%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU188+1 : TPTP v9.0.0. Released v3.3.0.
% 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 05:27:11 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU188+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:19:05 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(empty_type, type, (
% 0.21/0.39 empty: $i > $o)).
% 0.21/0.39 tff(relation_rng_type, type, (
% 0.21/0.39 relation_rng: $i > $i)).
% 0.21/0.39 tff(tptp_fun_A_13_type, type, (
% 0.21/0.39 tptp_fun_A_13: $i)).
% 0.21/0.39 tff(empty_set_type, type, (
% 0.21/0.39 empty_set: $i)).
% 0.21/0.39 tff(relation_dom_type, type, (
% 0.21/0.39 relation_dom: $i > $i)).
% 0.21/0.39 tff(in_type, type, (
% 0.21/0.39 in: ( $i * $i ) > $o)).
% 0.21/0.39 tff(ordered_pair_type, type, (
% 0.21/0.39 ordered_pair: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tptp_fun_C_11_type, type, (
% 0.21/0.39 tptp_fun_C_11: $i > $i)).
% 0.21/0.39 tff(tptp_fun_B_12_type, type, (
% 0.21/0.39 tptp_fun_B_12: $i > $i)).
% 0.21/0.39 tff(relation_type, type, (
% 0.21/0.39 relation: $i > $o)).
% 0.21/0.39 tff(1,assumption,(relation_dom(A!13) = empty_set), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (empty(relation_dom(A!13)) <=> empty(empty_set)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (empty(empty_set) <=> empty(relation_dom(A!13))),
% 0.21/0.39 inference(symmetry,[status(thm)],[2])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (empty(empty_set) <=> empty(empty_set)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(5,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (empty(empty_set)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (empty(relation_dom(A!13))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((~((A!13 = empty_set) | (~relation(A!13)) | (~((relation_dom(A!13) = empty_set) | (relation_rng(A!13) = empty_set))))) <=> (~((A!13 = empty_set) | (~relation(A!13)) | (~((relation_dom(A!13) = empty_set) | (relation_rng(A!13) = empty_set)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 ((~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))) <=> (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 ((~![A: $i] : (relation(A) => (((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)) => (A = empty_set)))) <=> (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(11,axiom,(~![A: $i] : (relation(A) => (((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set)) => (A = empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t64_relat_1')).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (~![A: $i] : ((A = empty_set) | (~relation(A)) | (~((relation_dom(A) = empty_set) | (relation_rng(A) = empty_set))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.21/0.39 tff(16,plain,(
% 0.21/0.39 ~((A!13 = empty_set) | (~relation(A!13)) | (~((relation_dom(A!13) = empty_set) | (relation_rng(A!13) = empty_set))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[15])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (~((A!13 = empty_set) | (~relation(A!13)) | (~((relation_dom(A!13) = empty_set) | (relation_rng(A!13) = empty_set))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 8])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (relation(A!13)),
% 0.21/0.39 inference(or_elim,[status(thm)],[17])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (~(A!13 = empty_set)),
% 0.21/0.39 inference(or_elim,[status(thm)],[17])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (^[A: $i] : refl(((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_12(A), tptp_fun_C_11(A)), A)) <=> ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_12(A), tptp_fun_C_11(A)), A)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_12(A), tptp_fun_C_11(A)), A)) <=> ![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_12(A), tptp_fun_C_11(A)), A))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A)))) <=> ![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (^[A: $i] : trans(monotonicity(rewrite((![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)) <=> ((~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (A = empty_set))), ((relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set))) <=> (relation(A) => ((~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (A = empty_set))))), rewrite((relation(A) => ((~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))) | (A = empty_set))) <=> ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))), ((relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set))) <=> ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set))) <=> ![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.39 tff(25,axiom,(![A: $i] : (relation(A) => (![B: $i, C: $i] : (~in(ordered_pair(B, C), A)) => (A = empty_set)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t56_relat_1')).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (![A: $i] : ((A = empty_set) | (~relation(A)) | (~![B: $i, C: $i] : (~in(ordered_pair(B, C), A))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.39 tff(28,plain,(
% 0.21/0.39 ![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_12(A), tptp_fun_C_11(A)), A))),
