%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL897+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.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 : Fri Sep 25 02:08:38 PM UTC 2026
% Result : Theorem 31.08s 5.86s
% Output : CNFRefutation 31.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 17
% Syntax : Number of formulae : 81 ( 81 unt; 9 def)
% Number of atoms : 182 ( 80 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
fof(f2,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(f3,axiom,
! [X0] : '+'(X0,'0') = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(f4,axiom,
! [X0] : '==>'(X0,X0) = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(f5,axiom,
! [X0] : '==>'(X0,'0') = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
fof(f7,axiom,
! [X0,X1,X2] : '==>'('+'(X0,X1),X2) = '==>'(X0,'==>'(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(f8,axiom,
! [X0,X1] : '+'(X0,'==>'(X0,X1)) = '+'(X1,'==>'(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(f9,conjecture,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_09) ).
fof(f10,negated_conjecture,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(flattening,[],[f10]) ).
fof(f12,plain,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(cnf_transformation,[],[f11]) ).
fof(f13,plain,
! [X0,X1] : '+'(X0,'==>'(X0,X1)) = '+'(X1,'==>'(X1,X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f14,plain,
! [X2,X0,X1] : '==>'('+'(X0,X1),X2) = '==>'(X0,'==>'(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X2,X0,X1] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
fof(f17,plain,
! [X0] : '+'(X0,'0') = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X0] : '0' = '==>'(X0,'0'),
inference(cnf_transformation,[],[f5]) ).
fof(f20,plain,
! [X0] : '0' = '==>'(X0,X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_49,negated_conjecture,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(cnf_transformation,[],[f12]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : '+'(X0,'==>'(X0,X1)) = '+'(X1,'==>'(X1,X0)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : '==>'('+'(X0,X1),X2) = '==>'(X0,'==>'(X1,X2)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[],[f15]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_54,plain,
! [X0: $i] : '+'(X0,'0') = X0,
inference(cnf_transformation,[],[f17]) ).
tcf(c_56,plain,
! [X0: $i] : '==>'(X0,'0') = '0',
inference(cnf_transformation,[],[f19]) ).
tcf(c_57,plain,
! [X0: $i] : '==>'(X0,X0) = '0',
inference(cnf_transformation,[],[f20]) ).
tcf(c_66,negated_conjecture,
'+'(a,'+'('==>'(a,b),'==>'('+'(a,'==>'(a,b)),c))) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(theory_normalisation,[status(thm)],[c_49,c_53,c_52]) ).
tcf(c_85,plain,
'+'(a,'+'('==>'(a,b),'==>'(a,'==>'('==>'(a,b),c)))) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(demodulation,[status(thm)],[c_66,c_51]) ).
tcf(c_90,definition,
iPr_def_10 = '==>'(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_91,definition,
iPr_def_11 = '==>'(iPr_def_10,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_92,definition,
iPr_def_12 = '==>'(a,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_93,definition,
iPr_def_13 = '+'(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_94,definition,
iPr_def_14 = '+'(a,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_95,definition,
iPr_def_15 = '==>'(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_96,definition,
iPr_def_16 = '+'(b,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_97,definition,
iPr_def_17 = '==>'(a,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_98,definition,
iPr_def_18 = '+'(a,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_99,plain,
iPr_def_14 != iPr_def_18,
inference(demodulation,[status(thm)],[c_85,c_95,c_96,c_97,c_98,c_91,c_92,c_90,c_93,c_94]) ).
tcf(c_163,plain,
'+'(iPr_def_13,a) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_94,c_53,c_52]) ).
tcf(c_164,plain,
'+'(iPr_def_15,b) = iPr_def_16,
inference(theory_normalisation,[status(thm)],[c_96,c_53,c_52]) ).
tcf(c_165,plain,
'+'(iPr_def_17,a) = iPr_def_18,
inference(theory_normalisation,[status(thm)],[c_98,c_53,c_52]) ).
tcf(c_166,plain,
! [X0: $i] : '+'('0',X0) = X0,
inference(superposition,[status(thm)],[c_54,c_52]) ).
tcf(c_184,plain,
'+'(iPr_def_16,'==>'(iPr_def_16,a)) = '+'(a,iPr_def_17),
inference(superposition,[status(thm)],[c_97,c_50]) ).
tcf(c_188,plain,
'+'(iPr_def_16,'==>'(iPr_def_16,a)) = '+'(iPr_def_17,a),
inference(theory_normalisation,[status(thm)],[c_184,c_53,c_52]) ).
