TSTP Solution File: HAL004+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HAL004+1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Fri Sep 16 22:35:03 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HAL004+1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n007.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 : Wed Aug 31 21:22:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(apply_type, type, (
% 0.20/0.41 apply: ( $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_E_8_type, type, (
% 0.20/0.41 tptp_fun_E_8: $i)).
% 0.20/0.41 tff(delta_type, type, (
% 0.20/0.41 delta: $i)).
% 0.20/0.41 tff(tptp_fun_ElDom_2_type, type, (
% 0.20/0.41 tptp_fun_ElDom_2: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(beta_type, type, (
% 0.20/0.41 beta: $i)).
% 0.20/0.41 tff(b_type, type, (
% 0.20/0.41 b: $i)).
% 0.20/0.41 tff(h_type, type, (
% 0.20/0.41 h: $i)).
% 0.20/0.41 tff(c_type, type, (
% 0.20/0.41 c: $i)).
% 0.20/0.41 tff(g_type, type, (
% 0.20/0.41 g: $i)).
% 0.20/0.41 tff(element_type, type, (
% 0.20/0.41 element: ( $i * $i ) > $o)).
% 0.20/0.41 tff(r_type, type, (
% 0.20/0.41 r: $i)).
% 0.20/0.41 tff(e_type, type, (
% 0.20/0.41 e: $i)).
% 0.20/0.41 tff(zero_type, type, (
% 0.20/0.41 zero: $i > $i)).
% 0.20/0.41 tff(morphism_type, type, (
% 0.20/0.41 morphism: ( $i * $i * $i ) > $o)).
% 0.20/0.41 tff(surjection_type, type, (
% 0.20/0.41 surjection: $i > $o)).
% 0.20/0.41 tff(commute_type, type, (
% 0.20/0.41 commute: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (morphism(delta, e, r) <=> morphism(delta, e, r)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(2,axiom,(morphism(delta, e, r)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','delta_morphism')).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (morphism(delta, e, r)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (^[Morphism: $i, Dom: $i, Cod: $i] : rewrite(((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod)))))) <=> ((~morphism(Morphism, Dom, Cod)) | (~((~(apply(Morphism, zero(Dom)) = zero(Cod))) | (~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod)))))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~(apply(Morphism, zero(Dom)) = zero(Cod))) | (~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (^[Morphism: $i, Dom: $i, Cod: $i] : refl(((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod)))))) <=> ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod)))))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (^[Morphism: $i, Dom: $i, Cod: $i] : rewrite(((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod)))))) <=> ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod)))))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod)))))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[9, 7])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (^[Morphism: $i, Dom: $i, Cod: $i] : rewrite(((~morphism(Morphism, Dom, Cod)) | (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod)))) <=> ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod)))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod)))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (^[Morphism: $i, Dom: $i, Cod: $i] : trans(monotonicity(rewrite((![El: $i] : (element(El, Dom) => element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod))) <=> (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod)))), ((morphism(Morphism, Dom, Cod) => (![El: $i] : (element(El, Dom) => element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod)))) <=> (morphism(Morphism, Dom, Cod) => (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod)))))), rewrite((morphism(Morphism, Dom, Cod) => (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod)))) <=> ((~morphism(Morphism, Dom, Cod)) | (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod))))), ((morphism(Morphism, Dom, Cod) => (![El: $i] : (element(El, Dom) => element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod)))) <=> ((~morphism(Morphism, Dom, Cod)) | (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![Morphism: $i, Dom: $i, Cod: $i] : (morphism(Morphism, Dom, Cod) => (![El: $i] : (element(El, Dom) => element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod)))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.41 tff(16,axiom,(![Morphism: $i, Dom: $i, Cod: $i] : (morphism(Morphism, Dom, Cod) => (![El: $i] : (element(El, Dom) => element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod))))), file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax','morphism')).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.41 tff(19,plain,(
% 0.20/0.41 ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod)) & (apply(Morphism, zero(Dom)) = zero(Cod))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[18])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))) | (~(apply(Morphism, zero(Dom)) = zero(Cod))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~(apply(Morphism, zero(Dom)) = zero(Cod))) | (~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 5])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~(apply(Morphism, zero(Dom)) = zero(Cod))) | (~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))))))) | ((~morphism(delta, e, r)) | (~((~(apply(delta, zero(e)) = zero(r))) | (~![El: $i] : ((~element(El, e)) | element(apply(delta, El), r))))))) <=> ((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~(apply(Morphism, zero(Dom)) = zero(Cod))) | (~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))))))) | (~morphism(delta, e, r)) | (~((~(apply(delta, zero(e)) = zero(r))) | (~![El: $i] : ((~element(El, e)) | element(apply(delta, El), r))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 ((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~(apply(Morphism, zero(Dom)) = zero(Cod))) | (~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))))))) | ((~morphism(delta, e, r)) | (~((~(apply(delta, zero(e)) = zero(r))) | (~![El: $i] : ((~element(El, e)) | element(apply(delta, El), r))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 ((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~((~(apply(Morphism, zero(Dom)) = zero(Cod))) | (~![El: $i] : ((~element(El, Dom)) | element(apply(Morphism, El), Cod))))))) | (~morphism(delta, e, r)) | (~((~(apply(delta, zero(e)) = zero(r))) | (~![El: $i] : ((~element(El, e)) | element(apply(delta, El), r)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (~((~(apply(delta, zero(e)) = zero(r))) | (~![El: $i] : ((~element(El, e)) | element(apply(delta, El), r))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[25, 22, 3])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (((~(apply(delta, zero(e)) = zero(r))) | (~![El: $i] : ((~element(El, e)) | element(apply(delta, El), r)))) | ![El: $i] : ((~element(El, e)) | element(apply(delta, El), r))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![El: $i] : ((~element(El, e)) | element(apply(delta, El), r))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (((~(~element(E!8, e))) & ![R: $i, B1: $i] : (~(element(R, r) & (apply(delta, E!8) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)))) <=> (element(E!8, e) & ![R: $i, B1: $i] : (~(element(R, r) & (apply(delta, E!8) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 ((~![E: $i] : ((~element(E, e)) | ?[R: $i, B1: $i] : (element(R, r) & (apply(delta, E) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)))) <=> (~![E: $i] : ((~element(E, e)) | ?[R: $i, B1: $i] : (element(R, r) & (apply(delta, E) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 ((~![E: $i] : (element(E, e) => ?[R: $i, B1: $i] : ((((element(R, r) & (apply(delta, E) = R)) & element(B1, b)) & (apply(h, apply(beta, B1)) = R)) & (apply(delta, apply(g, B1)) = R)))) <=> (~![E: $i] : ((~element(E, e)) | ?[R: $i, B1: $i] : (element(R, r) & (apply(delta, E) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(32,axiom,(~![E: $i] : (element(E, e) => ?[R: $i, B1: $i] : ((((element(R, r) & (apply(delta, E) = R)) & element(B1, b)) & (apply(h, apply(beta, B1)) = R)) & (apply(delta, apply(g, B1)) = R)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma3')).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (~![E: $i] : ((~element(E, e)) | ?[R: $i, B1: $i] : (element(R, r) & (apply(delta, E) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (~![E: $i] : ((~element(E, e)) | ?[R: $i, B1: $i] : (element(R, r) & (apply(delta, E) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (~![E: $i] : ((~element(E, e)) | ?[R: $i, B1: $i] : (element(R, r) & (apply(delta, E) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (~![E: $i] : ((~element(E, e)) | ?[R: $i, B1: $i] : (element(R, r) & (apply(delta, E) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (~![E: $i] : ((~element(E, e)) | ?[R: $i, B1: $i] : (element(R, r) & (apply(delta, E) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[36, 30])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (~![E: $i] : ((~element(E, e)) | ?[R: $i, B1: $i] : (element(R, r) & (apply(delta, E) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (~![E: $i] : ((~element(E, e)) | ?[R: $i, B1: $i] : (element(R, r) & (apply(delta, E) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[38, 30])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (element(E!8, e) & ![R: $i, B1: $i] : (~(element(R, r) & (apply(delta, E!8) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (element(E!8, e)),
% 0.20/0.42 inference(and_elim,[status(thm)],[40])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (((~![El: $i] : ((~element(El, e)) | element(apply(delta, El), r))) | ((~element(E!8, e)) | element(apply(delta, E!8), r))) <=> ((~![El: $i] : ((~element(El, e)) | element(apply(delta, El), r))) | (~element(E!8, e)) | element(apply(delta, E!8), r))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 ((~![El: $i] : ((~element(El, e)) | element(apply(delta, El), r))) | ((~element(E!8, e)) | element(apply(delta, E!8), r))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ((~![El: $i] : ((~element(El, e)) | element(apply(delta, El), r))) | (~element(E!8, e)) | element(apply(delta, E!8), r)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (element(apply(delta, E!8), r)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[44, 41, 28])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (surjection(h) <=> surjection(h)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(47,axiom,(surjection(h)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','h_surjection')).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (surjection(h)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (morphism(h, c, r) <=> morphism(h, c, r)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(50,axiom,(morphism(h, c, r)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','h_morphism')).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (morphism(h, c, r)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (^[Morphism: $i, Dom: $i, Cod: $i] : refl(((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))))) <=> ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (^[Morphism: $i, Dom: $i, Cod: $i] : rewrite(((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))))) <=> ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[55, 53])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (^[Morphism: $i, Dom: $i, Cod: $i] : trans(monotonicity(trans(monotonicity(rewrite((surjection(Morphism) & morphism(Morphism, Dom, Cod)) <=> (~((~surjection(Morphism)) | (~morphism(Morphism, Dom, Cod))))), ((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) <=> (~(~((~surjection(Morphism)) | (~morphism(Morphism, Dom, Cod))))))), rewrite((~(~((~surjection(Morphism)) | (~morphism(Morphism, Dom, Cod))))) <=> ((~surjection(Morphism)) | (~morphism(Morphism, Dom, Cod)))), ((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) <=> ((~surjection(Morphism)) | (~morphism(Morphism, Dom, Cod))))), quant_intro(proof_bind(^[ElCod: $i] : rewrite(((~element(ElCod, Cod)) | (element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom) & (apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))) <=> ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))), (![ElCod: $i] : ((~element(ElCod, Cod)) | (element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom) & (apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))) <=> ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))), (((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom) & (apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))) <=> (((~surjection(Morphism)) | (~morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))))))), rewrite((((~surjection(Morphism)) | (~morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))))) <=> ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))), (((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom) & (apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))) <=> ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom) & (apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod)))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod)))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (^[Morphism: $i, Dom: $i, Cod: $i] : trans(monotonicity(quant_intro(proof_bind(^[ElCod: $i] : rewrite((element(ElCod, Cod) => ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod))) <=> ((~element(ElCod, Cod)) | ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod))))), (![ElCod: $i] : (element(ElCod, Cod) => ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod))) <=> ![ElCod: $i] : ((~element(ElCod, Cod)) | ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod))))), (((surjection(Morphism) & morphism(Morphism, Dom, Cod)) => ![ElCod: $i] : (element(ElCod, Cod) => ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod)))) <=> ((surjection(Morphism) & morphism(Morphism, Dom, Cod)) => ![ElCod: $i] : ((~element(ElCod, Cod)) | ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod)))))), rewrite(((surjection(Morphism) & morphism(Morphism, Dom, Cod)) => ![ElCod: $i] : ((~element(ElCod, Cod)) | ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod)))) <=> ((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod))))), (((surjection(Morphism) & morphism(Morphism, Dom, Cod)) => ![ElCod: $i] : (element(ElCod, Cod) => ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod)))) <=> ((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((surjection(Morphism) & morphism(Morphism, Dom, Cod)) => ![ElCod: $i] : (element(ElCod, Cod) => ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod)))) <=> ![Morphism: $i, Dom: $i, Cod: $i] : ((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.42 tff(62,axiom,(![Morphism: $i, Dom: $i, Cod: $i] : ((surjection(Morphism) & morphism(Morphism, Dom, Cod)) => ![ElCod: $i] : (element(ElCod, Cod) => ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod))))), file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax','surjection_properties')).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | ?[ElDom: $i] : (element(ElDom, Dom) & (apply(Morphism, ElDom) = ElCod))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.42 tff(65,plain,(
% 0.20/0.42 ![Morphism: $i, Dom: $i, Cod: $i] : ((~(surjection(Morphism) & morphism(Morphism, Dom, Cod))) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom) & (apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[64])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))) | ((~morphism(h, c, r)) | (~surjection(h)) | ![ElCod: $i] : ((~element(ElCod, r)) | (~((~element(tptp_fun_ElDom_2(ElCod, c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(ElCod, c, h)) = ElCod))))))) <=> ((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))) | (~morphism(h, c, r)) | (~surjection(h)) | ![ElCod: $i] : ((~element(ElCod, r)) | (~((~element(tptp_fun_ElDom_2(ElCod, c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(ElCod, c, h)) = ElCod))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 ((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))) | ((~morphism(h, c, r)) | (~surjection(h)) | ![ElCod: $i] : ((~element(ElCod, r)) | (~((~element(tptp_fun_ElDom_2(ElCod, c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(ElCod, c, h)) = ElCod))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))) | (~morphism(h, c, r)) | (~surjection(h)) | ![ElCod: $i] : ((~element(ElCod, r)) | (~((~element(tptp_fun_ElDom_2(ElCod, c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(ElCod, c, h)) = ElCod)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (![ElCod: $i] : ((~element(ElCod, r)) | (~((~element(tptp_fun_ElDom_2(ElCod, c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(ElCod, c, h)) = ElCod)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[70, 67, 51, 48])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (((~![ElCod: $i] : ((~element(ElCod, r)) | (~((~element(tptp_fun_ElDom_2(ElCod, c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(ElCod, c, h)) = ElCod)))))) | ((~element(apply(delta, E!8), r)) | (~((~element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(apply(delta, E!8), c, h)) = apply(delta, E!8))))))) <=> ((~![ElCod: $i] : ((~element(ElCod, r)) | (~((~element(tptp_fun_ElDom_2(ElCod, c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(ElCod, c, h)) = ElCod)))))) | (~element(apply(delta, E!8), r)) | (~((~element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(apply(delta, E!8), c, h)) = apply(delta, E!8))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 ((~![ElCod: $i] : ((~element(ElCod, r)) | (~((~element(tptp_fun_ElDom_2(ElCod, c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(ElCod, c, h)) = ElCod)))))) | ((~element(apply(delta, E!8), r)) | (~((~element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(apply(delta, E!8), c, h)) = apply(delta, E!8))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 ((~![ElCod: $i] : ((~element(ElCod, r)) | (~((~element(tptp_fun_ElDom_2(ElCod, c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(ElCod, c, h)) = ElCod)))))) | (~element(apply(delta, E!8), r)) | (~((~element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(apply(delta, E!8), c, h)) = apply(delta, E!8)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (~((~element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(apply(delta, E!8), c, h)) = apply(delta, E!8))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[74, 71, 45])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (((~element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(apply(delta, E!8), c, h)) = apply(delta, E!8)))) | (apply(h, tptp_fun_ElDom_2(apply(delta, E!8), c, h)) = apply(delta, E!8))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (apply(h, tptp_fun_ElDom_2(apply(delta, E!8), c, h)) = apply(delta, E!8)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (((~element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)) | (~(apply(h, tptp_fun_ElDom_2(apply(delta, E!8), c, h)) = apply(delta, E!8)))) | element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (surjection(beta) <=> surjection(beta)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(81,axiom,(surjection(beta)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','beta_surjection')).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (surjection(beta)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (morphism(beta, b, c) <=> morphism(beta, b, c)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(84,axiom,(morphism(beta, b, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','beta_morphism')).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (morphism(beta, b, c)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))) | ((~morphism(beta, b, c)) | (~surjection(beta)) | ![ElCod: $i] : ((~element(ElCod, c)) | (~((~element(tptp_fun_ElDom_2(ElCod, b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(ElCod, b, beta)) = ElCod))))))) <=> ((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))) | (~morphism(beta, b, c)) | (~surjection(beta)) | ![ElCod: $i] : ((~element(ElCod, c)) | (~((~element(tptp_fun_ElDom_2(ElCod, b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(ElCod, b, beta)) = ElCod))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 ((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))) | ((~morphism(beta, b, c)) | (~surjection(beta)) | ![ElCod: $i] : ((~element(ElCod, c)) | (~((~element(tptp_fun_ElDom_2(ElCod, b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(ElCod, b, beta)) = ElCod))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 ((~![Morphism: $i, Dom: $i, Cod: $i] : ((~morphism(Morphism, Dom, Cod)) | (~surjection(Morphism)) | ![ElCod: $i] : ((~element(ElCod, Cod)) | (~((~element(tptp_fun_ElDom_2(ElCod, Dom, Morphism), Dom)) | (~(apply(Morphism, tptp_fun_ElDom_2(ElCod, Dom, Morphism)) = ElCod))))))) | (~morphism(beta, b, c)) | (~surjection(beta)) | ![ElCod: $i] : ((~element(ElCod, c)) | (~((~element(tptp_fun_ElDom_2(ElCod, b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(ElCod, b, beta)) = ElCod)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (![ElCod: $i] : ((~element(ElCod, c)) | (~((~element(tptp_fun_ElDom_2(ElCod, b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(ElCod, b, beta)) = ElCod)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[88, 67, 85, 82])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (((~![ElCod: $i] : ((~element(ElCod, c)) | (~((~element(tptp_fun_ElDom_2(ElCod, b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(ElCod, b, beta)) = ElCod)))))) | ((~element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)) | (~((~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)) = tptp_fun_ElDom_2(apply(delta, E!8), c, h))))))) <=> ((~![ElCod: $i] : ((~element(ElCod, c)) | (~((~element(tptp_fun_ElDom_2(ElCod, b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(ElCod, b, beta)) = ElCod)))))) | (~element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)) | (~((~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)) = tptp_fun_ElDom_2(apply(delta, E!8), c, h))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 ((~![ElCod: $i] : ((~element(ElCod, c)) | (~((~element(tptp_fun_ElDom_2(ElCod, b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(ElCod, b, beta)) = ElCod)))))) | ((~element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)) | (~((~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)) = tptp_fun_ElDom_2(apply(delta, E!8), c, h))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 ((~![ElCod: $i] : ((~element(ElCod, c)) | (~((~element(tptp_fun_ElDom_2(ElCod, b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(ElCod, b, beta)) = ElCod)))))) | (~element(tptp_fun_ElDom_2(apply(delta, E!8), c, h), c)) | (~((~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)) = tptp_fun_ElDom_2(apply(delta, E!8), c, h)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (~((~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)) = tptp_fun_ElDom_2(apply(delta, E!8), c, h))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[92, 89, 79])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (((~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)) = tptp_fun_ElDom_2(apply(delta, E!8), c, h)))) | (apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)) = tptp_fun_ElDom_2(apply(delta, E!8), c, h))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)) = tptp_fun_ElDom_2(apply(delta, E!8), c, h)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(h, tptp_fun_ElDom_2(apply(delta, E!8), c, h))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (((~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)) = tptp_fun_ElDom_2(apply(delta, E!8), c, h)))) | element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 (element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[97, 93])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (commute(beta, h, g, delta) <=> commute(beta, h, g, delta)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(100,axiom,(commute(beta, h, g, delta)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','beta_h_g_delta_commute')).