%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN002-1.007.008 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:37:56 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN002-1.007.008 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:26:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(p_type, type, (
% 0.11/0.37 p: $i > $o)).
% 0.11/0.37 tff(f_type, type, (
% 0.11/0.37 f: $i > $i)).
% 0.11/0.37 tff(elem_0_type, type, (
% 0.11/0.37 elem_0: $i)).
% 0.11/0.37 tff(1,assumption,(p(f(f(f(f(f(f(f(elem!0))))))))), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (^[X: $i] : refl(((~p(X)) | (~p(f(f(f(f(f(f(f(f(X))))))))))) <=> ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X))))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X))))))))))) <=> ![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X))))))))))) <=> ![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(5,axiom,(![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','negative')).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.37 tff(7,plain,(
% 0.11/0.37 ![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(elem!0))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(elem!0))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(elem!0))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(elem!0))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (^[X: $i] : refl((p(X) | p(f(f(f(f(f(f(f(X))))))))) <=> (p(X) | p(f(f(f(f(f(f(f(X))))))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X))))))))) <=> ![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X))))))))) <=> ![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,axiom,(![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','positive')).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.37 tff(18,plain,(
% 0.11/0.37 ![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[17])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(elem!0))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(elem!0))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(elem!0))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(elem!0))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (p(f(f(f(f(f(f(f(f(elem!0))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[22, 19])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (p(f(f(f(f(f(f(f(f(elem!0)))))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[23, 12])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(elem!0)))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(elem!0)))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(elem!0)))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(elem!0)))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 ((~p(f(f(f(f(f(f(f(f(elem!0)))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[27, 8])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[28, 24])).
% 0.11/0.37 tff(30,assumption,(p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))), introduced(assumption)).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 ((~p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[33, 8])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (~p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[34, 30])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[38, 19])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[39, 35])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 ((~p(f(f(f(f(f(f(f(f(f(elem!0))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[43, 8])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (~p(f(f(f(f(f(f(f(f(f(elem!0))))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[44, 40])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(elem!0)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(elem!0)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(elem!0)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(elem!0)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 (p(f(f(f(f(f(f(f(f(f(elem!0)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[48, 19])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[49, 45, 29])).
% 0.11/0.38 tff(51,plain,((~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))) | (~p(f(f(f(f(f(f(f(elem!0)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[51, 1])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (p(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[55, 19, 52])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[59, 8, 56])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 (p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[63, 19])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 (p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[64, 60])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 ((~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[68, 8])).
% 0.19/0.38 tff(70,plain,
% 0.19/0.38 (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[69, 65])).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 (p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[73, 19])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 (p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[74, 70])).
% 0.19/0.38 tff(76,plain,
% 0.19/0.38 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(77,plain,
% 0.19/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 (p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[78, 19])).
% 0.19/0.38 tff(80,plain,
% 0.19/0.38 (p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[79, 12])).
% 0.19/0.38 tff(81,plain,
% 0.19/0.38 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(82,plain,
% 0.19/0.38 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(83,plain,
% 0.19/0.38 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.38 tff(84,plain,
% 0.19/0.38 ((~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[83, 8])).
% 0.19/0.38 tff(85,plain,
% 0.19/0.38 (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[84, 80])).
% 0.19/0.38 tff(86,plain,
% 0.19/0.38 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(87,plain,
% 0.19/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(88,plain,
% 0.19/0.38 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.38 tff(89,plain,
% 0.19/0.38 (p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[88, 19])).
% 0.19/0.38 tff(90,plain,
% 0.19/0.38 (p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[89, 85])).
% 0.19/0.38 tff(91,plain,
% 0.19/0.38 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 ((~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[93, 8])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[94, 90, 75])).