tcf(c_189,plain,
'+'(iPr_def_16,'==>'(iPr_def_16,a)) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_188,c_165]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i] : '==>'('+'(X0,'==>'(X0,X1)),X2) = '==>'(X1,'==>'('==>'(X1,X0),X2)),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i] : '==>'('+'(X0,X1),X2) = '==>'(X1,'==>'(X0,X2)),
inference(superposition,[status(thm)],[c_52,c_51]) ).
tcf(c_206,plain,
! [X0: $i] : '==>'(iPr_def_15,'==>'(b,X0)) = '==>'(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_164,c_51]) ).
tcf(c_207,plain,
! [X0: $i] : '==>'(iPr_def_17,'==>'(a,X0)) = '==>'(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_165,c_51]) ).
tcf(c_209,plain,
! [X0: $i] : '==>'(iPr_def_16,'==>'('==>'(iPr_def_16,a),X0)) = '==>'(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_189,c_51]) ).
tcf(c_282,plain,
'==>'(iPr_def_15,iPr_def_15) = '==>'(iPr_def_16,c),
inference(superposition,[status(thm)],[c_95,c_206]) ).
tcf(c_284,plain,
'==>'(iPr_def_15,'0') = '==>'(iPr_def_16,b),
inference(superposition,[status(thm)],[c_57,c_206]) ).
tcf(c_285,plain,
'==>'(iPr_def_16,c) = '0',
inference(demodulation,[status(thm)],[c_282,c_57]) ).
tcf(c_286,plain,
'==>'(iPr_def_16,b) = '0',
inference(demodulation,[status(thm)],[c_284,c_56]) ).
tcf(c_288,plain,
'==>'(iPr_def_17,iPr_def_10) = '==>'(iPr_def_18,b),
inference(superposition,[status(thm)],[c_90,c_207]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i,X2: $i] : '==>'('==>'(X0,X1),'==>'(X0,X2)) = '==>'(X1,'==>'('==>'(X1,X0),X2)),
inference(demodulation,[status(thm)],[c_198,c_200]) ).
tcf(c_320,plain,
! [X0: $i] : '==>'(X0,'==>'('==>'(X0,b),c)) = '==>'('==>'(b,X0),iPr_def_15),
inference(superposition,[status(thm)],[c_95,c_297]) ).
tcf(c_327,plain,
! [X0: $i] : '==>'(X0,'==>'('==>'(X0,a),iPr_def_16)) = '==>'('==>'(a,X0),iPr_def_17),
inference(superposition,[status(thm)],[c_97,c_297]) ).
tcf(c_588,plain,
! [X0: $i,X1: $i,X2: $i] : '==>'(X0,'==>'(X1,X2)) = '==>'(X1,'==>'(X0,X2)),
inference(superposition,[status(thm)],[c_200,c_51]) ).
tcf(c_2299,plain,
! [X0: $i] : '==>'(iPr_def_16,'==>'(X0,c)) = '==>'(X0,'0'),
inference(superposition,[status(thm)],[c_285,c_588]) ).
tcf(c_2300,plain,
! [X0: $i] : '==>'(iPr_def_16,'==>'(X0,b)) = '==>'(X0,'0'),
inference(superposition,[status(thm)],[c_286,c_588]) ).
tcf(c_2418,plain,
! [X0: $i] : '==>'(iPr_def_16,'==>'(X0,b)) = '0',
inference(light_normalisation,[status(thm)],[c_2300,c_56]) ).
tcf(c_2419,plain,
! [X0: $i] : '==>'(iPr_def_16,'==>'(X0,c)) = '0',
inference(light_normalisation,[status(thm)],[c_2299,c_56]) ).
tcf(c_2598,plain,
'==>'(iPr_def_18,b) = '0',
inference(superposition,[status(thm)],[c_2418,c_209]) ).
tcf(c_2602,plain,
'==>'(iPr_def_17,iPr_def_10) = '0',
inference(demodulation,[status(thm)],[c_288,c_2598]) ).
tcf(c_2638,plain,
'+'(iPr_def_10,'==>'(iPr_def_10,iPr_def_17)) = '+'(iPr_def_17,'0'),
inference(superposition,[status(thm)],[c_2602,c_50]) ).
tcf(c_5183,plain,
'+'(iPr_def_10,'==>'(iPr_def_10,iPr_def_17)) = iPr_def_17,
inference(demodulation,[status(thm)],[c_2638,c_54]) ).
tcf(c_11172,plain,
'==>'('==>'(b,a),iPr_def_15) = '==>'(a,'==>'(iPr_def_10,c)),
inference(superposition,[status(thm)],[c_90,c_320]) ).
