_Y_5: $i > $i)).
% 0.19/0.39 tff(elem_22_type, type, (
% 0.19/0.39 elem_22: $i)).
% 0.19/0.39 tff(tptp_fun_X_21_type, type, (
% 0.19/0.39 tptp_fun_X_21: $i)).
% 0.19/0.39 tff(tptp_fun_X_3_type, type, (
% 0.19/0.39 tptp_fun_X_3: $i)).
% 0.19/0.39 tff(1,assumption,(~![X: $i] : (~p(X))), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (((~c) | (~![X: $i] : (~p(X)))) | ![X: $i] : (~p(X))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 ((~c) | (~![X: $i] : (~p(X)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.39 tff(4,assumption,(~p(X!11)), introduced(assumption)).
% 0.19/0.39 tff(5,assumption,(~((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))))), introduced(assumption)).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))))) | ((~c) | p(X!11) | p(X!18))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 ((~c) | p(X!11) | p(X!18)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.19/0.39 tff(8,assumption,(~c), introduced(assumption)).
% 0.19/0.39 tff(9,assumption,(~((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))))), introduced(assumption)).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X))))) | (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (![X: $i] : (~p(X)) | ![X: $i] : (~q(X))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 ((~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ![X: $i] : (~p(X)) | ![X: $i] : (~q(X))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![X: $i] : (~q(X))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X))))) | q(X!13)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (q(X!13)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[14, 9])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 ((~![X: $i] : (~q(X))) | (~q(X!13))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[16, 15, 13])).
% 0.19/0.39 tff(18,plain,(((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X))))) | ![X: $i] : (~p(X))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[18, 1])).
% 0.19/0.39 tff(20,assumption,(~![X: $i] : p(X)), introduced(assumption)).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((c | (~![X: $i] : p(X))) | ![X: $i] : p(X)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (c | (~![X: $i] : p(X))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,assumption,(~p(X!7)), introduced(assumption)).
% 0.19/0.39 tff(24,assumption,(![X: $i] : p(X)), introduced(assumption)).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((~![X: $i] : p(X)) | p(X!7)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[25, 24, 23])).
% 0.19/0.39 tff(27,plain,(p(X!7) | (~![X: $i] : p(X))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (~![X: $i] : p(X)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[27, 23])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (((~![X: $i] : p(X)) | (~![X: $i] : q(X))) | ![X: $i] : p(X)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((~![X: $i] : p(X)) | (~![X: $i] : q(X))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (((~p(X!7)) | (~q(X!7))) | p(X!7)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 ((~p(X!7)) | (~q(X!7))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[31, 23])).
% 0.19/0.39 tff(33,assumption,(![X: $i] : (~((~p(X)) | (~q(X))))), introduced(assumption)).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![X: $i] : (~((~p(X)) | (~q(X))))) | (~((~p(X!7)) | (~q(X!7))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 33, 32])).
% 0.19/0.39 tff(36,plain,((~![X: $i] : (~((~p(X)) | (~q(X))))) | p(X!7)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (~![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[36, 23])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ((~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))) | (~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[38, 37, 30])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (((~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))) | (~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))))) | ((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))) | (~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (c | (~![X: $i] : p(X))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[21, 28])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((c | (~p(X!7))) | p(X!7)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (c | (~p(X!7))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[43, 23])).
% 0.19/0.39 tff(45,assumption,(![X: $i] : (~(c | (~p(X))))), introduced(assumption)).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((~![X: $i] : (~(c | (~p(X))))) | (~(c | (~p(X!7))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[46, 45, 44])).
% 0.19/0.39 tff(48,plain,((~![X: $i] : (~(c | (~p(X))))) | p(X!7)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (~![X: $i] : (~(c | (~p(X))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[48, 23])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))) | ![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[50, 49, 42])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X))))))) | (![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.39 tff(54,assumption,(![X: $i] : (p(X) | c)), introduced(assumption)).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (((~![X: $i] : (p(X) | c)) | (c | p(X!11))) <=> ((~![X: $i] : (p(X) | c)) | c | p(X!11))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 ((p(X!11) | c) <=> (c | p(X!11))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (((~![X: $i] : (p(X) | c)) | (p(X!11) | c)) <=> ((~![X: $i] : (p(X) | c)) | (c | p(X!11)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[56])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (((~![X: $i] : (p(X) | c)) | (p(X!11) | c)) <=> ((~![X: $i] : (p(X) | c)) | c | p(X!11))),
% 0.19/0.40 inference(transitivity,[status(thm)],[57, 55])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 ((~![X: $i] : (p(X) | c)) | (p(X!11) | c)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((~![X: $i] : (p(X) | c)) | c | p(X!11)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[60, 4, 8, 54])).
% 0.19/0.40 tff(62,plain,((~![X: $i] : (p(X) | c)) | p(X!11) | c), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (~![X: $i] : (p(X) | c)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[62, 4, 8])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 ((~(c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c))) | c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (~(c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[64, 63, 20, 8])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (((~((~(c | p(X!16))) | (~(c | p(X!7))))) | (~(c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c)))) | (c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((~((~(c | p(X!16))) | (~(c | p(X!7))))) | (~(c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,assumption,(~((~(p(X!10) | q(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))))), introduced(assumption)).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (((~(p(X!10) | q(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))))))) | (p(X!10) | q(X!10) | p(X!11) | q(X!12))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (p(X!10) | q(X!10) | p(X!11) | q(X!12)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (((~(p(X!10) | q(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))))))) | (![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.19/0.40 tff(73,assumption,(p(X!10) | q(X!10) | p(X!11) | q(X!12)), introduced(assumption)).
% 0.19/0.40 tff(74,assumption,(![X: $i] : (~(p(X) | q(X)))), introduced(assumption)).
% 0.19/0.40 tff(75,assumption,(p(X!10) | q(X!10)), introduced(assumption)).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~![X: $i] : (~(p(X) | q(X)))) | (~(p(X!10) | q(X!10)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 74, 75])).
% 0.19/0.40 tff(78,plain,((~(p(X!10) | q(X!10))) | (~![X: $i] : (~(p(X) | q(X))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (~(p(X!10) | q(X!10))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 74])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 ((p(X!10) | q(X!10)) | (~p(X!10))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (~p(X!10)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((p(X!10) | q(X!10)) | (~q(X!10))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (~q(X!10)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ((~(p(X!10) | q(X!10) | p(X!11) | q(X!12))) | p(X!10) | q(X!10) | p(X!11) | q(X!12)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (q(X!12)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[84, 83, 4, 81, 73])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 ((p(X!12) | q(X!12)) | (~q(X!12))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (p(X!12) | q(X!12)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~![X: $i] : (~(p(X) | q(X)))) | (~(p(X!12) | q(X!12)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[88, 74, 87])).
% 0.19/0.40 tff(90,plain,((~![X: $i] : (~(p(X) | q(X)))) | p(X!11) | (~(p(X!10) | q(X!10) | p(X!11) | q(X!12)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (~![X: $i] : (~(p(X) | q(X)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[90, 70, 4])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))) | ![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[92, 91, 72])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))) | ![X: $i] : (~p(X))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (![X: $i] : (~p(X))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.40 tff(96,assumption,(p(X!10)), introduced(assumption)).
% 0.19/0.40 tff(97,assumption,(![X: $i] : (~p(X))), introduced(assumption)).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~![X: $i] : (~p(X))) | (~p(X!10))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 97, 96])).
% 0.19/0.40 tff(100,plain,((~p(X!10)) | (~![X: $i] : (~p(X)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (~p(X!10)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[100, 95])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))) | ![X: $i] : (~q(X))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (![X: $i] : (~q(X))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[102, 93])).
% 0.19/0.40 tff(104,assumption,(q(X!12)), introduced(assumption)).
% 0.19/0.40 tff(105,assumption,(![X: $i] : (~q(X))), introduced(assumption)).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 ((~![X: $i] : (~q(X))) | (~q(X!12))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[106, 105, 104])).
% 0.19/0.40 tff(108,plain,((~q(X!12)) | (~![X: $i] : (~q(X)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (~q(X!12)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[108, 103])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (q(X!10)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[84, 109, 4, 101, 70])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 ((~![X: $i] : (~q(X))) | (~q(X!10))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[111, 103, 110])).
% 0.19/0.40 tff(113,plain,(((~(p(X!10) | q(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))))))) | p(X!11)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 ((~(p(X!10) | q(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[113, 4])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (((~c) | p(X!20)) | c),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 ((~c) | p(X!20)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[115, 8])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (((~c) | p(X!7)) | c),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 ((~c) | p(X!7)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[117, 8])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 ((~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))) | (~((~c) | p(X!20))) | (~((~c) | p(X!7)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 (~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[119, 118, 116])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (((~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))) | (~((~c) | ![X: $i] : p(X) | ![X: $i] : ((~c) | p(X))))) | ((~((~c) | p(X!20))) | (~((~c) | p(X!7))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 ((~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))) | (~((~c) | ![X: $i] : p(X) | ![X: $i] : ((~c) | p(X))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 ((p(Y!15) | (~p(X!11)) | (~![Y: $i] : (~p(Y)))) | p(X!11)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 (p(Y!15) | (~p(X!11)) | (~![Y: $i] : (~p(Y)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[123, 4])).
