%------------------------------------------------------------------------------
% File : GKC---0.8
% Problem : LCL416-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : gkc %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:08:32 PM UTC 2026
% Result : Unsatisfiable 95.70s 12.63s
% Output : CNFRefutation 95.70s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named xcbERROR: Could not build tree for root '85'ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf('1',plain,
is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z))) = true,
inference(cnf_transformation,[],[xcb]) ).
cnf('2',plain,
ifeq(is_a_theorem(equivalent(X,Y)),true,ifeq(is_a_theorem(X),true,is_a_theorem(Y),true),true) = true,
inference(cnf_transformation,[],[condensed_detachment]) ).
cnf('3',plain,
ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),true),true) = true,
inference(paramodulation,[],['1','2']) ).
cnf('4',plain,
ifeq(X,X,Y,Z) = Y,
inference(cnf_transformation,[],[ifeq_axiom]) ).
cnf('5',plain,
ifeq(is_a_theorem(X),true,is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),true) = true,
inference(simplify,[],['3','4']) ).
cnf('6',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),U3),equivalent(V3,U3)),V3)),true) = true,
inference(paramodulation,[],['1','5']) ).
cnf('7',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),U),equivalent(V,U)),V)) = true,
inference(simplify,[],['6','4']) ).
cnf('8',plain,
ifeq(is_a_theorem(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),U3)),true,ifeq(true,true,is_a_theorem(U3),true),true) = true,
inference(paramodulation,[],['1','2']) ).
cnf('9',plain,
ifeq(is_a_theorem(equivalent(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),U)),true,is_a_theorem(U),true) = true,
inference(simplify,[],['8','4']) ).
cnf('10',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),U3),V3),equivalent(U3,V3))),true) = true,
inference(paramodulation,[],['7','9']) ).
cnf('11',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),U),V),equivalent(U,V))) = true,
inference(simplify,[],['10','4']) ).
cnf('12',plain,
ifeq(true,true,is_a_theorem(equivalent(X3,equivalent(equivalent(equivalent(equivalent(equivalent(Y3,equivalent(equivalent(equivalent(Y3,Z3),equivalent(U3,Z3)),U3)),X3),V3),equivalent(W3,V3)),W3))),true) = true,
inference(paramodulation,[],['11','9']) ).
cnf('13',plain,
is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(equivalent(Y,equivalent(equivalent(equivalent(Y,Z),equivalent(U,Z)),U)),X),V),equivalent(W,V)),W))) = true,
inference(simplify,[],['12','4']) ).
cnf('14',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),equivalent(U3,equivalent(equivalent(equivalent(U3,V3),equivalent(W3,V3)),W3))),X3006),equivalent(X3007,X3006)),X3007)),true) = true,
inference(paramodulation,[],['13','9']) ).
cnf('15',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),equivalent(U,equivalent(equivalent(equivalent(U,V),equivalent(W,V)),W))),X2006),equivalent(X2007,X2006)),X2007)) = true,
inference(simplify,[],['14','4']) ).
cnf('16',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),U3),equivalent(V3,U3)),V3),W3),equivalent(X3006,W3)),X3006)),true) = true,
inference(paramodulation,[],['7','5']) ).
cnf('17',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),U),equivalent(V,U)),V),W),equivalent(X2006,W)),X2006)) = true,
inference(simplify,[],['16','4']) ).
cnf('18',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),U3),equivalent(V3,U3)),V3),W3),X3006),equivalent(W3,X3006))),true) = true,
inference(paramodulation,[],['17','9']) ).
cnf('19',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),U),equivalent(V,U)),V),W),X2006),equivalent(W,X2006))) = true,
inference(simplify,[],['18','4']) ).
cnf('20',plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),U3),equivalent(V3,U3)),V3),W3),X3006)),true,is_a_theorem(equivalent(W3,X3006)),true),true) = true,
inference(paramodulation,[],['19','2']) ).
cnf('21',plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),U),equivalent(V,U)),V),W),X2006)),true,is_a_theorem(equivalent(W,X2006)),true) = true,
inference(simplify,[],['20','4']) ).
cnf('22',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,equivalent(Y3,equivalent(equivalent(equivalent(Y3,Z3),equivalent(U3,Z3)),U3))),X3)),true) = true,
inference(paramodulation,[],['15','21']) ).
cnf('23',plain,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,equivalent(equivalent(equivalent(Y,Z),equivalent(U,Z)),U))),X)) = true,
inference(simplify,[],['22','4']) ).
