%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS162+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:13:30 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS162+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:10:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(cA_type, type, (
% 0.20/0.39 cA: $i > $o)).
% 0.20/0.39 tff(tptp_fun_Y0_4_type, type, (
% 0.20/0.39 tptp_fun_Y0_4: $i)).
% 0.20/0.39 tff(tptp_fun_Y2_5_type, type, (
% 0.20/0.39 tptp_fun_Y2_5: $i)).
% 0.20/0.39 tff(tptp_fun_Y1_3_type, type, (
% 0.20/0.39 tptp_fun_Y1_3: $i)).
% 0.20/0.39 tff(cB_type, type, (
% 0.20/0.39 cB: $i > $o)).
% 0.20/0.39 tff(rp_type, type, (
% 0.20/0.39 rp: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_X_2_type, type, (
% 0.20/0.39 tptp_fun_X_2: $i)).
% 0.20/0.39 tff(rr_type, type, (
% 0.20/0.39 rr: ( $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_Y1_6_type, type, (
% 0.20/0.39 tptp_fun_Y1_6: $i)).
% 0.20/0.39 tff(tptp_fun_Y0_7_type, type, (
% 0.20/0.39 tptp_fun_Y0_7: $i)).
% 0.20/0.39 tff(rq_type, type, (
% 0.20/0.39 rq: ( $i * $i ) > $o)).
% 0.20/0.39 tff(cowlThing_type, type, (
% 0.20/0.39 cowlThing: $i > $o)).
% 0.20/0.39 tff(tptp_fun_X_0_type, type, (
% 0.20/0.39 tptp_fun_X_0: $i)).
% 0.20/0.39 tff(cowlNothing_type, type, (
% 0.20/0.39 cowlNothing: $i > $o)).
% 0.20/0.39 tff(xsd_string_type, type, (
% 0.20/0.39 xsd_string: $i > $o)).
% 0.20/0.39 tff(tptp_fun_X_1_type, type, (
% 0.20/0.39 tptp_fun_X_1: $i)).
% 0.20/0.39 tff(xsd_integer_type, type, (
% 0.20/0.39 xsd_integer: $i > $o)).
% 0.20/0.39 tff(1,assumption,(Y2!5 = Y1!3), introduced(assumption)).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (cB(Y2!5) <=> cB(Y1!3)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (cB(Y1!3) <=> cB(Y2!5)),
% 0.20/0.39 inference(symmetry,[status(thm)],[2])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 ((~cB(Y1!3)) <=> (~cB(Y2!5))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[3])).
% 0.20/0.39 tff(5,assumption,(cowlNothing(X!0) | (~cowlThing(X!0))), introduced(assumption)).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(11,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_0')).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.39 tff(13,plain,(
% 0.20/0.39 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[12])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(X!0) | (~cowlThing(X!0))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[16, 15, 5])).
% 0.20/0.39 tff(18,plain,(~(cowlNothing(X!0) | (~cowlThing(X!0)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 ((cowlNothing(X!0) | (~cowlThing(X!0))) | cowlThing(X!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (cowlThing(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 ((cowlNothing(X!0) | (~cowlThing(X!0))) | (~cowlNothing(X!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (~cowlNothing(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[21, 18])).
% 0.20/0.39 tff(23,assumption,(xsd_integer(X!1) <=> xsd_string(X!1)), introduced(assumption)).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (^[X: $i] : refl((~(xsd_integer(X) <=> xsd_string(X))) <=> (~(xsd_integer(X) <=> xsd_string(X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (^[X: $i] : trans(rewrite((xsd_string(X) <=> (~xsd_integer(X))) <=> (~(xsd_integer(X) <=> xsd_string(X)))), rewrite((~(xsd_integer(X) <=> xsd_string(X))) <=> (~(xsd_integer(X) <=> xsd_string(X)))), ((xsd_string(X) <=> (~xsd_integer(X))) <=> (~(xsd_integer(X) <=> xsd_string(X)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.40 tff(29,axiom,(![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_1')).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.40 tff(32,plain,(
% 0.20/0.40 ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))) | (~(xsd_integer(X!1) <=> xsd_string(X!1)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[34, 33, 23])).