% 0.19/0.39 tff(96,plain,(~p(f(f(f(f(f(f(f(elem!0))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(elem!0) | p(f(f(f(f(f(f(f(elem!0)))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(elem!0) | p(f(f(f(f(f(f(f(elem!0)))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(elem!0) | p(f(f(f(f(f(f(f(elem!0)))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(elem!0) | p(f(f(f(f(f(f(f(elem!0))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (p(elem!0) | p(f(f(f(f(f(f(f(elem!0))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[99, 19])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 (p(elem!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[100, 96])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(elem!0)) | (~p(f(f(f(f(f(f(f(f(elem!0)))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(elem!0)) | (~p(f(f(f(f(f(f(f(f(elem!0)))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(elem!0)) | (~p(f(f(f(f(f(f(f(f(elem!0)))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(elem!0)) | (~p(f(f(f(f(f(f(f(f(elem!0))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 (~p(f(f(f(f(f(f(f(f(elem!0)))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[104, 8, 101])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(elem!0)) | p(f(f(f(f(f(f(f(f(elem!0))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(elem!0)) | p(f(f(f(f(f(f(f(f(elem!0))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(107,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(elem!0)) | p(f(f(f(f(f(f(f(f(elem!0))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(108,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(elem!0)) | p(f(f(f(f(f(f(f(f(elem!0)))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 (p(f(elem!0)) | p(f(f(f(f(f(f(f(f(elem!0)))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[108, 19])).
% 0.19/0.39 tff(110,plain,
% 0.19/0.39 (p(f(elem!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[109, 105])).
% 0.19/0.39 tff(111,plain,
% 0.19/0.39 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(elem!0))) | (~p(f(f(f(f(f(f(f(f(f(elem!0))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(elem!0))) | (~p(f(f(f(f(f(f(f(f(f(elem!0))))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(112,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(elem!0))) | (~p(f(f(f(f(f(f(f(f(f(elem!0))))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(113,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(elem!0))) | (~p(f(f(f(f(f(f(f(f(f(elem!0)))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.39 tff(114,plain,
% 0.19/0.39 ((~p(f(elem!0))) | (~p(f(f(f(f(f(f(f(f(f(elem!0)))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[113, 8])).
% 0.19/0.39 tff(115,plain,
% 0.19/0.39 (~p(f(f(f(f(f(f(f(f(f(elem!0))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[114, 110])).
% 0.19/0.39 tff(116,plain,
% 0.19/0.39 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(elem!0))) | p(f(f(f(f(f(f(f(f(f(elem!0)))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(elem!0))) | p(f(f(f(f(f(f(f(f(f(elem!0)))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(117,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(elem!0))) | p(f(f(f(f(f(f(f(f(f(elem!0)))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(118,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(elem!0))) | p(f(f(f(f(f(f(f(f(f(elem!0))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.39 tff(119,plain,
% 0.19/0.39 (p(f(f(elem!0))) | p(f(f(f(f(f(f(f(f(f(elem!0))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[118, 19])).
% 0.19/0.39 tff(120,plain,
% 0.19/0.39 (p(f(f(elem!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[119, 115])).
% 0.19/0.39 tff(121,plain,
% 0.19/0.39 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(elem!0)))) | (~p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(elem!0)))) | (~p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(122,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(elem!0)))) | (~p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(123,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(elem!0)))) | (~p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.39 tff(124,plain,
% 0.19/0.39 ((~p(f(f(elem!0)))) | (~p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[123, 8])).
% 0.19/0.39 tff(125,plain,
% 0.19/0.39 (~p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[124, 120])).
% 0.19/0.39 tff(126,plain,
% 0.19/0.39 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(elem!0)))) | p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(elem!0)))) | p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(127,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(elem!0)))) | p(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(128,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(elem!0)))) | p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.39 tff(129,plain,
% 0.19/0.39 (p(f(f(f(elem!0)))) | p(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[128, 19])).
% 0.19/0.39 tff(130,plain,
% 0.19/0.39 (p(f(f(f(elem!0))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[129, 125])).