% 0.19/0.40 tff(125,assumption,((~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))) | (~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))))), introduced(assumption)).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 (((~c) | (~![X: $i] : (~p(X)))) | c),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 ((~c) | (~![X: $i] : (~p(X)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[126, 8])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 (((~c) | p(X!11)) | c),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 ((~c) | p(X!11)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[128, 8])).
% 0.19/0.40 tff(130,assumption,(![X: $i] : (~((~c) | p(X)))), introduced(assumption)).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 ((~![X: $i] : (~((~c) | p(X)))) | (~((~c) | p(X!11)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[131, 130, 129])).
% 0.19/0.40 tff(133,plain,((~![X: $i] : (~((~c) | p(X)))) | c), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(134,plain,
% 0.19/0.40 (~![X: $i] : (~((~c) | p(X)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[133, 8])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 ((~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))) | ![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(136,plain,
% 0.19/0.40 (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[135, 134, 127])).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 (((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))))) | (![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 ((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.19/0.40 tff(139,assumption,((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X))))))), introduced(assumption)).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 (((~c) | (~p(X!11))) | c),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 ((~c) | (~p(X!11))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[140, 8])).
% 0.19/0.40 tff(142,plain,
% 0.19/0.40 (((~c) | (~p(X!17))) | c),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 ((~c) | (~p(X!17))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[142, 8])).
% 0.19/0.40 tff(144,plain,
% 0.19/0.40 ((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(145,plain,
% 0.19/0.40 (~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[144, 143, 141])).
% 0.19/0.40 tff(146,plain,
% 0.19/0.40 (((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c))))) | ((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(147,plain,
% 0.19/0.40 ((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.19/0.40 tff(148,assumption,(~(p(X!9) | q(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X))))), introduced(assumption)).
% 0.19/0.40 tff(149,plain,
% 0.19/0.40 ((p(X!9) | q(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X)))) | (![X: $i] : p(X) | ![X: $i] : q(X))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(150,plain,
% 0.19/0.40 (![X: $i] : p(X) | ![X: $i] : q(X)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.19/0.40 tff(151,plain,
% 0.19/0.40 ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : p(X) | ![X: $i] : q(X)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(152,plain,
% 0.19/0.40 (![X: $i] : q(X)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[151, 150, 20])).
% 0.19/0.40 tff(153,plain,
% 0.19/0.40 ((p(X!9) | q(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X)))) | (~q(X!9))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(154,plain,
% 0.19/0.40 (~q(X!9)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[153, 148])).
% 0.19/0.40 tff(155,plain,
% 0.19/0.40 ((~![X: $i] : q(X)) | q(X!9)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(156,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[155, 154, 152])).
% 0.19/0.41 tff(157,plain,((p(X!9) | q(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X)))) | ![X: $i] : p(X)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(158,plain,
% 0.19/0.41 (p(X!9) | q(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[157, 20])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 ((p(Y!14) | (~![X: $i] : p(X))) | ![X: $i] : p(X)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 (p(Y!14) | (~![X: $i] : p(X))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[159, 20])).
% 0.19/0.41 tff(161,plain,
% 0.19/0.41 (((~![X: $i] : p(X)) | (~![X: $i] : (~p(X)))) | ![X: $i] : p(X)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(162,plain,
% 0.19/0.41 ((~![X: $i] : p(X)) | (~![X: $i] : (~p(X)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[161, 20])).
% 0.19/0.41 tff(163,assumption,(~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))), introduced(assumption)).
% 0.19/0.41 tff(164,plain,
% 0.19/0.41 (((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(165,plain,
% 0.19/0.41 (![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.19/0.41 tff(166,plain,
% 0.19/0.41 (((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ![V: $i] : (h(V) | (~g(V)) | (~f(V)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(167,plain,
% 0.19/0.41 (![V: $i] : (h(V) | (~g(V)) | (~f(V)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[166, 163])).
% 0.19/0.41 tff(168,assumption,(~((~g(X!4)) | (~f(X!4)) | h(X!4))), introduced(assumption)).
% 0.19/0.41 tff(169,plain,
% 0.19/0.41 (((~g(X!4)) | (~f(X!4)) | h(X!4)) | (~h(X!4))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(170,plain,
% 0.19/0.41 (~h(X!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.19/0.41 tff(171,plain,
% 0.19/0.41 (((~g(X!4)) | (~f(X!4)) | h(X!4)) | f(X!4)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(172,plain,
% 0.19/0.41 (f(X!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[171, 168])).
% 0.19/0.41 tff(173,plain,
% 0.19/0.41 (((~g(X!4)) | (~f(X!4)) | h(X!4)) | g(X!4)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(174,plain,
% 0.19/0.41 (g(X!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[173, 168])).
% 0.19/0.41 tff(175,assumption,(![V: $i] : (h(V) | (~g(V)) | (~f(V)))), introduced(assumption)).
% 0.19/0.41 tff(176,plain,
% 0.19/0.41 (((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | ((~g(X!4)) | (~f(X!4)) | h(X!4))) <=> ((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~g(X!4)) | (~f(X!4)) | h(X!4))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(177,plain,
% 0.19/0.41 ((h(X!4) | (~g(X!4)) | (~f(X!4))) <=> ((~g(X!4)) | (~f(X!4)) | h(X!4))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(178,plain,
% 0.19/0.41 (((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (h(X!4) | (~g(X!4)) | (~f(X!4)))) <=> ((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | ((~g(X!4)) | (~f(X!4)) | h(X!4)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[177])).
% 0.19/0.41 tff(179,plain,
% 0.19/0.41 (((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (h(X!4) | (~g(X!4)) | (~f(X!4)))) <=> ((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~g(X!4)) | (~f(X!4)) | h(X!4))),
% 0.19/0.41 inference(transitivity,[status(thm)],[178, 176])).
% 0.19/0.41 tff(180,plain,
% 0.19/0.41 ((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (h(X!4) | (~g(X!4)) | (~f(X!4)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(181,plain,
% 0.19/0.41 ((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~g(X!4)) | (~f(X!4)) | h(X!4)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.41 tff(182,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[181, 175, 174, 172, 170])).
% 0.19/0.41 tff(183,plain,(((~g(X!4)) | (~f(X!4)) | h(X!4)) | (~![V: $i] : (h(V) | (~g(V)) | (~f(V))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(184,plain,
% 0.19/0.41 ((~g(X!4)) | (~f(X!4)) | h(X!4)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[183, 167])).
% 0.19/0.41 tff(185,assumption,((~g(X!4)) | (~f(X!4)) | h(X!4)), introduced(assumption)).
% 0.19/0.41 tff(186,assumption,(g(Y!0) | (~f(Y!0))), introduced(assumption)).
% 0.19/0.41 tff(187,assumption,(![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))), introduced(assumption)).
% 0.19/0.41 tff(188,plain,
% 0.19/0.41 (((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | ((~(g(Y!0) | (~f(Y!0)))) | (~((~g(X!4)) | (~f(X!4)) | h(X!4))))) <=> ((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(g(Y!0) | (~f(Y!0)))) | (~((~g(X!4)) | (~f(X!4)) | h(X!4))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(189,plain,
% 0.19/0.41 (((~((~g(X!4)) | (~f(X!4)) | h(X!4))) | (~(g(Y!0) | (~f(Y!0))))) <=> ((~(g(Y!0) | (~f(Y!0)))) | (~((~g(X!4)) | (~f(X!4)) | h(X!4))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(190,plain,
% 0.19/0.41 ((~(h(X!4) | (~g(X!4)) | (~f(X!4)))) <=> (~((~g(X!4)) | (~f(X!4)) | h(X!4)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(191,plain,
% 0.19/0.41 (((~(h(X!4) | (~g(X!4)) | (~f(X!4)))) | (~(g(Y!0) | (~f(Y!0))))) <=> ((~((~g(X!4)) | (~f(X!4)) | h(X!4))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[190])).
% 0.19/0.41 tff(192,plain,
% 0.19/0.41 (((~(h(X!4) | (~g(X!4)) | (~f(X!4)))) | (~(g(Y!0) | (~f(Y!0))))) <=> ((~(g(Y!0) | (~f(Y!0)))) | (~((~g(X!4)) | (~f(X!4)) | h(X!4))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[191, 189])).
% 0.19/0.41 tff(193,plain,
% 0.19/0.41 (((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | ((~(h(X!4) | (~g(X!4)) | (~f(X!4)))) | (~(g(Y!0) | (~f(Y!0)))))) <=> ((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | ((~(g(Y!0) | (~f(Y!0)))) | (~((~g(X!4)) | (~f(X!4)) | h(X!4)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[192])).