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (commute(beta, h, g, delta)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (morphism(g, b, e) <=> morphism(g, b, e)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(103,axiom,(morphism(g, b, e)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','g_morphism')).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (morphism(g, b, e)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (^[M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : rewrite((![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))) <=> ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))) <=> ![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (^[M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : refl((![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))) <=> (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))) <=> ![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (^[M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : rewrite((![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))) <=> (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))) <=> ![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))) <=> ![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[110, 108])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (^[M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : trans(monotonicity(trans(monotonicity(rewrite((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod)) <=> (~((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))))), ((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) <=> (~(~((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))))))), rewrite((~(~((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))))) <=> ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)))), ((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) <=> ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))))), (((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))) <=> (((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))))), rewrite((((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))) <=> (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)))), (((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))) <=> (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))) <=> ![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))) <=> ![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (^[M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1)) & morphism(M2, DomCod1, Cod)) <=> (commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod))), ((((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1)) & morphism(M2, DomCod1, Cod)) & morphism(M3, Dom, DomCod2)) <=> ((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod)) & morphism(M3, Dom, DomCod2)))), rewrite(((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod)) & morphism(M3, Dom, DomCod2)) <=> (commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2))), ((((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1)) & morphism(M2, DomCod1, Cod)) & morphism(M3, Dom, DomCod2)) <=> (commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2)))), (((((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1)) & morphism(M2, DomCod1, Cod)) & morphism(M3, Dom, DomCod2)) & morphism(M4, DomCod2, Cod)) <=> ((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2)) & morphism(M4, DomCod2, Cod)))), rewrite(((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2)) & morphism(M4, DomCod2, Cod)) <=> (commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))), (((((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1)) & morphism(M2, DomCod1, Cod)) & morphism(M3, Dom, DomCod2)) & morphism(M4, DomCod2, Cod)) <=> (commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod)))), quant_intro(proof_bind(^[ElDom: $i] : rewrite((element(ElDom, Dom) => (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) <=> ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))), (![ElDom: $i] : (element(ElDom, Dom) => (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) <=> ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))), ((((((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1)) & morphism(M2, DomCod1, Cod)) & morphism(M3, Dom, DomCod2)) & morphism(M4, DomCod2, Cod)) => ![ElDom: $i] : (element(ElDom, Dom) => (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))) <=> ((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod)) => ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))))), rewrite(((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod)) => ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))) <=> ((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))), ((((((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1)) & morphism(M2, DomCod1, Cod)) & morphism(M3, Dom, DomCod2)) & morphism(M4, DomCod2, Cod)) => ![ElDom: $i] : (element(ElDom, Dom) => (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))) <=> ((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (((((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1)) & morphism(M2, DomCod1, Cod)) & morphism(M3, Dom, DomCod2)) & morphism(M4, DomCod2, Cod)) => ![ElDom: $i] : (element(ElDom, Dom) => (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom))))) <=> ![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[115])).