cnf('24',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),U3),V3),equivalent(U3,V3)),W3),equivalent(X3006,W3)),X3006)),true) = true,
inference(paramodulation,[],['11','5']) ).
cnf('25',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),U),V),equivalent(U,V)),W),equivalent(X2006,W)),X2006)) = true,
inference(simplify,[],['24','4']) ).
cnf('26',plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),U3),V3),equivalent(U3,V3)),W3),equivalent(X3006,W3))),true,is_a_theorem(X3006),true),true) = true,
inference(paramodulation,[],['25','2']) ).
cnf('27',plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),U),V),equivalent(U,V)),W),equivalent(X2006,W))),true,is_a_theorem(X2006),true) = true,
inference(simplify,[],['26','4']) ).
cnf('28',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),U3),equivalent(equivalent(equivalent(U3,V3),equivalent(W3,V3)),W3))),true) = true,
inference(paramodulation,[],['23','27']) ).
cnf('29',plain,
is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),U),equivalent(equivalent(equivalent(U,V),equivalent(W,V)),W))) = true,
inference(simplify,[],['28','4']) ).
cnf('30',plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,Y3),equivalent(Z3,Y3)),Z3)),U3),equivalent(V3,U3))),true,is_a_theorem(V3),true),true) = true,
inference(paramodulation,[],['7','2']) ).
cnf('31',plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(equivalent(equivalent(X,Y),equivalent(Z,Y)),Z)),U),equivalent(V,U))),true,is_a_theorem(V),true) = true,
inference(simplify,[],['30','4']) ).
cnf('32',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,Y3),equivalent(X3,Y3))),true) = true,
inference(paramodulation,[],['29','31']) ).
cnf('33',plain,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(X,Y))) = true,
inference(simplify,[],['32','4']) ).
cnf('34',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),Z3),equivalent(U3,Z3)),U3)),true) = true,
inference(paramodulation,[],['33','5']) ).
cnf('35',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),Z),equivalent(U,Z)),U)) = true,
inference(simplify,[],['34','4']) ).
cnf('36',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),Z3),U3),equivalent(Z3,U3))),true) = true,
inference(paramodulation,[],['35','9']) ).
cnf('37',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),Z),U),equivalent(Z,U))) = true,
inference(simplify,[],['36','4']) ).
cnf('38',plain,
ifeq(true,true,is_a_theorem(equivalent(X3,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y3,Z3),equivalent(Y3,Z3)),X3),U3),equivalent(V3,U3)),V3))),true) = true,
inference(paramodulation,[],['37','9']) ).
cnf('39',plain,
is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,Z)),X),U),equivalent(V,U)),V))) = true,
inference(simplify,[],['38','4']) ).
cnf('40',plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),Z3),equivalent(U3,Z3))),true,is_a_theorem(U3),true),true) = true,
inference(paramodulation,[],['35','2']) ).
cnf('41',plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),Z),equivalent(U,Z))),true,is_a_theorem(U),true) = true,
inference(simplify,[],['40','4']) ).
cnf('42',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),equivalent(equivalent(equivalent(Z3,U3),equivalent(Z3,U3)),V3)),W3),equivalent(V3,W3))),true) = true,
inference(paramodulation,[],['39','41']) ).
cnf('43',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),equivalent(equivalent(equivalent(Z,U),equivalent(Z,U)),V)),W),equivalent(V,W))) = true,
inference(simplify,[],['42','4']) ).
cnf('44',plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(X3,equivalent(Y3,equivalent(equivalent(equivalent(Y3,Z3),equivalent(U3,Z3)),U3)))),true,is_a_theorem(X3),true),true) = true,
inference(paramodulation,[],['23','2']) ).
cnf('45',plain,
ifeq(is_a_theorem(equivalent(X,equivalent(Y,equivalent(equivalent(equivalent(Y,Z),equivalent(U,Z)),U)))),true,is_a_theorem(X),true) = true,
inference(simplify,[],['44','4']) ).
cnf('46',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),equivalent(equivalent(equivalent(Z3,U3),equivalent(Z3,U3)),V3)),equivalent(equivalent(equivalent(V3,W3),equivalent(X3006,W3)),X3006))),true) = true,
inference(paramodulation,[],['43','45']) ).
cnf('47',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),equivalent(equivalent(equivalent(Z,U),equivalent(Z,U)),V)),equivalent(equivalent(equivalent(V,W),equivalent(X2006,W)),X2006))) = true,
inference(simplify,[],['46','4']) ).