% 0.19/0.41 tff(194,plain,
% 0.19/0.41 (((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | ((~(h(X!4) | (~g(X!4)) | (~f(X!4)))) | (~(g(Y!0) | (~f(Y!0)))))) <=> ((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(g(Y!0) | (~f(Y!0)))) | (~((~g(X!4)) | (~f(X!4)) | h(X!4))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[193, 188])).
% 0.19/0.41 tff(195,plain,
% 0.19/0.41 ((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | ((~(h(X!4) | (~g(X!4)) | (~f(X!4)))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(196,plain,
% 0.19/0.41 ((~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(g(Y!0) | (~f(Y!0)))) | (~((~g(X!4)) | (~f(X!4)) | h(X!4)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.19/0.41 tff(197,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[196, 187, 186, 185])).
% 0.19/0.41 tff(198,plain,((~((~g(X!4)) | (~f(X!4)) | h(X!4))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(g(Y!0) | (~f(Y!0))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(199,plain,
% 0.19/0.41 (~(g(Y!0) | (~f(Y!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[198, 184, 165])).
% 0.19/0.41 tff(200,plain,
% 0.19/0.41 ((g(Y!0) | (~f(Y!0))) | f(Y!0)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(201,plain,
% 0.19/0.41 (f(Y!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.19/0.41 tff(202,plain,
% 0.19/0.41 (((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(203,plain,
% 0.19/0.41 (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[202, 163])).
% 0.19/0.41 tff(204,assumption,(~(g(Y!0) | (~f(Y!0)))), introduced(assumption)).
% 0.19/0.41 tff(205,plain,
% 0.19/0.41 (f(Y!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[200, 204])).
% 0.19/0.41 tff(206,plain,
% 0.19/0.41 ((g(Y!0) | (~f(Y!0))) | (~g(Y!0))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(207,plain,
% 0.19/0.41 (~g(Y!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[206, 204])).
% 0.19/0.41 tff(208,assumption,(![W: $i] : (g(W) | (~f(W)))), introduced(assumption)).
% 0.19/0.41 tff(209,plain,
% 0.19/0.41 (((~![W: $i] : (g(W) | (~f(W)))) | (g(Y!0) | (~f(Y!0)))) <=> ((~![W: $i] : (g(W) | (~f(W)))) | g(Y!0) | (~f(Y!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(210,plain,
% 0.19/0.41 ((~![W: $i] : (g(W) | (~f(W)))) | (g(Y!0) | (~f(Y!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(211,plain,
% 0.19/0.41 ((~![W: $i] : (g(W) | (~f(W)))) | g(Y!0) | (~f(Y!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.19/0.41 tff(212,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[211, 208, 207, 205])).
% 0.19/0.41 tff(213,plain,((g(Y!0) | (~f(Y!0))) | (~![W: $i] : (g(W) | (~f(W))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(214,plain,
% 0.19/0.41 (~![W: $i] : (g(W) | (~f(W)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[213, 199])).
% 0.19/0.41 tff(215,plain,
% 0.19/0.41 ((~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(216,plain,
% 0.19/0.41 (![Z: $i] : (h(Z) | (~f(Z)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[215, 214, 203])).
% 0.19/0.41 tff(217,assumption,(~h(Y!0)), introduced(assumption)).
% 0.19/0.41 tff(218,assumption,(f(Y!0)), introduced(assumption)).
% 0.19/0.41 tff(219,assumption,(![Z: $i] : (h(Z) | (~f(Z)))), introduced(assumption)).
% 0.19/0.41 tff(220,plain,
% 0.19/0.41 (((~![Z: $i] : (h(Z) | (~f(Z)))) | (h(Y!0) | (~f(Y!0)))) <=> ((~![Z: $i] : (h(Z) | (~f(Z)))) | h(Y!0) | (~f(Y!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(221,plain,
% 0.19/0.41 ((~![Z: $i] : (h(Z) | (~f(Z)))) | (h(Y!0) | (~f(Y!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(222,plain,
% 0.19/0.41 ((~![Z: $i] : (h(Z) | (~f(Z)))) | h(Y!0) | (~f(Y!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.19/0.41 tff(223,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[222, 219, 218, 217])).
% 0.19/0.41 tff(224,plain,(h(Y!0) | (~![Z: $i] : (h(Z) | (~f(Z)))) | (~f(Y!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(225,plain,
% 0.19/0.41 (h(Y!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[224, 216, 201])).
% 0.19/0.41 tff(226,plain,
% 0.19/0.41 (~g(Y!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[206, 199])).
% 0.19/0.41 tff(227,plain,
% 0.19/0.41 (((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ![R: $i] : (g(R) | (~h(R)) | (~f(R)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(228,plain,
% 0.19/0.41 (![R: $i] : (g(R) | (~h(R)) | (~f(R)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[227, 163])).
% 0.19/0.41 tff(229,plain,
% 0.19/0.41 (((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (g(Y!0) | (~f(Y!0)) | (~h(Y!0)))) <=> ((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | g(Y!0) | (~f(Y!0)) | (~h(Y!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(230,plain,
% 0.19/0.41 ((g(Y!0) | (~h(Y!0)) | (~f(Y!0))) <=> (g(Y!0) | (~f(Y!0)) | (~h(Y!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(231,plain,
% 0.19/0.41 (((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (g(Y!0) | (~h(Y!0)) | (~f(Y!0)))) <=> ((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (g(Y!0) | (~f(Y!0)) | (~h(Y!0))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[230])).
% 0.19/0.41 tff(232,plain,
% 0.19/0.41 (((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (g(Y!0) | (~h(Y!0)) | (~f(Y!0)))) <=> ((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | g(Y!0) | (~f(Y!0)) | (~h(Y!0)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[231, 229])).
% 0.19/0.41 tff(233,plain,
% 0.19/0.41 ((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (g(Y!0) | (~h(Y!0)) | (~f(Y!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(234,plain,
% 0.19/0.41 ((~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | g(Y!0) | (~f(Y!0)) | (~h(Y!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.19/0.41 tff(235,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[234, 228, 226, 201, 225])).
% 0.19/0.41 tff(236,plain,((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(237,assumption,(~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))), introduced(assumption)).
% 0.19/0.42 tff(238,plain,
% 0.19/0.42 (((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))) | (~r(X!2, X!2))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(239,plain,
% 0.19/0.42 (~r(X!2, X!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.19/0.42 tff(240,plain,
% 0.19/0.42 (((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(241,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[240, 237])).
% 0.19/0.42 tff(242,plain,
% 0.19/0.42 (((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))) | r(X!2, Y!1)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(243,plain,
% 0.19/0.42 (r(X!2, Y!1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[242, 237])).
% 0.19/0.42 tff(244,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(X!2, Y!1)) | r(Y!1, X!2))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(X!2, Y!1)) | r(Y!1, X!2))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(245,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | ((~r(X!2, Y!1)) | r(Y!1, X!2))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(246,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~r(X!2, Y!1)) | r(Y!1, X!2)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.42 tff(247,plain,
% 0.19/0.42 (r(Y!1, X!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[246, 243, 241])).
% 0.19/0.42 tff(248,plain,
% 0.19/0.42 (((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))) | ![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(249,plain,
% 0.19/0.42 (![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[248, 237])).
% 0.19/0.42 tff(250,assumption,(~r(X!2, X!2)), introduced(assumption)).
% 0.19/0.42 tff(251,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | ((~r(X!2, Y!1)) | r(X!2, X!2) | (~r(Y!1, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (~r(X!2, Y!1)) | r(X!2, X!2) | (~r(Y!1, X!2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(252,plain,
% 0.19/0.42 ((r(X!2, X!2) | (~r(Y!1, X!2)) | (~r(X!2, Y!1))) <=> ((~r(X!2, Y!1)) | r(X!2, X!2) | (~r(Y!1, X!2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(253,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (r(X!2, X!2) | (~r(Y!1, X!2)) | (~r(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | ((~r(X!2, Y!1)) | r(X!2, X!2) | (~r(Y!1, X!2))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[252])).
% 0.19/0.42 tff(254,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (r(X!2, X!2) | (~r(Y!1, X!2)) | (~r(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (~r(X!2, Y!1)) | r(X!2, X!2) | (~r(Y!1, X!2)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[253, 251])).
% 0.19/0.42 tff(255,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (r(X!2, X!2) | (~r(Y!1, X!2)) | (~r(X!2, Y!1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(256,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))) | (~r(X!2, Y!1)) | r(X!2, X!2) | (~r(Y!1, X!2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.19/0.42 tff(257,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[256, 243, 250, 249, 247])).
% 0.19/0.42 tff(258,plain,(((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))) | r(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(259,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[258, 239, 237])).
% 0.19/0.42 tff(260,plain,((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(261,assumption,(![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X))))), introduced(assumption)).