% 0.20/0.44 tff(117,axiom,(![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (((((commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1)) & morphism(M2, DomCod1, Cod)) & morphism(M3, Dom, DomCod2)) & morphism(M4, DomCod2, Cod)) => ![ElDom: $i] : (element(ElDom, Dom) => (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))), file('/export/starexec/sandbox/benchmark/Axioms/HAL001+0.ax','commute_properties')).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.20/0.44 tff(120,plain,(
% 0.20/0.44 ![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~(commute(M1, M2, M3, M4) & morphism(M1, Dom, DomCod1) & morphism(M2, DomCod1, Cod) & morphism(M3, Dom, DomCod2) & morphism(M4, DomCod2, Cod))) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[119])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : (![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))) | (~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[122, 106])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (((~![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))) | ((~morphism(g, b, e)) | (~morphism(beta, b, c)) | (~morphism(h, c, r)) | (~morphism(delta, e, r)) | (~commute(beta, h, g, delta)) | ![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom)))))) <=> ((~![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))) | (~morphism(g, b, e)) | (~morphism(beta, b, c)) | (~morphism(h, c, r)) | (~morphism(delta, e, r)) | (~commute(beta, h, g, delta)) | ![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 (((~morphism(beta, b, c)) | (~morphism(h, c, r)) | (~morphism(g, b, e)) | (~morphism(delta, e, r)) | (~commute(beta, h, g, delta)) | ![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom))))) <=> ((~morphism(g, b, e)) | (~morphism(beta, b, c)) | (~morphism(h, c, r)) | (~morphism(delta, e, r)) | (~commute(beta, h, g, delta)) | ![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 (((~![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))) | ((~morphism(beta, b, c)) | (~morphism(h, c, r)) | (~morphism(g, b, e)) | (~morphism(delta, e, r)) | (~commute(beta, h, g, delta)) | ![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom)))))) <=> ((~![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))) | ((~morphism(g, b, e)) | (~morphism(beta, b, c)) | (~morphism(h, c, r)) | (~morphism(delta, e, r)) | (~commute(beta, h, g, delta)) | ![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[125])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 (((~![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))) | ((~morphism(beta, b, c)) | (~morphism(h, c, r)) | (~morphism(g, b, e)) | (~morphism(delta, e, r)) | (~commute(beta, h, g, delta)) | ![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom)))))) <=> ((~![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))) | (~morphism(g, b, e)) | (~morphism(beta, b, c)) | (~morphism(h, c, r)) | (~morphism(delta, e, r)) | (~commute(beta, h, g, delta)) | ![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom)))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[126, 124])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 ((~![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))) | ((~morphism(beta, b, c)) | (~morphism(h, c, r)) | (~morphism(g, b, e)) | (~morphism(delta, e, r)) | (~commute(beta, h, g, delta)) | ![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 ((~![M1: $i, M2: $i, M3: $i, M4: $i, Dom: $i, DomCod1: $i, DomCod2: $i, Cod: $i] : ((~morphism(M1, Dom, DomCod1)) | (~morphism(M2, DomCod1, Cod)) | (~morphism(M3, Dom, DomCod2)) | (~morphism(M4, DomCod2, Cod)) | (~commute(M1, M2, M3, M4)) | ![ElDom: $i] : ((~element(ElDom, Dom)) | (apply(M2, apply(M1, ElDom)) = apply(M4, apply(M3, ElDom)))))) | (~morphism(g, b, e)) | (~morphism(beta, b, c)) | (~morphism(h, c, r)) | (~morphism(delta, e, r)) | (~commute(beta, h, g, delta)) | ![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[129, 123, 85, 3, 104, 51, 101])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (((~![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom))))) | ((~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)))))) <=> ((~![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom))))) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 ((~![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom))))) | ((~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 ((~![ElDom: $i] : ((~element(ElDom, b)) | (apply(h, apply(beta, ElDom)) = apply(delta, apply(g, ElDom))))) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[133, 130, 98])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta)))),
% 0.20/0.45 inference(symmetry,[status(thm)],[134])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8)),
% 0.20/0.45 inference(transitivity,[status(thm)],[135, 96, 77])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 ((apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8)) <=> (apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 ((apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8)) <=> (apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))),