cnf('48',plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),Z3)),true,ifeq(true,true,is_a_theorem(Z3),true),true) = true,
inference(paramodulation,[],['33','2']) ).
cnf('49',plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),Z)),true,is_a_theorem(Z),true) = true,
inference(simplify,[],['48','4']) ).
cnf('50',plain,
ifeq(true,true,is_a_theorem(equivalent(X3,equivalent(equivalent(equivalent(Y3,Z3),equivalent(Y3,Z3)),X3))),true) = true,
inference(paramodulation,[],['37','49']) ).
cnf('51',plain,
is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(Y,Z),equivalent(Y,Z)),X))) = true,
inference(simplify,[],['50','4']) ).
cnf('52',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),equivalent(equivalent(Z3,U3),equivalent(Z3,U3)))),true) = true,
inference(paramodulation,[],['51','49']) ).
cnf('53',plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),equivalent(equivalent(Z,U),equivalent(Z,U)))) = true,
inference(simplify,[],['52','4']) ).
cnf('54',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),equivalent(equivalent(Z3,U3),equivalent(Z3,U3))),V3),equivalent(W3,V3)),W3)),true) = true,
inference(paramodulation,[],['53','5']) ).
cnf('55',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),equivalent(equivalent(Z,U),equivalent(Z,U))),V),equivalent(W,V)),W)) = true,
inference(simplify,[],['54','4']) ).
cnf('56',plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),equivalent(equivalent(Z3,U3),equivalent(Z3,U3))),V3),equivalent(W3,V3))),true,is_a_theorem(W3),true),true) = true,
inference(paramodulation,[],['55','2']) ).
cnf('57',plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),equivalent(equivalent(Z,U),equivalent(Z,U))),V),equivalent(W,V))),true,is_a_theorem(W),true) = true,
inference(simplify,[],['56','4']) ).
cnf('58',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,Y3),equivalent(equivalent(equivalent(equivalent(Z3,U3),equivalent(Z3,U3)),X3),Y3))),true) = true,
inference(paramodulation,[],['47','57']) ).
cnf('59',plain,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(Z,U)),X),Y))) = true,
inference(simplify,[],['58','4']) ).
cnf('60',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(equivalent(equivalent(equivalent(Z3,U3),equivalent(Z3,U3)),X3),Y3)),V3),equivalent(W3,V3)),W3)),true) = true,
inference(paramodulation,[],['59','5']) ).
cnf('61',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(Z,U)),X),Y)),V),equivalent(W,V)),W)) = true,
inference(simplify,[],['60','4']) ).
cnf('62',plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),Z3),U3)),true,is_a_theorem(equivalent(Z3,U3)),true),true) = true,
inference(paramodulation,[],['37','2']) ).
cnf('63',plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),Z),U)),true,is_a_theorem(equivalent(Z,U)),true) = true,
inference(simplify,[],['62','4']) ).
cnf('64',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,equivalent(equivalent(Y3,Z3),equivalent(equivalent(equivalent(equivalent(U3,V3),equivalent(U3,V3)),Y3),Z3))),X3)),true) = true,
inference(paramodulation,[],['61','63']) ).
cnf('65',plain,
is_a_theorem(equivalent(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(equivalent(equivalent(U,V),equivalent(U,V)),Y),Z))),X)) = true,
inference(simplify,[],['64','4']) ).
cnf('66',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,equivalent(Y3,equivalent(equivalent(equivalent(Y3,Z3),equivalent(U3,Z3)),U3))),X3),V3),equivalent(W3,V3)),W3)),true) = true,
inference(paramodulation,[],['23','5']) ).
cnf('67',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,equivalent(Y,equivalent(equivalent(equivalent(Y,Z),equivalent(U,Z)),U))),X),V),equivalent(W,V)),W)) = true,
inference(simplify,[],['66','4']) ).
cnf('68',plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,equivalent(Y3,equivalent(equivalent(equivalent(Y3,Z3),equivalent(U3,Z3)),U3))),X3),V3),equivalent(W3,V3))),true,is_a_theorem(W3),true),true) = true,
inference(paramodulation,[],['67','2']) ).
cnf('69',plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,equivalent(Y,equivalent(equivalent(equivalent(Y,Z),equivalent(U,Z)),U))),X),V),equivalent(W,V))),true,is_a_theorem(W),true) = true,
inference(simplify,[],['68','4']) ).
cnf('70',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X3,Y3),equivalent(equivalent(equivalent(equivalent(Z3,U3),equivalent(Z3,U3)),X3),Y3)),equivalent(V3,equivalent(equivalent(equivalent(V3,W3),equivalent(X3006,W3)),X3006)))),true) = true,
inference(paramodulation,[],['65','69']) ).