% 0.19/0.42 tff(262,plain,
% 0.19/0.42 ((~![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X))))) | (~(q(elem!22) | (~p(elem!22)) | p(tptp_fun_Y_5(elem!22))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(263,plain,
% 0.19/0.42 (~(q(elem!22) | (~p(elem!22)) | p(tptp_fun_Y_5(elem!22)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.19/0.42 tff(264,plain,
% 0.19/0.42 ((q(elem!22) | (~p(elem!22)) | p(tptp_fun_Y_5(elem!22))) | (~p(tptp_fun_Y_5(elem!22)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(265,plain,
% 0.19/0.42 (~p(tptp_fun_Y_5(elem!22))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.19/0.42 tff(266,plain,
% 0.19/0.42 ((q(tptp_fun_Y_5(elem!22)) | (~p(tptp_fun_Y_5(elem!22))) | p(tptp_fun_Y_5(tptp_fun_Y_5(elem!22)))) | p(tptp_fun_Y_5(elem!22))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(267,plain,
% 0.19/0.42 (q(tptp_fun_Y_5(elem!22)) | (~p(tptp_fun_Y_5(elem!22))) | p(tptp_fun_Y_5(tptp_fun_Y_5(elem!22)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[266, 265])).
% 0.19/0.42 tff(268,plain,
% 0.19/0.42 ((~![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X))))) | (~(q(tptp_fun_Y_5(elem!22)) | (~p(tptp_fun_Y_5(elem!22))) | p(tptp_fun_Y_5(tptp_fun_Y_5(elem!22)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(269,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[268, 261, 267])).
% 0.19/0.42 tff(270,plain,(~![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(271,plain,
% 0.19/0.42 ((c | (~p(X!11))) | p(X!11)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(272,plain,
% 0.19/0.42 (c | (~p(X!11))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[271, 4])).
% 0.19/0.42 tff(273,assumption,((~((~(c | p(X!16))) | (~(c | p(X!7))))) | (~(c | ![X: $i] : p(X) | ![X: $i] : (p(X) | c)))), introduced(assumption)).
% 0.19/0.42 tff(274,assumption,((~(p(X!10) | q(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X)))))))), introduced(assumption)).
% 0.19/0.42 tff(275,assumption,(p(Y!15) | (~p(X!11)) | (~![Y: $i] : (~p(Y)))), introduced(assumption)).
% 0.19/0.42 tff(276,assumption,(p(X!9) | q(X!9) | (~(![X: $i] : p(X) | ![X: $i] : q(X)))), introduced(assumption)).
% 0.19/0.42 tff(277,assumption,(p(Y!14) | (~![X: $i] : p(X))), introduced(assumption)).
% 0.19/0.42 tff(278,assumption,((~![X: $i] : p(X)) | (~![X: $i] : (~p(X)))), introduced(assumption)).
% 0.19/0.42 tff(279,assumption,(c | (~p(X!11))), introduced(assumption)).
% 0.19/0.42 tff(280,assumption,(~((~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))) | (~(c | ![X: $i] : (~p(X)) | ![X: $i] : (c | (~p(X))))))), introduced(assumption)).
% 0.19/0.42 tff(281,plain,
% 0.19/0.42 (((~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))) | (~(c | ![X: $i] : (~p(X)) | ![X: $i] : (c | (~p(X)))))) | (c | ![X: $i] : (~p(X)) | ![X: $i] : (c | (~p(X))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(282,plain,
% 0.19/0.42 (c | ![X: $i] : (~p(X)) | ![X: $i] : (c | (~p(X)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[281, 280])).
% 0.19/0.42 tff(283,plain,
% 0.19/0.42 ((~(c | ![X: $i] : (~p(X)) | ![X: $i] : (c | (~p(X))))) | c | ![X: $i] : (~p(X)) | ![X: $i] : (c | (~p(X)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(284,plain,
% 0.19/0.42 (![X: $i] : (c | (~p(X)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[283, 282, 8, 1])).
% 0.19/0.42 tff(285,plain,
% 0.19/0.42 (((~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))) | (~(c | ![X: $i] : (~p(X)) | ![X: $i] : (c | (~p(X)))))) | ((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(286,plain,
% 0.19/0.42 ((~(c | (~p(X!21)))) | (~(c | (~p(X!11))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[285, 280])).
% 0.19/0.42 tff(287,plain,
% 0.19/0.42 ((~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))) | (~(c | (~p(X!21)))) | (~(c | (~p(X!11))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(288,plain,
% 0.19/0.42 (~(c | (~p(X!21)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[287, 286, 279])).
% 0.19/0.42 tff(289,plain,
% 0.19/0.42 ((c | (~p(X!21))) | p(X!21)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(290,plain,
% 0.19/0.42 (p(X!21)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.20/0.42 tff(291,plain,
% 0.20/0.42 (((~![X: $i] : (c | (~p(X)))) | (c | (~p(X!21)))) <=> ((~![X: $i] : (c | (~p(X)))) | c | (~p(X!21)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(292,plain,
% 0.20/0.42 ((~![X: $i] : (c | (~p(X)))) | (c | (~p(X!21)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(293,plain,
% 0.20/0.42 ((~![X: $i] : (c | (~p(X)))) | c | (~p(X!21))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.20/0.42 tff(294,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[293, 8, 290, 284])).
% 0.20/0.42 tff(295,plain,(((~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))) | (~(c | ![X: $i] : (~p(X)) | ![X: $i] : (c | (~p(X)))))) | c | ![X: $i] : (~p(X)) | (~(c | (~p(X!11))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(296,plain,
% 0.20/0.42 ((~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))) | (~(c | ![X: $i] : (~p(X)) | ![X: $i] : (c | (~p(X)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[295, 1, 8, 279])).
% 0.20/0.42 tff(297,plain,
% 0.20/0.42 (((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | $false) <=> (~![Y: $i] : (~((~p(Y)) | p(X!7))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(298,plain,
% 0.20/0.42 ((~$true) <=> $false),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(299,plain,
% 0.20/0.42 (((~p(X!7)) | p(X!7)) <=> $true),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(300,plain,
% 0.20/0.42 ((~((~p(X!7)) | p(X!7))) <=> (~$true)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[299])).
% 0.20/0.42 tff(301,plain,
% 0.20/0.42 ((~((~p(X!7)) | p(X!7))) <=> $false),
% 0.20/0.42 inference(transitivity,[status(thm)],[300, 298])).
% 0.20/0.42 tff(302,plain,
% 0.20/0.42 (((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | (~((~p(X!7)) | p(X!7)))) <=> ((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | $false)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[301])).
% 0.20/0.42 tff(303,plain,
% 0.20/0.42 (((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | (~((~p(X!7)) | p(X!7)))) <=> (~![Y: $i] : (~((~p(Y)) | p(X!7))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[302, 297])).
% 0.20/0.42 tff(304,plain,
% 0.20/0.42 ((~![Y: $i] : (~((~p(Y)) | p(X!7)))) | (~((~p(X!7)) | p(X!7)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(305,plain,
% 0.20/0.42 (~![Y: $i] : (~((~p(Y)) | p(X!7)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.20/0.42 tff(306,assumption,(![Y: $i] : (~((~p(Y)) | p(X!7)))), introduced(assumption)).
% 0.20/0.42 tff(307,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[306, 305])).
% 0.20/0.42 tff(308,plain,(~![Y: $i] : (~((~p(Y)) | p(X!7)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(309,assumption,(~((~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))) | (~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))), introduced(assumption)).
% 0.20/0.42 tff(310,plain,
% 0.20/0.42 (((~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))) | (~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(311,plain,
% 0.20/0.42 ((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[310, 309])).
% 0.20/0.42 tff(312,plain,
% 0.20/0.42 (((~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))) | (~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ![V: $i] : (h(V) | (~g(V)) | (~f(V)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(313,plain,
% 0.20/0.42 (![V: $i] : (h(V) | (~g(V)) | (~f(V)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[312, 309])).
% 0.20/0.42 tff(314,assumption,(~(h(X!3) | (~f(X!3)) | (~g(X!3)))), introduced(assumption)).
% 0.20/0.42 tff(315,plain,
% 0.20/0.42 ((h(X!3) | (~f(X!3)) | (~g(X!3))) | g(X!3)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(316,plain,
% 0.20/0.42 (g(X!3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[315, 314])).
% 0.20/0.42 tff(317,plain,
% 0.20/0.42 ((h(X!3) | (~f(X!3)) | (~g(X!3))) | f(X!3)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(318,plain,
% 0.20/0.42 (f(X!3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[317, 314])).
% 0.20/0.42 tff(319,plain,
% 0.20/0.42 ((h(X!3) | (~f(X!3)) | (~g(X!3))) | (~h(X!3))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(320,plain,
% 0.20/0.42 (~h(X!3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[319, 314])).
% 0.20/0.42 tff(321,plain,
% 0.20/0.42 (((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (h(X!3) | (~f(X!3)) | (~g(X!3)))) <=> ((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | h(X!3) | (~f(X!3)) | (~g(X!3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(322,plain,
% 0.20/0.42 ((h(X!3) | (~g(X!3)) | (~f(X!3))) <=> (h(X!3) | (~f(X!3)) | (~g(X!3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(323,plain,
% 0.20/0.42 (((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (h(X!3) | (~g(X!3)) | (~f(X!3)))) <=> ((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (h(X!3) | (~f(X!3)) | (~g(X!3))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[322])).