% 0.20/0.45 inference(symmetry,[status(thm)],[137])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[136, 138])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 (^[R: $i, B1: $i] : refl(((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R))) <=> ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 (![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R))) <=> ![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (^[R: $i, B1: $i] : trans(monotonicity(rewrite((element(R, r) & (apply(delta, E!8) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)) <=> (~((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R))))), ((~(element(R, r) & (apply(delta, E!8) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R))) <=> (~(~((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R))))))), rewrite((~(~((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R))))) <=> ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))), ((~(element(R, r) & (apply(delta, E!8) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R))) <=> ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 (![R: $i, B1: $i] : (~(element(R, r) & (apply(delta, E!8) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R))) <=> ![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[142])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 (![R: $i, B1: $i] : (~(element(R, r) & (apply(delta, E!8) = R) & element(B1, b) & (apply(h, apply(beta, B1)) = R) & (apply(delta, apply(g, B1)) = R)))),
% 0.20/0.46 inference(and_elim,[status(thm)],[40])).
% 0.20/0.46 tff(145,plain,
% 0.20/0.46 (![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 (![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.20/0.46 tff(147,plain,
% 0.20/0.46 (((~![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))) | ((~element(apply(delta, E!8), r)) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))))) <=> ((~![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))) | (~element(apply(delta, E!8), r)) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(148,plain,
% 0.20/0.46 (((~element(apply(delta, E!8), r)) | $false | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8)))) <=> ((~element(apply(delta, E!8), r)) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 ((~$true) <=> $false),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 ((apply(delta, E!8) = apply(delta, E!8)) <=> $true),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 ((~(apply(delta, E!8) = apply(delta, E!8))) <=> (~$true)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 ((~(apply(delta, E!8) = apply(delta, E!8))) <=> $false),
% 0.20/0.46 inference(transitivity,[status(thm)],[151, 149])).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 (((~element(apply(delta, E!8), r)) | (~(apply(delta, E!8) = apply(delta, E!8))) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8)))) <=> ((~element(apply(delta, E!8), r)) | $false | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[152])).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 (((~element(apply(delta, E!8), r)) | (~(apply(delta, E!8) = apply(delta, E!8))) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8)))) <=> ((~element(apply(delta, E!8), r)) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[153, 148])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (((~![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))) | ((~element(apply(delta, E!8), r)) | (~(apply(delta, E!8) = apply(delta, E!8))) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))))) <=> ((~![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))) | ((~element(apply(delta, E!8), r)) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (((~![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))) | ((~element(apply(delta, E!8), r)) | (~(apply(delta, E!8) = apply(delta, E!8))) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))))) <=> ((~![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))) | (~element(apply(delta, E!8), r)) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[155, 147])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 ((~![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))) | ((~element(apply(delta, E!8), r)) | (~(apply(delta, E!8) = apply(delta, E!8))) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 ((~![R: $i, B1: $i] : ((~element(R, r)) | (~(apply(delta, E!8) = R)) | (~element(B1, b)) | (~(apply(h, apply(beta, B1)) = R)) | (~(apply(delta, apply(g, B1)) = R)))) | (~element(apply(delta, E!8), r)) | (~element(tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta), b)) | (~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 ((~(apply(h, apply(beta, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8))) | (~(apply(delta, apply(g, tptp_fun_ElDom_2(tptp_fun_ElDom_2(apply(delta, E!8), c, h), b, beta))) = apply(delta, E!8)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[158, 146, 45, 98])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[159, 139, 136])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------