cnf('71',plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(equivalent(equivalent(Z,U),equivalent(Z,U)),X),Y)),equivalent(V,equivalent(equivalent(equivalent(V,W),equivalent(X2006,W)),X2006)))) = true,
inference(simplify,[],['70','4']) ).
cnf('72',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),Z3),equivalent(U3,Z3)),U3),V3),equivalent(W3,V3)),W3)),true) = true,
inference(paramodulation,[],['35','5']) ).
cnf('73',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),Z),equivalent(U,Z)),U),V),equivalent(W,V)),W)) = true,
inference(simplify,[],['72','4']) ).
cnf('74',plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),Z3),equivalent(U3,Z3)),U3),V3),equivalent(W3,V3))),true,is_a_theorem(W3),true),true) = true,
inference(paramodulation,[],['73','2']) ).
cnf('75',plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),Z),equivalent(U,Z)),U),V),equivalent(W,V))),true,is_a_theorem(W),true) = true,
inference(simplify,[],['74','4']) ).
cnf('76',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),Z3),Z3)),true) = true,
inference(paramodulation,[],['71','75']) ).
cnf('77',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),Z),Z)) = true,
inference(simplify,[],['76','4']) ).
cnf('78',plain,
ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),equivalent(equivalent(Z3,U3),equivalent(Z3,U3))),V3),W3),equivalent(V3,W3))),true) = true,
inference(paramodulation,[],['55','9']) ).
cnf('79',plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),equivalent(equivalent(Z,U),equivalent(Z,U))),V),W),equivalent(V,W))) = true,
inference(simplify,[],['78','4']) ).
cnf('80',plain,
ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3,Y3),equivalent(X3,Y3)),equivalent(equivalent(Z3,U3),equivalent(Z3,U3))),V3),W3)),true,is_a_theorem(equivalent(V3,W3)),true),true) = true,
inference(paramodulation,[],['79','2']) ).
cnf('81',plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Y)),equivalent(equivalent(Z,U),equivalent(Z,U))),V),W)),true,is_a_theorem(equivalent(V,W)),true) = true,
inference(simplify,[],['80','4']) ).
cnf('82',plain,
ifeq(true,true,is_a_theorem(equivalent(X3,X3)),true) = true,
inference(paramodulation,[],['77','81']) ).
cnf('83',plain,
is_a_theorem(equivalent(X,X)) = true,
inference(simplify,[],['82','4']) ).
cnf('84',plain,
is_a_theorem(equivalent(a,a)) != true,
inference(cnf_transformation,[],[prove_reflexivity]) ).
cnf('85',plain,
$false,
inference(resolution,[],['83','84']) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL416-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : gkc %s
% 0.11/0.35 % Computer : n005.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Fri Sep 4 14:23:36 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.24/0.49
% 0.24/0.49 input clause set summed statistics:
% 0.24/0.49 ----------------------------------
% 0.24/0.49 in_clause_count: 4
% 0.24/0.49 in_rule_clause_count: 4
% 0.24/0.49 in_fact_clause_count: 0
% 0.24/0.49 in_answer_clause_count: 0
% 0.24/0.49 in_ground_clause_count: 1
% 0.24/0.49 in_unit_clause_count: 4
% 0.24/0.49 in_horn_clause_count: 4
% 0.24/0.49 in_pos_clause_count: 3
% 0.24/0.49 in_neg_clause_count: 1
% 0.24/0.49 in_poseq_clause_count: 3
% 0.24/0.49 in_negeq_clause_count: 1
% 0.24/0.49 in_unitposeq_clause_count: 3
% 0.24/0.49 in_chain_clause_count: 0
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% 0.24/0.49
% 0.24/0.49 auto guide:
% 0.24/0.49 -----------
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% 37.51/5.29
% 37.51/5.29 **** run 95 fork 6 starts with strategy
% 37.51/5.29 {"max_dseconds":10,"strategy":["unit","prohibit_deep_para","prohibit_unordered_para"],"query_preference":0}
% 41.53/5.77
% 41.53/5.77
% 41.53/5.77 fork 4: search terminated without proof.
% 42.33/5.81
% 42.33/5.81 **** run 101 fork 4 starts with strategy
% 42.33/5.81 {"max_dseconds":10,"strategy":["unit","prohibit_deep_para","prohibit_unordered_para"],"query_preference":1,"weight_select_ratio":20,"depth_penalty":50}
% 43.10/6.04
% 43.10/6.04
% 43.10/6.04 fork 5: search terminated without proof.