% 0.20/0.40 tff(36,plain,(~(xsd_integer(X!1) <=> xsd_string(X!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (((~cowlThing(X!0)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))))) | cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1))) <=> ((~cowlThing(X!0)) | cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ((~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6))) <=> (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (((~cowlThing(X!0)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6))) | cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1))) <=> ((~cowlThing(X!0)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))))) | cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (((~cowlThing(X!0)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6))) | cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1))) <=> ((~cowlThing(X!0)) | cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[39, 37])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (((~cowlThing(X!0)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6))) | cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1))) <=> ((~cowlThing(X!0)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6))) | cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 ((((~cowlThing(X!0)) | cowlNothing(X!0)) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6)))) <=> ((~cowlThing(X!0)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6))) | cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ((rp(X!2, Y0!4) & rp(X!2, Y1!3) & (~(Y0!4 = Y1!3)) & rq(X!2, Y0!7) & rq(X!2, Y1!6) & rq(X!2, Y2!5) & (~(Y0!7 = Y1!6)) & (~(Y0!7 = Y2!5)) & (~(Y1!6 = Y2!5)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) <=> (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (^[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : trans(monotonicity(rewrite((rr(X!2, Y0) & rr(X!2, Y1) & rr(X!2, Y2) & rr(X!2, Y3) & rr(X!2, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))) <=> (~((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4))))), ((~(rr(X!2, Y0) & rr(X!2, Y1) & rr(X!2, Y2) & rr(X!2, Y3) & rr(X!2, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))) <=> (~(~((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4))))))), rewrite((~(~((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4))))) <=> ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))), ((~(rr(X!2, Y0) & rr(X!2, Y1) & rr(X!2, Y2) & rr(X!2, Y3) & rr(X!2, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))) <=> ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!2, Y0) & rr(X!2, Y1) & rr(X!2, Y2) & rr(X!2, Y3) & rr(X!2, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))) <=> ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 ((rp(X!2, Y0!4) & rp(X!2, Y1!3) & (~(Y0!4 = Y1!3)) & rq(X!2, Y0!7) & rq(X!2, Y1!6) & rq(X!2, Y2!5) & (~(Y0!7 = Y1!6)) & (~(Y0!7 = Y2!5)) & (~(Y1!6 = Y2!5)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!2, Y0) & rr(X!2, Y1) & rr(X!2, Y2) & rr(X!2, Y3) & rr(X!2, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))) <=> (rp(X!2, Y0!4) & rp(X!2, Y1!3) & (~(Y0!4 = Y1!3)) & rq(X!2, Y0!7) & rq(X!2, Y1!6) & rq(X!2, Y2!5) & (~(Y0!7 = Y1!6)) & (~(Y0!7 = Y2!5)) & (~(Y1!6 = Y2!5)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ((rp(X!2, Y0!4) & rp(X!2, Y1!3) & (~(Y0!4 = Y1!3)) & rq(X!2, Y0!7) & rq(X!2, Y1!6) & rq(X!2, Y2!5) & (~(Y0!7 = Y1!6)) & (~(Y0!7 = Y2!5)) & (~(Y1!6 = Y2!5)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!2, Y0) & rr(X!2, Y1) & rr(X!2, Y2) & rr(X!2, Y3) & rr(X!2, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))) <=> (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[46, 43])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ((~(~((~cowlThing(X!0)) | cowlNothing(X!0)))) <=> ((~cowlThing(X!0)) | cowlNothing(X!0))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ((cowlThing(X!0) & (~cowlNothing(X!0))) <=> (~((~cowlThing(X!0)) | cowlNothing(X!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) <=> (~(~((~cowlThing(X!0)) | cowlNothing(X!0))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) <=> ((~cowlThing(X!0)) | cowlNothing(X!0))),