% 0.20/0.42 tff(324,plain,
% 0.20/0.42 (((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (h(X!3) | (~g(X!3)) | (~f(X!3)))) <=> ((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | h(X!3) | (~f(X!3)) | (~g(X!3)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[323, 321])).
% 0.20/0.42 tff(325,plain,
% 0.20/0.42 ((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (h(X!3) | (~g(X!3)) | (~f(X!3)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(326,plain,
% 0.20/0.42 ((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | h(X!3) | (~f(X!3)) | (~g(X!3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.20/0.42 tff(327,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[326, 175, 320, 318, 316])).
% 0.20/0.42 tff(328,plain,((h(X!3) | (~f(X!3)) | (~g(X!3))) | (~![V: $i] : (h(V) | (~g(V)) | (~f(V))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(329,plain,
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% 0.20/0.44 inference(rewrite,[status(thm)],[])).
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% 0.20/0.44 inference(monotonicity,[status(thm)],[396, 393, 392, 389, 388, 387, 386, 385, 381, 380, 376, 375, 374, 371, 366, 362])).
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% 0.20/0.45 inference(transitivity,[status(thm)],[397, 361])).
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% 0.20/0.45 inference(rewrite,[status(thm)],[])).
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% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(401,plain,
% 0.20/0.46 (((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))) <=> (~((~(c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))) | (~((~(c | (~p(X!21)))) | (~(c | (~p(X!11))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(402,plain,
% 0.20/0.46 (((~(c | (~p(X!21)))) | (~(c | (~p(X!11))))) <=> ((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(403,plain,
% 0.20/0.46 (((~c) & p(X!11)) <=> (~(c | (~p(X!11))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(404,plain,
% 0.20/0.46 (((~(c | (~p(X!21)))) | ((~c) & p(X!11))) <=> ((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[403])).
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% 0.20/0.47 inference(rewrite,[status(thm)],[])).
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% 0.20/0.47 inference(monotonicity,[status(thm)],[459])).
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% 0.20/0.47 inference(transitivity,[status(thm)],[460, 458])).
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% 0.20/0.47 (((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8))) <=> (((~p(X!6)) | (~q(X!6))) | (~p(X!7)) | (~q(X!8)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[461])).
% 0.20/0.47 tff(463,plain,
% 0.20/0.47 (((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8))) <=> ((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[462, 457])).
% 0.20/0.47 tff(464,plain,
% 0.20/0.47 (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) <=> ((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(465,plain,
% 0.20/0.47 ((((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) <=> (((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X))))) & ((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[464, 463])).
% 0.20/0.47 tff(466,plain,
% 0.20/0.47 ((((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) <=> (~((~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))) | (~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[465, 456])).
% 0.20/0.47 tff(467,plain,
% 0.20/0.47 ((![V: $i] : (h(V) | (~g(V)) | (~f(V))) & ![R: $i] : (g(R) | (~h(R)) | (~f(R))) & ((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3))))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(468,plain,
% 0.20/0.47 ((![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))) <=> (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(469,plain,
% 0.20/0.47 (((~(h(X!3) | (~f(X!3)) | (~g(X!3)))) | (~(g(X!4) | (~f(X!4))))) <=> ((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(470,plain,
% 0.20/0.47 ((f(X!4) & (~g(X!4))) <=> (~(g(X!4) | (~f(X!4))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(471,plain,
% 0.20/0.47 ((~(h(X!3) | (~(f(X!3) & g(X!3))))) <=> (~(h(X!3) | (~f(X!3)) | (~g(X!3))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(472,plain,
% 0.20/0.47 (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) <=> ((~(h(X!3) | (~f(X!3)) | (~g(X!3)))) | (~(g(X!4) | (~f(X!4)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[471, 470])).
% 0.20/0.47 tff(473,plain,
% 0.20/0.47 (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) <=> ((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[472, 469])).
% 0.20/0.47 tff(474,plain,
% 0.20/0.47 (^[R: $i] : trans(monotonicity(trans(monotonicity(rewrite((f(R) & h(R)) <=> (~((~f(R)) | (~h(R))))), ((~(f(R) & h(R))) <=> (~(~((~f(R)) | (~h(R))))))), rewrite((~(~((~f(R)) | (~h(R))))) <=> ((~f(R)) | (~h(R)))), ((~(f(R) & h(R))) <=> ((~f(R)) | (~h(R))))), ((g(R) | (~(f(R) & h(R)))) <=> (g(R) | ((~f(R)) | (~h(R)))))), rewrite((g(R) | ((~f(R)) | (~h(R)))) <=> (g(R) | (~h(R)) | (~f(R)))), ((g(R) | (~(f(R) & h(R)))) <=> (g(R) | (~h(R)) | (~f(R)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(475,plain,
% 0.20/0.47 (![R: $i] : (g(R) | (~(f(R) & h(R)))) <=> ![R: $i] : (g(R) | (~h(R)) | (~f(R)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[474])).
% 0.20/0.47 tff(476,plain,
% 0.20/0.47 (^[V: $i] : trans(monotonicity(rewrite((f(V) & g(V) & (~h(V))) <=> (~(h(V) | (~g(V)) | (~f(V))))), ((~(f(V) & g(V) & (~h(V)))) <=> (~(~(h(V) | (~g(V)) | (~f(V))))))), rewrite((~(~(h(V) | (~g(V)) | (~f(V))))) <=> (h(V) | (~g(V)) | (~f(V)))), ((~(f(V) & g(V) & (~h(V)))) <=> (h(V) | (~g(V)) | (~f(V)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(477,plain,
% 0.20/0.47 (![V: $i] : (~(f(V) & g(V) & (~h(V)))) <=> ![V: $i] : (h(V) | (~g(V)) | (~f(V)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[476])).
% 0.20/0.47 tff(478,plain,
% 0.20/0.47 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (![V: $i] : (h(V) | (~g(V)) | (~f(V))) & ![R: $i] : (g(R) | (~h(R)) | (~f(R))) & ((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3))))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[477, 475, 473, 468])).
% 0.20/0.47 tff(479,plain,
% 0.20/0.47 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[478, 467])).
% 0.20/0.47 tff(480,plain,
% 0.20/0.47 ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> (~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(481,plain,
% 0.20/0.47 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((r(X, Y) & r(Y, Z)) <=> (~((~r(Y, Z)) | (~r(X, Y))))), ((~(r(X, Y) & r(Y, Z))) <=> (~(~((~r(Y, Z)) | (~r(X, Y))))))), rewrite((~(~((~r(Y, Z)) | (~r(X, Y))))) <=> ((~r(Y, Z)) | (~r(X, Y)))), ((~(r(X, Y) & r(Y, Z))) <=> ((~r(Y, Z)) | (~r(X, Y))))), (((~(r(X, Y) & r(Y, Z))) | r(X, Z)) <=> (((~r(Y, Z)) | (~r(X, Y))) | r(X, Z)))), rewrite((((~r(Y, Z)) | (~r(X, Y))) | r(X, Z)) <=> (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))), (((~(r(X, Y) & r(Y, Z))) | r(X, Z)) <=> (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(482,plain,
% 0.20/0.47 (![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[481])).
% 0.20/0.47 tff(483,plain,
% 0.20/0.47 ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))) & (~((~r(X!2, Y!1)) | r(X!2, X!2))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[482])).
% 0.20/0.47 tff(484,plain,
% 0.20/0.47 ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> (~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[483, 480])).
% 0.20/0.47 tff(485,plain,
% 0.20/0.47 ((![V: $i] : (h(V) | (~g(V)) | (~f(V))) & ![R: $i] : (g(R) | (~h(R)) | (~f(R))) & ![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(486,plain,
% 0.20/0.47 (^[X: $i] : trans(monotonicity(rewrite((~(h(X) | (~(f(X) & g(X))))) <=> (~(h(X) | (~g(X)) | (~f(X))))), rewrite((f(Y!0) & (~g(Y!0))) <=> (~(g(Y!0) | (~f(Y!0))))), (((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) <=> ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))))), rewrite(((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))) <=> ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))), (((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) <=> ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(487,plain,
% 0.20/0.47 (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) <=> ![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[486])).
% 0.20/0.47 tff(488,plain,
% 0.20/0.47 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (![V: $i] : (h(V) | (~g(V)) | (~f(V))) & ![R: $i] : (g(R) | (~h(R)) | (~f(R))) & ![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0))))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[477, 475, 487, 468])).
% 0.20/0.47 tff(489,plain,
% 0.20/0.47 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[488, 485])).