% 44.35/6.07
% 44.35/6.07
% 44.35/6.07 fork 3: search terminated without proof.
% 44.35/6.10
% 44.35/6.10 **** run 102 fork 5 starts with strategy
% 44.35/6.10 {"max_dseconds":10,"strategy":["unit","prohibit_deep_para","prohibit_unordered_para"],"query_preference":0,"weight_select_ratio":20,"depth_penalty":50}
% 44.35/6.13
% 44.35/6.13 **** run 100 fork 3 starts with strategy
% 44.35/6.13 {"max_dseconds":10,"strategy":["unit","prohibit_deep_para","prohibit_unordered_para"],"query_preference":0,"weight_select_ratio":20}
% 44.35/6.15
% 44.35/6.15
% 44.35/6.15 fork 1: search terminated without proof.
% 44.35/6.15
% 44.35/6.15
% 44.35/6.15 fork 2: search terminated without proof.
% 45.17/6.18
% 45.17/6.18 **** run 99 fork 2 starts with strategy
% 45.17/6.18 {"max_dseconds":10,"strategy":["unit","prohibit_deep_para","prohibit_unordered_para"],"query_preference":1,"weight_select_ratio":20}
% 45.17/6.19
% 45.17/6.19
% 45.17/6.19 fork 7: search terminated without proof.
% 45.48/6.20
% 45.48/6.20 **** run 106 fork 1 starts with strategy
% 45.48/6.20 {"max_dseconds":10,"strategy":["unit"],"query_preference":1,"weight_select_ratio":20,"depth_penalty":50,"var_weight":1,"repeat_var_weight":1}
% 45.48/6.22
% 45.48/6.22 **** run 104 fork 7 starts with strategy
% 45.48/6.22 {"max_dseconds":10,"strategy":["unit"],"query_preference":1,"weight_select_ratio":20,"rewrite":0}
% 46.28/6.30
% 46.28/6.30
% 46.28/6.30 fork 0: search terminated without proof.
% 46.28/6.35
% 46.28/6.35 **** run 105 fork 0 starts with strategy
% 46.28/6.35 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"weight_select_ratio":2}
% 47.09/6.41
% 47.09/6.41
% 47.09/6.41 fork 6: search terminated without proof.
% 47.09/6.45
% 47.09/6.45 **** run 103 fork 6 starts with strategy
% 47.09/6.45 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"rewrite":0}
% 50.27/6.82
% 50.27/6.82
% 50.27/6.82 fork 4: search terminated without proof.
% 50.27/6.86
% 50.27/6.86 **** run 109 fork 4 starts with strategy
% 50.27/6.86 {"max_dseconds":10,"strategy":["query_focus"],"query_preference":1}
% 52.32/7.12
% 52.32/7.12
% 52.32/7.12 fork 5: search terminated without proof.
% 52.32/7.14
% 52.32/7.14
% 52.32/7.14 fork 3: search terminated without proof.
% 53.12/7.17
% 53.12/7.17 **** run 110 fork 5 starts with strategy
% 53.12/7.17 {"max_dseconds":10,"strategy":["query_focus"],"query_preference":2}
% 53.43/7.20
% 53.43/7.20 **** run 108 fork 3 starts with strategy
% 53.43/7.20 {"max_dseconds":10,"strategy":["query_focus"],"query_preference":0}
% 53.43/7.21
% 53.43/7.21
% 53.43/7.21 fork 2: search terminated without proof.
% 53.43/7.22
% 53.43/7.22
% 53.43/7.22 fork 1: search terminated without proof.
% 53.43/7.24
% 53.43/7.24 **** run 107 fork 2 starts with strategy
% 53.43/7.24 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"weight_select_ratio":20,"depth_penalty":50,"var_weight":1,"repeat_var_weight":1}
% 53.43/7.25
% 53.43/7.25
% 53.43/7.25 fork 7: search terminated without proof.
% 53.43/7.28
% 53.43/7.28 **** run 112 fork 7 starts with strategy
% 53.43/7.28 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_depth":2}
% 53.43/7.28
% 53.43/7.28 **** run 114 fork 1 starts with strategy
% 53.43/7.28 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_depth":6}
% 53.43/7.29
% 53.43/7.29 fork 1: search finished without proof.
% 54.24/7.30
% 54.24/7.30 fork 7: search finished without proof.