% 0.20/0.41 inference(transitivity,[status(thm)],[50, 48])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (rp(X!2, Y0!4) & rp(X!2, Y1!3) & (~(Y0!4 = Y1!3)) & rq(X!2, Y0!7) & rq(X!2, Y1!6) & rq(X!2, Y2!5) & (~(Y0!7 = Y1!6)) & (~(Y0!7 = Y2!5)) & (~(Y1!6 = Y2!5)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!2, Y0) & rr(X!2, Y1) & rr(X!2, Y2) & rr(X!2, Y3) & rr(X!2, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))) <=> (((~cowlThing(X!0)) | cowlNothing(X!0)) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[51, 47])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (rp(X!2, Y0!4) & rp(X!2, Y1!3) & (~(Y0!4 = Y1!3)) & rq(X!2, Y0!7) & rq(X!2, Y1!6) & rq(X!2, Y2!5) & (~(Y0!7 = Y1!6)) & (~(Y0!7 = Y2!5)) & (~(Y1!6 = Y2!5)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!2, Y0) & rr(X!2, Y1) & rr(X!2, Y2) & rr(X!2, Y3) & rr(X!2, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))) <=> ((~cowlThing(X!0)) | (~((Y0!7 = Y2!5) | (~rp(X!2, Y0!4)) | (~rp(X!2, Y1!3)) | (~rq(X!2, Y2!5)) | (~rq(X!2, Y0!7)) | (~rq(X!2, Y1!6)) | (~![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((Y3 = Y4) | (Y2 = Y3) | (Y2 = Y4) | (Y1 = Y4) | (Y1 = Y3) | (Y1 = Y2) | (Y0 = Y4) | (Y0 = Y3) | (Y0 = Y2) | (Y0 = Y1) | (~rr(X!2, Y1)) | (~rr(X!2, Y0)) | (~rr(X!2, Y2)) | (~rr(X!2, Y3)) | (~rr(X!2, Y4)))) | (Y1!6 = Y2!5) | (Y0!4 = Y1!3) | (Y0!7 = Y1!6))) | cowlNothing(X!0) | (xsd_integer(X!1) <=> xsd_string(X!1)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[52, 42])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (((rp(X!2, Y0!4) & rp(X!2, Y1!3) & (~(Y0!4 = Y1!3))) & (rq(X!2, Y0!7) & rq(X!2, Y1!6) & rq(X!2, Y2!5) & (~(Y0!7 = Y1!6)) & (~(Y0!7 = Y2!5)) & (~(Y1!6 = Y2!5)))) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!2, Y0) & rr(X!2, Y1) & rr(X!2, Y2) & rr(X!2, Y3) & rr(X!2, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))) <=> ((~(cowlThing(X!0) & (~cowlNothing(X!0)))) | (xsd_integer(X!1) <=> xsd_string(X!1)) | (rp(X!2, Y0!4) & rp(X!2, Y1!3) & (~(Y0!4 = Y1!3)) & rq(X!2, Y0!7) & rq(X!2, Y1!6) & rq(X!2, Y2!5) & (~(Y0!7 = Y1!6)) & (~(Y0!7 = Y2!5)) & (~(Y1!6 = Y2!5)) & ![Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (~(rr(X!2, Y0) & rr(X!2, Y1) & rr(X!2, Y2) & rr(X!2, Y3) & rr(X!2, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 ((~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : ((?[Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (((((rq(X, Y0) & rq(X, Y1)) & rq(X, Y2)) & (~(Y0 = Y1))) & (~(Y0 = Y2))) & (~(Y1 = Y2)))) => ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((((((((((((((rr(X, Y0) & rr(X, Y1)) & rr(X, Y2)) & rr(X, Y3)) & rr(X, Y4)) & (~(Y0 = Y1))) & (~(Y0 = Y2))) & (~(Y0 = Y3))) & (~(Y0 = Y4))) & (~(Y1 = Y2))) & (~(Y1 = Y3))) & (~(Y1 = Y4))) & (~(Y2 = Y3))) & (~(Y2 = Y4))) & (~(Y3 = Y4)))))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(59,axiom,(~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : ((?[Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (((((rq(X, Y0) & rq(X, Y1)) & rq(X, Y2)) & (~(Y0 = Y1))) & (~(Y0 = Y2))) & (~(Y1 = Y2)))) => ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((((((((((((((rr(X, Y0) & rr(X, Y1)) & rr(X, Y2)) & rr(X, Y3)) & rr(X, Y4)) & (~(Y0 = Y1))) & (~(Y0 = Y2))) & (~(Y0 = Y3))) & (~(Y0 = Y4))) & (~(Y1 = Y2))) & (~(Y1 = Y3))) & (~(Y1 = Y4))) & (~(Y2 = Y3))) & (~(Y2 = Y4))) & (~(Y3 = Y4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~(?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ?[Y0: $i, Y1: $i, Y2: $i] : (rq(X, Y0) & rq(X, Y1) & rq(X, Y2) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y1 = Y2))))) | ?[Y0: $i, Y1: $i, Y2: $i, Y3: $i, Y4: $i] : (rr(X, Y0) & rr(X, Y1) & rr(X, Y2) & rr(X, Y3) & rr(X, Y4) & (~(Y0 = Y1)) & (~(Y0 = Y2)) & (~(Y0 = Y3)) & (~(Y0 = Y4)) & (~(Y1 = Y2)) & (~(Y1 = Y3)) & (~(Y1 = Y4)) & (~(Y2 = Y3)) & (~(Y2 = Y4)) & (~(Y3 = Y4)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[62, 56])).