% 0.21/0.39 inference(skolemize,[status(sab)],[27])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_12(A), tptp_fun_C_11(A)), A))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (((~![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_12(A), tptp_fun_C_11(A)), A))) | ((A!13 = empty_set) | (~relation(A!13)) | in(ordered_pair(tptp_fun_B_12(A!13), tptp_fun_C_11(A!13)), A!13))) <=> ((~![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_12(A), tptp_fun_C_11(A)), A))) | (A!13 = empty_set) | (~relation(A!13)) | in(ordered_pair(tptp_fun_B_12(A!13), tptp_fun_C_11(A!13)), A!13))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 ((~![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_12(A), tptp_fun_C_11(A)), A))) | ((A!13 = empty_set) | (~relation(A!13)) | in(ordered_pair(tptp_fun_B_12(A!13), tptp_fun_C_11(A!13)), A!13))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 ((~![A: $i] : ((A = empty_set) | (~relation(A)) | in(ordered_pair(tptp_fun_B_12(A), tptp_fun_C_11(A)), A))) | (A!13 = empty_set) | (~relation(A!13)) | in(ordered_pair(tptp_fun_B_12(A!13), tptp_fun_C_11(A!13)), A!13)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (in(ordered_pair(tptp_fun_B_12(A!13), tptp_fun_C_11(A!13)), A!13)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[32, 29, 19, 18])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(39,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.40 tff(41,plain,(
% 0.21/0.40 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[40])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(A!13)) | (~in(ordered_pair(tptp_fun_B_12(A!13), tptp_fun_C_11(A!13)), A!13)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(A!13)) | (~in(ordered_pair(tptp_fun_B_12(A!13), tptp_fun_C_11(A!13)), A!13)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(A!13)) | (~in(ordered_pair(tptp_fun_B_12(A!13), tptp_fun_C_11(A!13)), A!13)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(A!13)) | (~in(ordered_pair(tptp_fun_B_12(A!13), tptp_fun_C_11(A!13)), A!13))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (~empty(A!13)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[46, 43, 33])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (^[A: $i] : refl((empty(A) | (~empty(relation_dom(A))) | (~relation(A))) <=> (empty(A) | (~empty(relation_dom(A))) | (~relation(A))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A))) <=> ![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty(A)) & relation(A)) <=> (~(empty(A) | (~relation(A))))), ((~((~empty(A)) & relation(A))) <=> (~(~(empty(A) | (~relation(A))))))), rewrite((~(~(empty(A) | (~relation(A))))) <=> (empty(A) | (~relation(A)))), ((~((~empty(A)) & relation(A))) <=> (empty(A) | (~relation(A))))), (((~empty(relation_dom(A))) | (~((~empty(A)) & relation(A)))) <=> ((~empty(relation_dom(A))) | (empty(A) | (~relation(A)))))), rewrite(((~empty(relation_dom(A))) | (empty(A) | (~relation(A)))) <=> (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))), (((~empty(relation_dom(A))) | (~((~empty(A)) & relation(A)))) <=> (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (![A: $i] : ((~empty(relation_dom(A))) | (~((~empty(A)) & relation(A)))) <=> ![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (![A: $i] : ((~empty(relation_dom(A))) | (~((~empty(A)) & relation(A)))) <=> ![A: $i] : ((~empty(relation_dom(A))) | (~((~empty(A)) & relation(A))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (^[A: $i] : rewrite((((~empty(A)) & relation(A)) => (~empty(relation_dom(A)))) <=> ((~empty(relation_dom(A))) | (~((~empty(A)) & relation(A)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (![A: $i] : (((~empty(A)) & relation(A)) => (~empty(relation_dom(A)))) <=> ![A: $i] : ((~empty(relation_dom(A))) | (~((~empty(A)) & relation(A))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.40 tff(55,axiom,(![A: $i] : (((~empty(A)) & relation(A)) => (~empty(relation_dom(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc5_relat_1')).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (![A: $i] : ((~empty(relation_dom(A))) | (~((~empty(A)) & relation(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (![A: $i] : ((~empty(relation_dom(A))) | (~((~empty(A)) & relation(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.21/0.40 tff(58,plain,(
% 0.21/0.40 ![A: $i] : ((~empty(relation_dom(A))) | (~((~empty(A)) & relation(A))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[57])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (((~![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))) | ((~relation(A!13)) | empty(A!13) | (~empty(relation_dom(A!13))))) <=> ((~![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))) | (~relation(A!13)) | empty(A!13) | (~empty(relation_dom(A!13))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 ((empty(A!13) | (~empty(relation_dom(A!13))) | (~relation(A!13))) <=> ((~relation(A!13)) | empty(A!13) | (~empty(relation_dom(A!13))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (((~![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))) | (empty(A!13) | (~empty(relation_dom(A!13))) | (~relation(A!13)))) <=> ((~![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))) | ((~relation(A!13)) | empty(A!13) | (~empty(relation_dom(A!13)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[62])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (((~![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))) | (empty(A!13) | (~empty(relation_dom(A!13))) | (~relation(A!13)))) <=> ((~![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))) | (~relation(A!13)) | empty(A!13) | (~empty(relation_dom(A!13))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[63, 61])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 ((~![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))) | (empty(A!13) | (~empty(relation_dom(A!13))) | (~relation(A!13)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 ((~![A: $i] : (empty(A) | (~empty(relation_dom(A))) | (~relation(A)))) | (~relation(A!13)) | empty(A!13) | (~empty(relation_dom(A!13)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (empty(A!13) | (~empty(relation_dom(A!13)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[66, 60, 18])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (~empty(relation_dom(A!13))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[67, 47])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[68, 7])).