% 54.24/7.32
% 54.24/7.32 **** run 120 fork 7 starts with strategy
% 54.24/7.32 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_size":20,"weight_select_ratio":2}
% 54.24/7.34
% 54.24/7.34 **** run 122 fork 1 starts with strategy
% 54.24/7.34 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_size":40}
% 54.24/7.34
% 54.24/7.34 fork 7: search finished without proof.
% 54.24/7.36
% 54.24/7.36 **** run 128 fork 7 starts with strategy
% 54.24/7.36 {"max_dseconds":10,"strategy":["unit"],"var_weight":70,"repeat_var_weight":70,"depth_penalty":100,"query_preference":0}
% 55.08/7.43
% 55.08/7.43
% 55.08/7.43 fork 0: search terminated without proof.
% 55.08/7.46
% 55.08/7.46 **** run 113 fork 0 starts with strategy
% 55.08/7.46 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_depth":4}
% 55.08/7.48
% 55.08/7.48 fork 0: search finished without proof.
% 55.83/7.52
% 55.83/7.52 **** run 121 fork 0 starts with strategy
% 55.83/7.52 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_size":30}
% 55.83/7.54
% 55.83/7.54 fork 0: search finished without proof.
% 55.83/7.58
% 55.83/7.58
% 55.83/7.58 fork 6: search terminated without proof.
% 55.83/7.58
% 55.83/7.58 **** run 129 fork 0 starts with strategy
% 55.83/7.58 {"max_dseconds":10,"strategy":["unit"],"var_weight":70,"repeat_var_weight":70,"query_preference":1}
% 56.66/7.61
% 56.66/7.61 **** run 111 fork 6 starts with strategy
% 56.66/7.61 {"max_dseconds":10,"strategy":["unit"],"query_preference":1,"reverse_clauselist":1}
% 58.24/7.87
% 58.24/7.87
% 58.24/7.87 fork 4: search terminated without proof.
% 59.06/7.92
% 59.06/7.92 **** run 117 fork 4 starts with strategy
% 59.06/7.92 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_size":10}
% 59.06/7.93
% 59.06/7.93 fork 4: search finished without proof.
% 59.06/7.95
% 59.06/7.95 **** run 125 fork 4 starts with strategy
% 59.06/7.95 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_size":30,"depth_penalty":50}
% 59.06/7.97
% 59.06/7.97 fork 4: search finished without proof.
% 59.06/7.99
% 59.06/7.99 **** run 133 fork 4 starts with strategy
% 59.06/7.99 {"max_dseconds":50,"strategy":["unit"],"query_preference":1}
% 61.36/8.22
% 61.36/8.22
% 61.36/8.22 fork 5: search terminated without proof.
% 61.36/8.22
% 61.36/8.22
% 61.36/8.22 fork 3: search terminated without proof.
% 61.36/8.27
% 61.36/8.27
% 61.36/8.27 fork 2: search terminated without proof.
% 61.36/8.29
% 61.36/8.29 **** run 118 fork 5 starts with strategy
% 61.36/8.29 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_size":15}
% 61.36/8.30
% 61.36/8.30 **** run 115 fork 2 starts with strategy
% 61.36/8.30 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_depth":8}
% 61.36/8.30
% 61.36/8.30 **** run 116 fork 3 starts with strategy
% 61.36/8.30 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_depth":10}
% 62.16/8.32
% 62.16/8.32 fork 3: search finished without proof.
% 62.16/8.32
% 62.16/8.32 fork 2: search finished without proof.
% 62.16/8.34
% 62.16/8.34 **** run 123 fork 2 starts with strategy
% 62.16/8.34 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"var_weight":1}
% 62.16/8.36
% 62.16/8.36
% 62.16/8.36 fork 1: search terminated without proof.
% 62.16/8.36
% 62.16/8.36 **** run 124 fork 3 starts with strategy
% 62.16/8.36 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"var_weight":1,"repeat_var_weight":1}
% 62.16/8.39
% 62.16/8.39
% 62.16/8.39 fork 7: search terminated without proof.
% 62.96/8.41
% 62.96/8.41 **** run 130 fork 1 starts with strategy
% 62.96/8.41 {"max_dseconds":10,"strategy":["unit"],"var_weight":70,"repeat_var_weight":70,"query_preference":0,"weight_select_ratio":20}
% 62.96/8.42
% 62.96/8.42 **** run 136 fork 7 starts with strategy
% 62.96/8.42 {"max_dseconds":50,"strategy":["unit"],"query_preference":0,"weight_select_ratio":20,"depth_penalty":100}
% 62.96/8.43
% 62.96/8.43 fork 5: search finished without proof.