% 0.20/0.43 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (and (cowlThing X) (not (cowlNothing X)))))
% 0.20/0.43 (a!2 (not (and (cowlThing X!0) (not (cowlNothing X!0)))))
% 0.20/0.43 (a!3 (forall ((X $i)) (not (= (xsd_integer X) (xsd_string X)))))
% 0.20/0.43 (a!5 (forall ((X $i))
% 0.20/0.43 (let ((a!1 (exists ((Y0 $i) (Y1 $i))
% 0.20/0.43 (and (rp X Y0) (rp X Y1) (not (= Y0 Y1)))))
% 0.20/0.43 (a!2 (exists ((Y0 $i) (Y1 $i) (Y2 $i))
% 0.20/0.43 (and (rq X Y0)
% 0.20/0.43 (rq X Y1)
% 0.20/0.43 (rq X Y2)
% 0.20/0.43 (not (= Y0 Y1))
% 0.20/0.43 (not (= Y0 Y2))
% 0.20/0.43 (not (= Y1 Y2)))))
% 0.20/0.43 (a!3 (exists ((Y0 $i) (Y1 $i) (Y2 $i) (Y3 $i) (Y4 $i))
% 0.20/0.43 (and (rr X Y0)
% 0.20/0.43 (rr X Y1)
% 0.20/0.43 (rr X Y2)
% 0.20/0.43 (rr X Y3)
% 0.20/0.43 (rr X Y4)
% 0.20/0.43 (not (= Y0 Y1))
% 0.20/0.43 (not (= Y0 Y2))
% 0.20/0.43 (not (= Y0 Y3))
% 0.20/0.43 (not (= Y0 Y4))
% 0.20/0.43 (not (= Y1 Y2))
% 0.20/0.43 (not (= Y1 Y3))
% 0.20/0.43 (not (= Y1 Y4))
% 0.20/0.43 (not (= Y2 Y3))
% 0.20/0.43 (not (= Y2 Y4))
% 0.20/0.43 (not (= Y3 Y4))))))
% 0.20/0.43 (or (not (and a!1 a!2)) a!3))))
% 0.20/0.43 (a!6 (exists ((Y0 $i) (Y1 $i))
% 0.20/0.43 (and (rp X!2 Y0) (rp X!2 Y1) (not (= Y0 Y1)))))
% 0.20/0.43 (a!7 (exists ((Y0 $i) (Y1 $i) (Y2 $i))
% 0.20/0.43 (and (rq X!2 Y0)
% 0.20/0.43 (rq X!2 Y1)
% 0.20/0.43 (rq X!2 Y2)
% 0.20/0.43 (not (= Y0 Y1))
% 0.20/0.43 (not (= Y0 Y2))
% 0.20/0.43 (not (= Y1 Y2)))))
% 0.20/0.43 (a!8 (exists ((Y0 $i) (Y1 $i) (Y2 $i) (Y3 $i) (Y4 $i))
% 0.20/0.43 (and (rr X!2 Y0)
% 0.20/0.43 (rr X!2 Y1)
% 0.20/0.43 (rr X!2 Y2)
% 0.20/0.43 (rr X!2 Y3)
% 0.20/0.43 (rr X!2 Y4)
% 0.20/0.43 (not (= Y0 Y1))
% 0.20/0.43 (not (= Y0 Y2))
% 0.20/0.43 (not (= Y0 Y3))
% 0.20/0.43 (not (= Y0 Y4))
% 0.20/0.43 (not (= Y1 Y2))
% 0.20/0.43 (not (= Y1 Y3))
% 0.20/0.43 (not (= Y1 Y4))
% 0.20/0.43 (not (= Y2 Y3))
% 0.20/0.43 (not (= Y2 Y4))
% 0.20/0.43 (not (= Y3 Y4)))))
% 0.20/0.43 (a!10 (and (rp X!2 Y0!4) (rp X!2 Y1!3) (not (= Y0!4 Y1!3))))
% 0.20/0.43 (a!11 (and (rq X!2 Y0!7)
% 0.20/0.43 (rq X!2 Y1!6)
% 0.20/0.43 (rq X!2 Y2!5)
% 0.20/0.43 (not (= Y0!7 Y1!6))