% 0.20/0.47 tff(490,plain,
% 0.20/0.47 ((![X: $i] : p(X) & ![X: $i] : (~p(X))) <=> (~((~![X: $i] : p(X)) | (~![X: $i] : (~p(X)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(491,plain,
% 0.20/0.47 (((~p(Y!14)) & ![X: $i] : p(X)) <=> (~(p(Y!14) | (~![X: $i] : p(X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(492,plain,
% 0.20/0.47 (^[Y: $i] : rewrite((p(Y) & (~p(X!7))) <=> (~((~p(Y)) | p(X!7))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(493,plain,
% 0.20/0.47 (![Y: $i] : (p(Y) & (~p(X!7))) <=> ![Y: $i] : (~((~p(Y)) | p(X!7)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[492])).
% 0.20/0.47 tff(494,plain,
% 0.20/0.47 (((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) <=> (~((~(![X: $i] : p(X) | ![X: $i] : q(X))) | p(X!9) | q(X!9)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(495,plain,
% 0.20/0.47 ((![X: $i] : p(X) | ![X: $i] : q(X)) <=> (![X: $i] : p(X) | ![X: $i] : q(X))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(496,plain,
% 0.20/0.47 (((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) <=> ((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[495])).
% 0.20/0.47 tff(497,plain,
% 0.20/0.47 (((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) <=> (~((~(![X: $i] : p(X) | ![X: $i] : q(X))) | p(X!9) | q(X!9)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[496, 494])).
% 0.20/0.48 tff(498,plain,
% 0.20/0.48 ((((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ![Y: $i] : (p(Y) & (~p(X!7))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((p(X!10) | q(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11))))) <=> ((~((~(![X: $i] : p(X) | ![X: $i] : q(X))) | p(X!9) | q(X!9))) | ![Y: $i] : (~((~p(Y)) | p(X!7))) | (~(p(Y!14) | (~![X: $i] : p(X)))) | (~((~![X: $i] : p(X)) | (~![X: $i] : (~p(X))))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) | (~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (~((~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))) | (~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))))) | (~((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))))) | (~(p(Y!15) | (~![Y: $i] : (~p(Y))) | (~p(X!11)))) | (~((~(p(X!10) | q(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))))) | (~((~(![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X)))) | (~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))))) | (~((~(![X: $i] : p(X) | c | ![X: $i] : (p(X) | c))) | (~((~(c | p(X!16))) | (~(c | p(X!7))))))) | (~((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))))) | (~((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c)))))) | (~((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))))) | (~((~(c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))) | (~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[497, 493, 491, 490, 489, 484, 479, 466, 455, 451, 450, 442, 437, 432, 425, 416, 408])).
% 0.20/0.48 tff(499,plain,
% 0.20/0.48 ((((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ![Y: $i] : (p(Y) & (~p(X!7))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((p(X!10) | q(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11))))) <=> ((~((~![X: $i] : p(X)) | (~![X: $i] : (~p(X))))) | (~((~(![X: $i] : p(X) | ![X: $i] : q(X))) | p(X!9) | q(X!9))) | ![Y: $i] : (~((~p(Y)) | p(X!7))) | (~(p(Y!14) | (~![X: $i] : p(X)))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~![X: $i] : ((~(h(X) | (~g(X)) | (~f(X)))) | (~(g(Y!0) | (~f(Y!0)))))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) | (~((~r(X!2, Y!1)) | r(X!2, X!2) | (~![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X))) | (~![X: $i, Y: $i, Z: $i] : (r(X, Z) | (~r(Y, Z)) | (~r(X, Y)))))) | (~((~![V: $i] : (h(V) | (~g(V)) | (~f(V)))) | (~![R: $i] : (g(R) | (~h(R)) | (~f(R)))) | (~(![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (~((~(g(X!4) | (~f(X!4)))) | (~(h(X!3) | (~f(X!3)) | (~g(X!3)))))))) | (~((~((~((~![X: $i] : p(X)) | (~![X: $i] : q(X)))) | ![X: $i] : (~((~p(X)) | (~q(X)))))) | (~((~p(X!7)) | (~q(X!8)) | (~p(X!6)) | (~q(X!6)))))) | (~((~p(X!13)) | (~q(X!13)) | (~(![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))))) | (~(p(Y!15) | (~![Y: $i] : (~p(Y))) | (~p(X!11)))) | (~((~(p(X!10) | q(X!10) | p(X!11) | q(X!12))) | (~(![X: $i] : (~(p(X) | q(X))) | (~((~![X: $i] : (~p(X))) | (~![X: $i] : (~q(X))))))))) | (~((~(![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X)))) | (~((~((~c) | p(X!20))) | (~((~c) | p(X!7))))))) | (~((~(![X: $i] : p(X) | c | ![X: $i] : (p(X) | c))) | (~((~(c | p(X!16))) | (~(c | p(X!7))))))) | (~((~((~c) | p(X!11) | p(X!18))) | (~(![X: $i] : (~((~c) | p(X))) | (~((~c) | (~![X: $i] : (~p(X))))))))) | (~((~((~((~c) | (~p(X!17)))) | (~((~c) | (~p(X!11)))))) | (~((~c) | ![X: $i] : (~p(X)) | ![X: $i] : ((~p(X)) | (~c)))))) | (~((~(c | (~p(X!7)) | (~p(X!19)))) | (~(![X: $i] : (~(c | (~p(X)))) | (~(c | (~![X: $i] : p(X)))))))) | (~((~(c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X)))) | (~((~(c | (~p(X!21)))) | (~(c | (~p(X!11)))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[498, 400])).
% 0.20/0.48 tff(500,plain,
% 0.20/0.48 (((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | ((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ((p(X!10) | q(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ![Y: $i] : (p(Y) & (~p(X!7))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11))))) <=> (((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ![Y: $i] : (p(Y) & (~p(X!7))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((p(X!10) | q(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(501,plain,
% 0.20/0.48 (((![X: $i] : (c | (~p(X))) | (c | ![X: $i] : (~p(X)))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))) <=> ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(502,plain,
% 0.20/0.48 (((![X: $i] : ((~c) | p(X)) | ((~c) | ![X: $i] : p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) <=> ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(503,plain,
% 0.20/0.48 ((((c | (~p(X!19))) | (c | (~p(X!7)))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) <=> ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(504,plain,
% 0.20/0.48 (((((~c) | p(X!18)) | ((~c) | p(X!11))) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) <=> (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(505,plain,
% 0.20/0.48 ((((p(X!17) & c) | (p(X!11) & c)) & (![X: $i] : (~(p(X) & c)) | (![X: $i] : (~p(X)) | (~c)))) <=> (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(506,plain,
% 0.20/0.48 (((![X: $i] : (p(X) | c) | (![X: $i] : p(X) | c)) & ((~(p(X!16) | c)) | ((~p(X!7)) & (~c)))) <=> ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(507,plain,
% 0.20/0.48 ((![Y: $i] : (~p(Y)) & ((~p(Y!15)) & p(X!11))) <=> (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(508,plain,
% 0.20/0.48 (((p(X!13) & q(X!13)) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) <=> (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(509,plain,
% 0.20/0.48 ((((p(X!10) | q(X!10)) | (p(X!11) | q(X!12))) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) <=> ((p(X!10) | q(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(510,plain,
% 0.20/0.48 (((![X: $i] : (p(X) & q(X)) | (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(p(X!6) & q(X!6))) | ((~p(X!7)) | (~q(X!8))))) <=> (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(511,plain,
% 0.20/0.48 (^[X: $i] : rewrite((~(q(X) | p(tptp_fun_Y_5(X)) | (~p(X)))) <=> (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(512,plain,
% 0.20/0.48 (![X: $i] : (~(q(X) | p(tptp_fun_Y_5(X)) | (~p(X)))) <=> ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[511])).
% 0.20/0.48 tff(513,plain,
% 0.20/0.48 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(514,plain,
% 0.20/0.48 ((((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[468])).
% 0.20/0.48 tff(515,plain,
% 0.20/0.48 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[514])).
% 0.20/0.48 tff(516,plain,
% 0.20/0.48 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[515, 513])).
% 0.20/0.48 tff(517,plain,
% 0.20/0.48 (((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(518,plain,
% 0.20/0.48 ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) <=> (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(519,plain,
% 0.20/0.48 (((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[518])).
% 0.20/0.49 tff(520,plain,
% 0.20/0.49 (((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) <=> (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[519, 517])).
% 0.20/0.49 tff(521,plain,
% 0.20/0.49 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(522,plain,
% 0.20/0.49 ((![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) <=> (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(523,plain,
% 0.20/0.49 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[522])).
% 0.20/0.49 tff(524,plain,
% 0.20/0.49 ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) <=> (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[523, 521])).