% 62.96/8.45
% 62.96/8.45 **** run 126 fork 5 starts with strategy
% 62.96/8.45 {"max_dseconds":10,"strategy":["unit","prohibit_nested_para"],"query_preference":1,"reverse_clauselist":1}
% 64.54/8.60
% 64.54/8.60
% 64.54/8.60 fork 0: search terminated without proof.
% 64.54/8.66
% 64.54/8.66 **** run 137 fork 0 starts with strategy
% 64.54/8.66 {"max_dseconds":50,"strategy":["unit"],"query_preference":0,"var_weight":1,"weight_select_ratio":20,"repeat_var_weight":1,"depth_penalty":100}
% 64.54/8.70
% 64.54/8.70
% 64.54/8.70 fork 6: search terminated without proof.
% 65.32/8.73
% 65.32/8.73 **** run 119 fork 6 starts with strategy
% 65.32/8.73 {"max_dseconds":10,"strategy":["unit"],"query_preference":0,"max_size":20}
% 65.32/8.78
% 65.32/8.78 fork 6: search finished without proof.
% 66.17/8.83
% 66.17/8.83 **** run 127 fork 6 starts with strategy
% 66.17/8.83 {"max_dseconds":10,"strategy":["unit","prohibit_nested_para"],"query_preference":1,"depth_penalty":100}
% 70.10/9.35
% 70.10/9.35
% 70.10/9.35 fork 2: search terminated without proof.
% 70.10/9.38
% 70.10/9.38
% 70.10/9.38 fork 3: search terminated without proof.
% 70.95/9.41
% 70.95/9.41 **** run 131 fork 2 starts with strategy
% 70.95/9.41 {"max_dseconds":10,"strategy":["unit","prohibit_nested_para"],"var_weight":70,"repeat_var_weight":70,"depth_penalty":100}
% 70.95/9.42
% 70.95/9.42
% 70.95/9.42 fork 1: search terminated without proof.
% 70.95/9.44
% 70.95/9.44 **** run 132 fork 3 starts with strategy
% 70.95/9.44 {"max_dseconds":10,"strategy":["unit"],"var_weight":70,"repeat_var_weight":70,"query_preference":0,"max_depth":4}
% 70.95/9.46
% 70.95/9.46 fork 3: search finished without proof.
% 70.95/9.48
% 70.95/9.48
% 70.95/9.48 fork 5: search terminated without proof.
% 70.95/9.49
% 70.95/9.49 **** run 138 fork 1 starts with strategy
% 70.95/9.49 {"max_dseconds":50,"strategy":["unit"],"query_preference":1,"weight_select_ratio":20}
% 71.69/9.50
% 71.69/9.50 **** run 140 fork 3 starts with strategy
% 71.69/9.50 {"max_dseconds":50,"strategy":["unit"],"query_preference":1,"weight_select_ratio":20,"depth_penalty":50}
% 71.69/9.51
% 71.69/9.51 **** run 134 fork 5 starts with strategy
% 71.69/9.51 {"max_dseconds":50,"strategy":["unit"],"query_preference":0}
% 74.11/9.87
% 74.11/9.87
% 74.11/9.87 fork 6: search terminated without proof.
% 74.89/9.93
% 74.89/9.93 **** run 135 fork 6 starts with strategy
% 74.89/9.93 {"max_dseconds":50,"strategy":["unit"],"query_preference":0,"var_weight":1,"weight_select_ratio":100,"repeat_var_weight":1}
% 79.65/10.52
% 79.65/10.52
% 79.65/10.52 fork 2: search terminated without proof.