% 0.20/0.43 (not (= Y0!7 Y2!5))
% 0.20/0.43 (not (= Y1!6 Y2!5))))
% 0.20/0.43 (a!14 (lambda ((Y0 $i) (Y1 $i) (Y2 $i) (Y3 $i) (Y4 $i))
% 0.20/0.43 (let ((a!1 (and (rr X!2 Y0)
% 0.20/0.43 (rr X!2 Y1)
% 0.20/0.43 (rr X!2 Y2)
% 0.20/0.43 (rr X!2 Y3)
% 0.20/0.43 (rr X!2 Y4)
% 0.20/0.43 (not (= Y0 Y1))
% 0.20/0.43 (not (= Y0 Y2))
% 0.20/0.43 (not (= Y0 Y3))
% 0.20/0.43 (not (= Y0 Y4))
% 0.20/0.43 (not (= Y1 Y2))
% 0.20/0.43 (not (= Y1 Y3))
% 0.20/0.43 (not (= Y1 Y4))
% 0.20/0.43 (not (= Y2 Y3))
% 0.20/0.43 (not (= Y2 Y4))
% 0.20/0.43 (not (= Y3 Y4)))))
% 0.20/0.43 (refl (~ (not a!1) (not a!1))))))
% 0.20/0.43 (a!15 (forall ((Y0 $i) (Y1 $i) (Y2 $i) (Y3 $i) (Y4 $i))
% 0.20/0.43 (let ((a!1 (and (rr X!2 Y0)
% 0.20/0.43 (rr X!2 Y1)
% 0.20/0.43 (rr X!2 Y2)
% 0.20/0.43 (rr X!2 Y3)
% 0.20/0.43 (rr X!2 Y4)
% 0.20/0.43 (not (= Y0 Y1))
% 0.20/0.43 (not (= Y0 Y2))
% 0.20/0.43 (not (= Y0 Y3))
% 0.20/0.43 (not (= Y0 Y4))
% 0.20/0.43 (not (= Y1 Y2))
% 0.20/0.43 (not (= Y1 Y3))
% 0.20/0.43 (not (= Y1 Y4))
% 0.20/0.43 (not (= Y2 Y3))
% 0.20/0.43 (not (= Y2 Y4))
% 0.20/0.43 (not (= Y3 Y4)))))
% 0.20/0.43 (not a!1)))))
% 0.20/0.43 (let ((a!4 (sk (~ (not a!3) (= (xsd_integer X!1) (xsd_string X!1)))))
% 0.20/0.43 (a!9 (not (or (not (and a!6 a!7)) a!8)))
% 0.20/0.43 (a!12 (~ (not (not (and a!6 a!7))) (and a!10 a!11)))
% 0.20/0.43 (a!18 (~ (not (and a!1 a!3 a!5))
% 0.20/0.43 (or a!2
% 0.20/0.43 (= (xsd_integer X!1) (xsd_string X!1))
% 0.20/0.43 (and (and a!10 a!11) a!15)))))
% 0.20/0.43 (let ((a!13 (nnf-neg (monotonicity (sk (~ a!6 a!10))
% 0.20/0.43 (sk (~ a!7 a!11))
% 0.20/0.43 (~ (and a!6 a!7) (and a!10 a!11)))
% 0.20/0.43 a!12)))
% 0.20/0.43 (let ((a!16 (nnf-neg a!13
% 0.20/0.43 (nnf-neg (proof-bind a!14) (~ (not a!8) a!15))
% 0.20/0.43 (~ a!9 (and (and a!10 a!11) a!15)))))
% 0.20/0.43 (let ((a!17 (trans (sk (~ (not a!5) a!9))
% 0.20/0.43 a!16
% 0.20/0.43 (~ (not a!5) (and (and a!10 a!11) a!15)))))
% 0.20/0.43 (nnf-neg (sk (~ (not a!1) a!2)) a!4 a!17 a!18))))))
% 0.20/0.43 Proof display could not be completed: unexpected number of arguments
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------