% 0.20/0.49 tff(525,plain,
% 0.20/0.49 (((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ![X: $i] : (~(q(X) | p(tptp_fun_Y_5(X)) | (~p(X)))) | ((![X: $i] : (p(X) & q(X)) | (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(p(X!6) & q(X!6))) | ((~p(X!7)) | (~q(X!8))))) | ((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | (((p(X!10) | q(X!10)) | (p(X!11) | q(X!12))) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ![Y: $i] : (p(Y) & (~p(X!7))) | ((p(X!13) & q(X!13)) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![Y: $i] : (~p(Y)) & ((~p(Y!15)) & p(X!11))) | ((![X: $i] : (p(X) | c) | (![X: $i] : p(X) | c)) & ((~(p(X!16) | c)) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & (![X: $i] : (~(p(X) & c)) | (![X: $i] : (~p(X)) | (~c)))) | ((((~c) | p(X!18)) | ((~c) | p(X!11))) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | (((c | (~p(X!19))) | (c | (~p(X!7)))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : ((~c) | p(X)) | ((~c) | ![X: $i] : p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) | ((![X: $i] : (c | (~p(X))) | (c | ![X: $i] : (~p(X)))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11))))) <=> ((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | ((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ((p(X!10) | q(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ![Y: $i] : (p(Y) & (~p(X!7))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[524, 520, 516, 512, 510, 509, 508, 507, 506, 505, 504, 503, 502, 501])).
% 0.20/0.49 tff(526,plain,
% 0.20/0.49 (((![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ((![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z))) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & (((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z)))))) | ![X: $i] : (~(q(X) | p(tptp_fun_Y_5(X)) | (~p(X)))) | ((![X: $i] : (p(X) & q(X)) | (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(p(X!6) & q(X!6))) | ((~p(X!7)) | (~q(X!8))))) | ((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | (((p(X!10) | q(X!10)) | (p(X!11) | q(X!12))) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ![Y: $i] : (p(Y) & (~p(X!7))) | ((p(X!13) & q(X!13)) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![Y: $i] : (~p(Y)) & ((~p(Y!15)) & p(X!11))) | ((![X: $i] : (p(X) | c) | (![X: $i] : p(X) | c)) & ((~(p(X!16) | c)) | ((~p(X!7)) & (~c)))) | (((p(X!17) & c) | (p(X!11) & c)) & (![X: $i] : (~(p(X) & c)) | (![X: $i] : (~p(X)) | (~c)))) | ((((~c) | p(X!18)) | ((~c) | p(X!11))) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | (((c | (~p(X!19))) | (c | (~p(X!7)))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((![X: $i] : ((~c) | p(X)) | ((~c) | ![X: $i] : p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) | ((![X: $i] : (c | (~p(X))) | (c | ![X: $i] : (~p(X)))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11))))) <=> (((![X: $i] : p(X) | ![X: $i] : q(X)) & (~(p(X!9) | q(X!9)))) | ![Y: $i] : (p(Y) & (~p(X!7))) | ((~p(Y!14)) & ![X: $i] : p(X)) | (![X: $i] : p(X) & ![X: $i] : (~p(X))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | (f(Y!0) & (~g(Y!0)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | (![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)) & (~((~r(X!2, Y!1)) | r(X!2, X!2)))) | (![V: $i] : (~(f(V) & g(V) & (~h(V)))) & ![R: $i] : (g(R) | (~(f(R) & h(R)))) & ((~(h(X!3) | (~(f(X!3) & g(X!3))))) | (f(X!4) & (~g(X!4)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))) | ![X: $i] : (~(q(X) | (~p(X)) | p(tptp_fun_Y_5(X)))) | (((![X: $i] : p(X) & ![X: $i] : q(X)) | ![X: $i] : (p(X) & q(X))) & ((~(p(X!6) & q(X!6))) | (~p(X!7)) | (~q(X!8)))) | (p(X!13) & q(X!13) & (![X: $i] : (~p(X)) | ![X: $i] : (~q(X)))) | (![Y: $i] : (~p(Y)) & (~p(Y!15)) & p(X!11)) | ((p(X!10) | q(X!10) | p(X!11) | q(X!12)) & (![X: $i] : (~(p(X) | q(X))) | (![X: $i] : (~p(X)) & ![X: $i] : (~q(X))))) | ((![X: $i] : p(X) | (~c) | ![X: $i] : ((~c) | p(X))) & ((~((~c) | p(X!20))) | (c & (~p(X!7))))) | ((![X: $i] : p(X) | c | ![X: $i] : (p(X) | c)) & ((~(c | p(X!16))) | ((~p(X!7)) & (~c)))) | (((~c) | p(X!11) | p(X!18)) & (![X: $i] : (~((~c) | p(X))) | (c & ![X: $i] : (~p(X))))) | (((p(X!17) & c) | (p(X!11) & c)) & ((~c) | ![X: $i] : (~p(X)) | ![X: $i] : (~(p(X) & c)))) | ((c | (~p(X!7)) | (~p(X!19))) & (![X: $i] : (~(c | (~p(X)))) | ((~c) & ![X: $i] : p(X)))) | ((c | ![X: $i] : (c | (~p(X))) | ![X: $i] : (~p(X))) & ((~(c | (~p(X!21)))) | ((~c) & p(X!11)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[525, 500])).
% 0.20/0.49 tff(527,plain,
% 0.20/0.49 ((~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | p(Y)) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))) <=> (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(528,plain,
% 0.20/0.49 ((~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))) <=> (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | p(Y)) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(529,plain,
% 0.20/0.49 ((~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))) <=> (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(530,plain,
% 0.20/0.50 (((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))) <=> ((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(531,plain,
% 0.20/0.50 ((~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))) <=> (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[530])).
% 0.20/0.50 tff(532,plain,
% 0.20/0.50 ((~(((((((((((((((((((((![X: $i] : (((f(X) & g(X)) => h(X)) => ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (f(W) => g(W)) | ![Z: $i] : (f(Z) => h(Z)))) => (![R: $i] : ((f(R) & h(R)) => g(R)) => ?[V: $i] : ((f(V) & g(V)) & (~h(V))))) & ((![X: $i, Y: $i] : (r(X, Y) => r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((r(X, Y) & r(Y, Z)) => r(X, Z))) => ![X: $i, Y: $i] : (r(X, Y) => r(X, X)))) & (((![X: $i] : ((f(X) & g(X)) => h(X)) => ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (f(W) => g(W)) | ![Z: $i] : (f(Z) => h(Z)))) => (![R: $i] : ((f(R) & h(R)) => g(R)) => ?[V: $i] : ((f(V) & g(V)) & (~h(V)))))) & ?[X: $i] : ![Y: $i] : ((p(Y) => q(X)) => (p(X) => q(X)))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))) & ((![X: $i] : p(X) | ![X: $i] : q(X)) => ![X: $i] : (p(X) | q(X)))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X)))) & ?[Y: $i] : (p(Y) => ![X: $i] : p(X))) & (?[X: $i] : (p(X) & q(X)) => (?[X: $i] : p(X) & ?[X: $i] : q(X)))) & ![Y: $i] : (![X: $i] : p(X) => p(Y))) & (![X: $i] : p(X) => ?[X: $i] : p(X))) & ((~?[Y: $i] : p(Y)) => ![Y: $i] : (?[X: $i] : p(X) => p(Y)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c))) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c))) & (?[X: $i] : c <=> c)) & (![X: $i] : c <=> c)) & (?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X)))) & (?[X: $i] : (p(X) => c) <=> (![X: $i] : p(X) => c))) & (![X: $i] : (c => p(X)) <=> (c => ![X: $i] : p(X)))) & (![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c)))) <=> (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(533,axiom,(~(((((((((((((((((((((![X: $i] : (((f(X) & g(X)) => h(X)) => ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (f(W) => g(W)) | ![Z: $i] : (f(Z) => h(Z)))) => (![R: $i] : ((f(R) & h(R)) => g(R)) => ?[V: $i] : ((f(V) & g(V)) & (~h(V))))) & ((![X: $i, Y: $i] : (r(X, Y) => r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((r(X, Y) & r(Y, Z)) => r(X, Z))) => ![X: $i, Y: $i] : (r(X, Y) => r(X, X)))) & (((![X: $i] : ((f(X) & g(X)) => h(X)) => ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (f(W) => g(W)) | ![Z: $i] : (f(Z) => h(Z)))) => (![R: $i] : ((f(R) & h(R)) => g(R)) => ?[V: $i] : ((f(V) & g(V)) & (~h(V)))))) & ?[X: $i] : ![Y: $i] : ((p(Y) => q(X)) => (p(X) => q(X)))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X)))) & ((![X: $i] : p(X) | ![X: $i] : q(X)) => ![X: $i] : (p(X) | q(X)))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X)))) & ?[Y: $i] : (p(Y) => ![X: $i] : p(X))) & (?[X: $i] : (p(X) & q(X)) => (?[X: $i] : p(X) & ?[X: $i] : q(X)))) & ![Y: $i] : (![X: $i] : p(X) => p(Y))) & (![X: $i] : p(X) => ?[X: $i] : p(X))) & ((~?[Y: $i] : p(Y)) => ![Y: $i] : (?[X: $i] : p(X) => p(Y)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c))) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c))) & (?[X: $i] : c <=> c)) & (![X: $i] : c <=> c)) & (?[X: $i] : (c => p(X)) <=> (c => ?[X: $i] : p(X)))) & (?[X: $i] : (p(X) => c) <=> (![X: $i] : p(X) => c))) & (![X: $i] : (c => p(X)) <=> (c => ![X: $i] : p(X)))) & (![X: $i] : (p(X) => c) <=> (?[X: $i] : p(X) => c)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.50 tff(534,plain,
% 0.20/0.50 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.20/0.50 tff(535,plain,
% 0.20/0.50 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[534, 531])).