% 79.65/10.55
% 79.65/10.55 **** run 139 fork 2 starts with strategy
% 79.65/10.55 {"max_dseconds":50,"strategy":["unit"],"query_preference":0,"weight_select_ratio":20}
% 95.70/12.63
% 95.70/12.63
% 95.70/12.63 result: proof found
% 95.70/12.63 for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 95.70/12.63 by run 133 fork 4 strategy {"max_dseconds":50,"strategy":["unit"],"query_preference":1}
% 95.70/12.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 95.70/12.63
% 95.70/12.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 95.70/12.64
% 95.70/12.64 run 133 fork 4 statistics:
% 95.70/12.64 ----------------------------------
% 95.70/12.64 this run seconds: 3.880373
% 95.70/12.64 total seconds: 11.381353
% 95.70/12.64 stat_given_used: 1595
% 95.70/12.64 stat_given_used_at_endgame: 0
% 95.70/12.64 stat_given_candidates: 2223
% 95.70/12.64 stat_given_candidates_at_endgame: 0
% 95.70/12.64 stat_given_candidates_h: 0
% 95.70/12.64 stat_binres_derived_cl: 1
% 95.70/12.64 stat_binres_derived_cl_h: 0
% 95.70/12.64 stat_factor_derived_cl: 0
% 95.70/12.64 stat_para_derived_cl: 498321
% 95.70/12.64 stat_tautologies_discarded: 0
% 95.70/12.64 stat_forward_subsumed: 150389
% 95.70/12.64 stat_derived_cut: 0
% 95.70/12.64 stat_derived_rewritten: 1014
% 95.70/12.64 stat_weight_discarded_building: 0
% 95.70/12.64 stat_weight_discarded_cl: 80160
% 95.70/12.64 stat_internlimit_discarded_cl: 0
% 95.70/12.64 stat_simplified: 1014 simplified 0 derived 0 given
% 95.70/12.64 stat_kept_cl: 210498
% 95.70/12.64 stat_built_cl: 294862
% 95.70/12.64 stat_hyperres_partial_cl: 0
% 95.70/12.64 stat_made_rewriters: 1594
% 95.70/12.64 stat_backward_subsumed: 0
% 95.70/12.64 stat_propagated_subsumed: 0
% 95.70/12.64 stat_clsubs_attempted: 241175
% 95.70/12.64 stat_clsubs_fact_groundunit_found: 0
% 95.70/12.64 stat_clsubs_rule_groundunit_found: 1
% 95.70/12.64 stat_clsubs_top_meta_attempted: 1269621
% 95.70/12.64 stat_clsubs_top_meta_failed: 1028446
% 95.70/12.64 stat_clsubs_top_meta_nonpref_attempted: 1269621
% 95.70/12.64 stat_clsubs_top_meta_nonpref_succeeded: 444281
% 95.70/12.64 stat_clsubs_top_meta_pref_attempted: 444281
% 95.70/12.64 stat_clsubs_top_meta_pref1_succeeded: 444281
% 95.70/12.64 stat_clsubs_top_meta_pref2_succeeded: 241175
% 95.70/12.64 stat_clsubs_top_meta_pref3_succeeded: 241175
% 95.70/12.64 stat_clsubs_top_meta_pref_succeeded: 241175
% 95.70/12.64 stat_clsubs_meta_attempted: 241175
% 95.70/12.64 stat_clsubs_meta_failed: 0
% 95.70/12.64 stat_clsubs_predsymbs_attempted: 0
% 95.70/12.64 stat_clsubs_unit_attempted: 241175
% 95.70/12.64 stat_clsubs_full_attempted: 0
% 95.70/12.64 stat_forwardsubs_attempted: 441047
% 95.70/12.64 stat_lit_hash_added: 210503
% 95.70/12.64 stat_lit_hash_computed: 653194
% 95.70/12.64 stat_lit_hash_match_found: 150436
% 95.70/12.64 stat_lit_hash_match_miss: 583927
% 95.70/12.64 stat_lit_hash_cut_ok: 0
% 95.70/12.64 stat_lit_strong_cut_ok: 0
% 95.70/12.64 stat_lit_hash_subsume_ok: 150389
% 95.70/12.64 clqueue els 10000000 used 1
% 95.70/12.64 clactive els 10000000 used 1596
% 95.70/12.64 clactivesubsume els 10000000 used 9565
% 95.70/12.64 queue_termbuf els 200000000 used 41119699
% 95.70/12.64 hyper_termbuf els 100000000 used 1
% 95.70/12.64 active_termbuf els 100000000 used 178719
% 95.70/12.64 varstack els 5000 last used 1
% 95.70/12.64 given_termbuf els 10000000 last used 27
% 95.70/12.64 simplified_termbuf els 10000000 last used 1
% 95.70/12.64 derived_termbuf els 10000000 last used 3
% 95.70/12.64 wr_mallocs: 198830
% 95.70/12.64 wr_callocs: 19
% 95.70/12.64 wr_reallocs: 39253
% 95.70/12.64 wr_frees: 2
% 95.70/12.64 wr_malloc_bytes: 4171568996
% 95.70/12.64 wr_calloc_bytes: 96065504
% 95.70/12.64 wr_realloc_bytes: 7726560
% 95.70/12.64 wr_realloc_freebytes: 0
% 95.70/12.64 ----------------------------------
%------------------------------------------------------------------------------