tcf(c_11209,plain,
'==>'('==>'(b,iPr_def_16),iPr_def_15) = '0',
inference(superposition,[status(thm)],[c_320,c_2419]) ).
tcf(c_11222,plain,
'==>'('==>'(b,a),iPr_def_15) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_11172,c_91,c_92]) ).
tcf(c_11403,plain,
'+'(iPr_def_15,'==>'(iPr_def_15,'==>'(b,iPr_def_16))) = '+'('==>'(b,iPr_def_16),'0'),
inference(superposition,[status(thm)],[c_11209,c_50]) ).
tcf(c_11421,plain,
'+'(iPr_def_15,'==>'(iPr_def_15,'==>'(b,iPr_def_16))) = '+'('0','==>'(b,iPr_def_16)),
inference(theory_normalisation,[status(thm)],[c_11403,c_53,c_52]) ).
tcf(c_96515,plain,
'==>'(b,iPr_def_16) = iPr_def_15,
inference(demodulation,[status(thm)],[c_11421,c_54,c_57,c_166,c_206]) ).
tcf(c_96544,plain,
! [X0: $i] : '==>'(b,'==>'(X0,iPr_def_16)) = '==>'(X0,iPr_def_15),
inference(superposition,[status(thm)],[c_96515,c_588]) ).
tcf(c_98272,plain,
'==>'('==>'(a,b),iPr_def_17) = '==>'('==>'(b,a),iPr_def_15),
inference(superposition,[status(thm)],[c_96544,c_327]) ).
tcf(c_98285,plain,
'==>'(iPr_def_10,iPr_def_17) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_98272,c_90,c_11222]) ).
tcf(c_98304,plain,
'+'(iPr_def_10,iPr_def_12) = iPr_def_17,
inference(demodulation,[status(thm)],[c_5183,c_98285]) ).
tcf(c_98305,plain,
iPr_def_13 = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_98304,c_93]) ).
tcf(c_98449,plain,
'+'(iPr_def_13,a) = iPr_def_18,
inference(demodulation,[status(thm)],[c_165,c_98305]) ).
tcf(c_98451,plain,
iPr_def_14 = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_98449,c_163]) ).
tcf(c_98452,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_98451,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL897+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 00:37:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 31.08/5.86 % SZS status Started for theBenchmark.p
% 31.08/5.86 % SZS status Theorem for theBenchmark.p
% 31.08/5.86
% 31.08/5.86 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.08/5.86
% 31.08/5.86 % ------ iProver source info
% 31.08/5.86
% 31.08/5.86 % git: date: 2026-07-19 20:42:38 +0200
% 31.08/5.86 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.08/5.86 % git: non_committed_changes: false
% 31.08/5.86
% 31.08/5.86 % ------ Parsing...
% 31.08/5.86 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 31.08/5.86 %
% 31.08/5.86
% 31.08/5.86 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 31.08/5.86
% 31.08/5.86 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 31.08/5.86 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 31.08/5.86
% 31.08/5.86 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 31.08/5.86 % ------ Proving...
% 31.08/5.86 % ------ Problem Properties
% 31.08/5.86
% 31.08/5.86 %
% 31.08/5.86 % clauses 18
% 31.08/5.86 % conjectures 0
% 31.08/5.86 % EPR 1
% 31.08/5.86 % Horn 18
% 31.08/5.86 % unary 18
% 31.08/5.86 % binary 0
% 31.08/5.86 % lits 18
% 31.08/5.86 % lits eq 18
% 31.08/5.86 % fd_pure 0
% 31.08/5.86 % fd_pseudo 0
% 31.08/5.86 % fd_cond 0
% 31.08/5.86 % fd_pseudo_cond 0
% 31.08/5.86 % AC symbols 1
% 31.08/5.86
% 31.08/5.86 % ------ Schedule UEQ
% 31.08/5.86
% 31.08/5.86 % ------ Option_UEQ Time Limit: 10.
% 31.08/5.86
% 31.08/5.86
% 31.08/5.86 % ------
% 31.08/5.86 % Current options:
% 31.08/5.86 % ------
% 31.08/5.86
% 31.08/5.86
% 31.08/5.86 %
% 31.08/5.86
% 31.08/5.86 % ------ Proving...
% 31.08/5.86 %
% 31.08/5.86
% 31.08/5.86 % SZS status Theorem for theBenchmark.p
% 31.08/5.86
% 31.08/5.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.08/5.86
% 31.08/5.86
%------------------------------------------------------------------------------