% 0.20/0.50 tff(536,plain,
% 0.20/0.50 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[535, 529])).
% 0.20/0.54 tff(537,plain,
% 0.20/0.54 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | p(Y)) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[536, 528])).
% 0.20/0.54 tff(538,plain,
% 0.20/0.54 (~((?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(![X: $i] : ((~(h(X) | (~(f(X) & g(X))))) | ?[Y: $i] : (f(Y) & (~g(Y)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ((~(![X: $i, Y: $i] : ((~r(X, Y)) | r(Y, X)) & ![X: $i, Y: $i, Z: $i] : ((~(r(X, Y) & r(Y, Z))) | r(X, Z)))) | ![X: $i, Y: $i] : ((~r(X, Y)) | r(X, X))) & (?[V: $i] : (f(V) & g(V) & (~h(V))) | (~![R: $i] : (g(R) | (~(f(R) & h(R))))) | (~(((~![X: $i] : (h(X) | (~(f(X) & g(X))))) | ?[X: $i] : (f(X) & (~g(X)))) & (![W: $i] : (g(W) | (~f(W))) | ![Z: $i] : (h(Z) | (~f(Z))))))) & ?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X))) & (![X: $i] : (p(X) & q(X)) <=> (![X: $i] : p(X) & ![X: $i] : q(X))) & ((~(![X: $i] : p(X) | ![X: $i] : q(X))) | ![X: $i] : (p(X) | q(X))) & (?[X: $i] : (p(X) | q(X)) <=> (?[X: $i] : p(X) | ?[X: $i] : q(X))) & ?[Y: $i] : ((~p(Y)) | ![X: $i] : p(X)) & ((~?[X: $i] : (p(X) & q(X))) | (?[X: $i] : p(X) & ?[X: $i] : q(X))) & ![Y: $i] : (p(Y) | (~![X: $i] : p(X))) & ((~![X: $i] : p(X)) | ?[X: $i] : p(X)) & (?[Y: $i] : p(Y) | ![Y: $i] : (p(Y) | (~?[X: $i] : p(X)))) & (![X: $i] : (p(X) | c) <=> (![X: $i] : p(X) | c)) & (?[X: $i] : (p(X) & c) <=> (?[X: $i] : p(X) & c)) & (?[X: $i] : ((~c) | p(X)) <=> ((~c) | ?[X: $i] : p(X))) & (?[X: $i] : (c | (~p(X))) <=> (c | (~![X: $i] : p(X)))) & (![X: $i] : ((~c) | p(X)) <=> ((~c) | ![X: $i] : p(X))) & (![X: $i] : (c | (~p(X))) <=> (c | (~?[X: $i] : p(X)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[537, 527])).
% 0.20/0.54 unexpected number of arguments: (let ((a!1 (proof-bind (lambda ((V $i))
% 0.20/0.54 (let ((a!1 (not (and (f V) (g V) (not (h V))))))
% 0.20/0.54 (refl (~ a!1 a!1))))))
% 0.20/0.54 (a!2 (exists ((V $i)) (and (f V) (g V) (not (h V)))))
% 0.20/0.54 (a!3 (forall ((V $i)) (not (and (f V) (g V) (not (h V))))))
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% 0.20/0.54 (or a!2 (not a!5) a!38)
% 0.20/0.54 a!43
% 0.20/0.54 (= a!46 (and a!49 a!51))
% 0.20/0.54 (or (not (or a!49 a!51)) a!60)
% 0.20/0.54 (= a!64 (or a!68 a!69))
% 0.20/0.54 a!79
% 0.20/0.54 (or (not a!81) (and a!68 a!69))
% 0.20/0.54 a!86
% 0.20/0.54 (or (not a!49) a!68)
% 0.20/0.54 (or a!95 a!97)
% 0.20/0.54 (= a!106 (or a!49 c))
% 0.20/0.54 (= a!113 (and a!68 c))
% 0.20/0.54 (= a!121 (or (not c) a!68))
% 0.20/0.54 (= a!130 (or c (not a!49)))
% 0.20/0.54 (= a!142 (or (not c) a!49))
% 0.20/0.54 (= a!150 (or c (not a!68)))))
% 0.20/0.54 (a!160 (or (and a!3 a!5 (and a!9 (or a!10 a!12)))
% 0.20/0.54 (and (and a!21 a!24) a!28)
% 0.20/0.54 (and a!3 a!5 (and a!35 (or a!10 a!12)))
% 0.20/0.54 a!44
% 0.20/0.54 (and (or a!46 (and a!49 a!51)) a!55)
% 0.20/0.54 a!63
% 0.20/0.54 a!76
% 0.20/0.54 a!80
% 0.20/0.54 (and (and (p X!13) (q X!13)) (or a!72 a!74))
% 0.20/0.54 (and (not (p Y!14)) a!49)
% 0.20/0.54 (and a!49 a!72)
% 0.20/0.54 a!103
% 0.20/0.54 (and (or a!106 (or a!49 c)) a!110)
% 0.20/0.54 a!119
% 0.20/0.54 a!129
% 0.20/0.54 a!139
% 0.20/0.54 a!148
% 0.20/0.54 a!157)))
% 0.20/0.54 (let ((a!15 (monotonicity (nnf-pos (proof-bind a!7) (~ a!8 a!9))
% 0.20/0.54 a!14
% 0.20/0.54 (~ (and a!8 (or a!10 a!12)) (and a!9 (or a!10 a!12)))))
% 0.20/0.54 (a!30 (nnf-neg a!26
% 0.20/0.54 (sk (~ (not a!27) a!28))
% 0.20/0.54 (~ a!29 (and (and a!21 a!24) a!28))))
% 0.20/0.54 (a!39 (nnf-neg (monotonicity a!36 a!14 a!37)
% 0.20/0.54 (~ (not a!38) (and a!35 (or a!10 a!12)))))
% 0.20/0.54 (a!112 (nnf-neg (nnf-pos (proof-bind a!105) (~ a!106 a!106))
% 0.20/0.54 (sk a!107)
% 0.20/0.54 (monotonicity (nnf-pos (proof-bind a!48) (~ a!49 a!49))
% 0.20/0.54 (refl (~ c c))
% 0.20/0.54 (~ (or a!49 c) (or a!49 c)))
% 0.20/0.54 a!109
% 0.20/0.54 a!111))
% 0.20/0.54 (a!140 (nnf-neg (sk a!131)
% 0.20/0.54 (nnf-neg a!132 (~ (not a!130) a!133))
% 0.20/0.54 (monotonicity (refl (~ c c)) a!52 a!134)
% 0.20/0.54 a!136
% 0.20/0.54 (~ a!137 a!139)))
% 0.20/0.54 (a!158 (nnf-neg a!151
% 0.20/0.54 (sk (~ (not a!150) a!152))
% 0.20/0.54 a!153
% 0.20/0.54 a!155
% 0.20/0.54 (~ a!156 a!157))))
% 0.20/0.54 (let ((a!17 (nnf-neg a!15 (~ a!16 (and a!9 (or a!10 a!12)))))
% 0.20/0.54 (a!41 (nnf-neg (nnf-neg a!1 (~ (not a!2) a!3)) a!6 a!39 a!40)))
% 0.20/0.54 (let ((a!20 (nnf-neg (nnf-neg a!1 (~ (not a!2) a!3)) a!6 a!17 a!19)))
% 0.20/0.54 (nnf-neg a!20
% 0.20/0.54 a!30
% 0.20/0.54 a!41
% 0.20/0.54 (nnf-neg (proof-bind a!42) (~ (not a!43) a!44))
% 0.20/0.54 a!57
% 0.20/0.54 (nnf-neg a!59 (sk a!61) (~ a!62 a!63))
% 0.20/0.54 (nnf-neg a!65 a!67 a!70 a!75 a!77)
% 0.20/0.54 (nnf-neg (proof-bind a!78) (~ (not a!79) a!80))
% 0.20/0.54 (nnf-neg a!83 a!84 a!85)
% 0.20/0.54 (trans (sk a!87) (nnf-neg a!88 a!89 a!90) a!91)
% 0.20/0.54 a!93
% 0.20/0.54 a!104
% 0.20/0.54 a!112
% 0.20/0.54 (nnf-neg a!114 a!116 a!117 a!118 a!120)
% 0.20/0.54 (nnf-neg a!122 a!124 a!125 a!127 (~ a!128 a!129))
% 0.20/0.54 a!140
% 0.20/0.54 a!149
% 0.20/0.54 a!158
% 0.20/0.54 (~ (not a!159) a!160))))))))
% 0.20/0.54 Proof display could not be completed: unexpected number of arguments
% 0.20/0.54 % E exiting
%------------------------------------------------------------------------------