% 0.19/0.39 tff(131,plain,
% 0.19/0.39 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(elem!0))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(elem!0))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(132,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(elem!0))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(133,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(elem!0))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.39 tff(134,plain,
% 0.19/0.39 ((~p(f(f(f(elem!0))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[133, 8])).
% 0.19/0.39 tff(135,plain,
% 0.19/0.39 (~p(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[134, 130])).
% 0.19/0.39 tff(136,plain,
% 0.19/0.39 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(elem!0))))) | p(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(elem!0))))) | p(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(137,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(elem!0))))) | p(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(138,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(elem!0))))) | p(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.39 tff(139,plain,
% 0.19/0.39 (p(f(f(f(f(elem!0))))) | p(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[138, 19])).
% 0.19/0.39 tff(140,plain,
% 0.19/0.39 (p(f(f(f(f(elem!0)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[139, 135])).
% 0.19/0.39 tff(141,plain,
% 0.19/0.39 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(elem!0)))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(elem!0)))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(142,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(elem!0)))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(143,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(elem!0)))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.39 tff(144,plain,
% 0.19/0.39 ((~p(f(f(f(f(elem!0)))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[143, 8])).
% 0.19/0.39 tff(145,plain,
% 0.19/0.39 (~p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[144, 140])).
% 0.19/0.39 tff(146,plain,
% 0.19/0.39 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(elem!0)))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(elem!0)))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(147,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(elem!0)))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(148,plain,
% 0.19/0.39 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(elem!0)))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.39 tff(149,plain,
% 0.19/0.39 (p(f(f(f(f(f(elem!0)))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[148, 19])).
% 0.19/0.39 tff(150,plain,
% 0.19/0.39 (p(f(f(f(f(f(elem!0))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[149, 145])).
% 0.19/0.39 tff(151,plain,
% 0.19/0.39 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(elem!0))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(elem!0))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(152,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(elem!0))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(153,plain,
% 0.19/0.39 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(elem!0))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.39 tff(154,plain,
% 0.19/0.39 ((~p(f(f(f(f(f(elem!0))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[153, 8])).
% 0.19/0.39 tff(155,plain,
% 0.19/0.39 (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[154, 150])).
% 0.19/0.39 tff(156,plain,
% 0.19/0.39 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(elem!0))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(elem!0))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(157,plain,
% 0.19/0.40 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(elem!0))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(158,plain,
% 0.19/0.40 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(elem!0))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.19/0.40 tff(159,plain,
% 0.19/0.40 (p(f(f(f(f(f(f(elem!0))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[158, 19])).
% 0.19/0.40 tff(160,plain,
% 0.19/0.40 (p(f(f(f(f(f(f(elem!0)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[159, 155])).
% 0.19/0.40 tff(161,plain,
% 0.19/0.40 (((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(elem!0)))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(elem!0)))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(162,plain,
% 0.19/0.40 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | ((~p(f(f(f(f(f(f(elem!0)))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(163,plain,
% 0.19/0.40 ((~![X: $i] : ((~p(X)) | (~p(f(f(f(f(f(f(f(f(X)))))))))))) | (~p(f(f(f(f(f(f(elem!0)))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.40 tff(164,plain,
% 0.19/0.40 ((~p(f(f(f(f(f(f(elem!0)))))))) | (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[163, 8])).
% 0.19/0.40 tff(165,plain,
% 0.19/0.40 (~p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[164, 160])).
% 0.19/0.40 tff(166,plain,
% 0.19/0.40 (((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(elem!0)))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))) <=> ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(elem!0)))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(167,plain,
% 0.19/0.40 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | (p(f(f(f(f(f(f(f(elem!0)))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0))))))))))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(168,plain,
% 0.19/0.40 ((~![X: $i] : (p(X) | p(f(f(f(f(f(f(f(X)))))))))) | p(f(f(f(f(f(f(f(elem!0)))))))) | p(f(f(f(f(f(f(f(f(f(f(f(f(f(f(elem!0)))))))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.19/0.40 tff(169,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[168, 19, 96, 165])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------