% 0.21/0.40 tff(70,plain,(~(relation_dom(A!13) = empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 ((relation_dom(A!13) = empty_set) | (relation_rng(A!13) = empty_set)),
% 0.21/0.40 inference(or_elim,[status(thm)],[17])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (relation_rng(A!13) = empty_set),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (empty(relation_rng(A!13)) <=> empty(empty_set)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[72])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 (empty(empty_set) <=> empty(relation_rng(A!13))),
% 0.21/0.40 inference(symmetry,[status(thm)],[73])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (empty(relation_rng(A!13))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[6, 74])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (^[A: $i] : refl((empty(A) | (~empty(relation_rng(A))) | (~relation(A))) <=> (empty(A) | (~empty(relation_rng(A))) | (~relation(A))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 (![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A))) <=> ![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty(A)) & relation(A)) <=> (~(empty(A) | (~relation(A))))), ((~((~empty(A)) & relation(A))) <=> (~(~(empty(A) | (~relation(A))))))), rewrite((~(~(empty(A) | (~relation(A))))) <=> (empty(A) | (~relation(A)))), ((~((~empty(A)) & relation(A))) <=> (empty(A) | (~relation(A))))), (((~empty(relation_rng(A))) | (~((~empty(A)) & relation(A)))) <=> ((~empty(relation_rng(A))) | (empty(A) | (~relation(A)))))), rewrite(((~empty(relation_rng(A))) | (empty(A) | (~relation(A)))) <=> (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))), (((~empty(relation_rng(A))) | (~((~empty(A)) & relation(A)))) <=> (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 (![A: $i] : ((~empty(relation_rng(A))) | (~((~empty(A)) & relation(A)))) <=> ![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 (![A: $i] : ((~empty(relation_rng(A))) | (~((~empty(A)) & relation(A)))) <=> ![A: $i] : ((~empty(relation_rng(A))) | (~((~empty(A)) & relation(A))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (^[A: $i] : rewrite((((~empty(A)) & relation(A)) => (~empty(relation_rng(A)))) <=> ((~empty(relation_rng(A))) | (~((~empty(A)) & relation(A)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 (![A: $i] : (((~empty(A)) & relation(A)) => (~empty(relation_rng(A)))) <=> ![A: $i] : ((~empty(relation_rng(A))) | (~((~empty(A)) & relation(A))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.40 tff(83,axiom,(![A: $i] : (((~empty(A)) & relation(A)) => (~empty(relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc6_relat_1')).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (![A: $i] : ((~empty(relation_rng(A))) | (~((~empty(A)) & relation(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (![A: $i] : ((~empty(relation_rng(A))) | (~((~empty(A)) & relation(A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.21/0.40 tff(86,plain,(
% 0.21/0.40 ![A: $i] : ((~empty(relation_rng(A))) | (~((~empty(A)) & relation(A))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[85])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 (![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 (((~![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))) | ((~relation(A!13)) | empty(A!13) | (~empty(relation_rng(A!13))))) <=> ((~![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))) | (~relation(A!13)) | empty(A!13) | (~empty(relation_rng(A!13))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 ((empty(A!13) | (~empty(relation_rng(A!13))) | (~relation(A!13))) <=> ((~relation(A!13)) | empty(A!13) | (~empty(relation_rng(A!13))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(91,plain,
% 0.21/0.40 (((~![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))) | (empty(A!13) | (~empty(relation_rng(A!13))) | (~relation(A!13)))) <=> ((~![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))) | ((~relation(A!13)) | empty(A!13) | (~empty(relation_rng(A!13)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 (((~![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))) | (empty(A!13) | (~empty(relation_rng(A!13))) | (~relation(A!13)))) <=> ((~![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))) | (~relation(A!13)) | empty(A!13) | (~empty(relation_rng(A!13))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[91, 89])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 ((~![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))) | (empty(A!13) | (~empty(relation_rng(A!13))) | (~relation(A!13)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 ((~![A: $i] : (empty(A) | (~empty(relation_rng(A))) | (~relation(A)))) | (~relation(A!13)) | empty(A!13) | (~empty(relation_rng(A!13)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 (empty(A!13) | (~empty(relation_rng(A!13)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[94, 88, 18])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (~empty(relation_rng(A!13))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[95, 47])).
% 0.21/0.40 tff(97,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[96, 75])).
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------