%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL138-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 02:05:45 PM UTC 2026
% Result : Unsatisfiable 34.23s 10.52s
% Output : CNFRefutation 34.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 57 unt; 4 def)
% Number of atoms : 99 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 76 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
fof(f2,axiom,
! [X2,X0,X1] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
fof(f3,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
fof(f7,negated_conjecture,
implies(x,implies(y,z)) != implies(y,implies(x,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_lemma) ).
tcf(c_54,plain,
! [X0: $i] : implies(truth,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_58,negated_conjecture,
implies(x,implies(y,z)) != implies(y,implies(x,z)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_76,definition,
iPr_def_10 = implies(y,z),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_77,definition,
iPr_def_11 = implies(x,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_78,definition,
iPr_def_12 = implies(x,z),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_79,definition,
iPr_def_13 = implies(y,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_80,negated_conjecture,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_58,c_78,c_79,c_76,c_77]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_84,plain,
! [X0: $i] : implies(truth,X0) = X0,
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_1727,plain,
! [X0: $i,X1: $i] : implies(implies(truth,X0),implies(implies(X0,X1),X1)) = truth,
inference(superposition,[status(thm)],[c_84,c_83]) ).
tcf(c_1743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : implies(implies(X0,implies(X1,X2)),implies(truth,implies(X0,implies(implies(X2,X3),implies(X1,X3))))) = truth,
inference(superposition,[status(thm)],[c_83,c_83]) ).
tcf(c_1748,plain,
! [X0: $i,X1: $i] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(demodulation,[status(thm)],[c_1727,c_84]) ).
tcf(c_1762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : implies(implies(X0,implies(X1,X2)),implies(X0,implies(implies(X2,X3),implies(X1,X3)))) = truth,
inference(demodulation,[status(thm)],[c_1743,c_84]) ).
tcf(c_27866,plain,
! [X0: $i,X1: $i,X2: $i] : implies(truth,implies(X0,implies(implies(X1,X2),implies(implies(X0,X1),X2)))) = truth,
inference(superposition,[status(thm)],[c_1748,c_1762]) ).
tcf(c_28278,plain,
! [X0: $i,X1: $i,X2: $i] : implies(X0,implies(implies(X1,X2),implies(implies(X0,X1),X2))) = truth,
inference(demodulation,[status(thm)],[c_27866,c_84]) ).
tcf(c_34169,plain,
! [X0: $i] : implies(y,implies(implies(z,X0),implies(iPr_def_10,X0))) = truth,
inference(superposition,[status(thm)],[c_76,c_28278]) ).
tcf(c_34170,plain,
! [X0: $i] : implies(x,implies(implies(z,X0),implies(iPr_def_12,X0))) = truth,
inference(superposition,[status(thm)],[c_78,c_28278]) ).
tcf(c_34176,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X1),implies(implies(truth,X0),X1)) = truth,
inference(superposition,[status(thm)],[c_28278,c_84]) ).
tcf(c_34181,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X1),implies(X0,X1)) = truth,
inference(demodulation,[status(thm)],[c_34176,c_84]) ).
tcf(c_34280,plain,
! [X0: $i] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[status(thm)],[c_84,c_82]) ).
tcf(c_34362,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X0)),implies(X2,X0)) = implies(truth,implies(implies(X0,X1),implies(X2,X1))),
inference(superposition,[status(thm)],[c_83,c_82]) ).
tcf(c_34388,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X0)),implies(X2,X0)) = implies(implies(X0,X1),implies(X2,X1)),
inference(demodulation,[status(thm)],[c_34362,c_84]) ).
tcf(c_34570,plain,
! [X0: $i] : implies(implies(implies(implies(iPr_def_10,X0),implies(x,X0)),iPr_def_11),iPr_def_11) = implies(implies(iPr_def_10,X0),implies(x,X0)),
inference(superposition,[status(thm)],[c_77,c_34388]) ).
tcf(c_34571,plain,
! [X0: $i] : implies(implies(implies(implies(iPr_def_12,X0),implies(y,X0)),iPr_def_13),iPr_def_13) = implies(implies(iPr_def_12,X0),implies(y,X0)),
inference(superposition,[status(thm)],[c_79,c_34388]) ).
tcf(c_34731,plain,
! [X0: $i] : implies(X0,X0) = truth,
inference(superposition,[status(thm)],[c_84,c_34181]) ).
tcf(c_34786,plain,
implies(x,implies(truth,implies(iPr_def_12,z))) = truth,
inference(superposition,[status(thm)],[c_34731,c_34170]) ).
tcf(c_34787,plain,
implies(y,implies(truth,implies(iPr_def_10,z))) = truth,
inference(superposition,[status(thm)],[c_34731,c_34169]) ).
tcf(c_34797,plain,
implies(y,implies(iPr_def_10,z)) = truth,
inference(demodulation,[status(thm)],[c_34787,c_84]) ).
tcf(c_34798,plain,
implies(x,implies(iPr_def_12,z)) = truth,
inference(demodulation,[status(thm)],[c_34786,c_84]) ).
tcf(c_34835,plain,
! [X0: $i] : implies(implies(X0,truth),truth) = truth,
inference(light_normalisation,[status(thm)],[c_34280,c_34731]) ).
tcf(c_34858,plain,
! [X0: $i] : implies(X0,implies(implies(truth,truth),truth)) = truth,
inference(superposition,[status(thm)],[c_34835,c_28278]) ).
tcf(c_34859,plain,
! [X0: $i] : implies(X0,truth) = truth,
inference(demodulation,[status(thm)],[c_34858,c_34835]) ).
tcf(c_34879,plain,
! [X0: $i,X1: $i] : implies(truth,implies(implies(truth,X0),implies(X1,X0))) = truth,
inference(superposition,[status(thm)],[c_34859,c_83]) ).
tcf(c_34903,plain,
! [X0: $i,X1: $i] : implies(X0,implies(X1,X0)) = truth,
inference(demodulation,[status(thm)],[c_34879,c_84]) ).
tcf(c_35037,plain,
! [X0: $i] : implies(truth,implies(implies(implies(iPr_def_10,z),X0),implies(y,X0))) = truth,
inference(superposition,[status(thm)],[c_34797,c_83]) ).
tcf(c_35051,plain,
! [X0: $i] : implies(implies(implies(iPr_def_10,z),X0),implies(y,X0)) = truth,
inference(demodulation,[status(thm)],[c_35037,c_84]) ).
tcf(c_35057,plain,
! [X0: $i] : implies(truth,implies(implies(implies(iPr_def_12,z),X0),implies(x,X0))) = truth,
inference(superposition,[status(thm)],[c_34798,c_83]) ).
tcf(c_35071,plain,
! [X0: $i] : implies(implies(implies(iPr_def_12,z),X0),implies(x,X0)) = truth,
inference(demodulation,[status(thm)],[c_35057,c_84]) ).
tcf(c_35111,plain,
! [X0: $i,X1: $i,X2: $i] : implies(truth,implies(implies(implies(X0,X1),X2),implies(X1,X2))) = truth,
inference(superposition,[status(thm)],[c_34903,c_83]) ).
tcf(c_35143,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(implies(X0,X1),X2),implies(X1,X2)) = truth,
inference(demodulation,[status(thm)],[c_35111,c_84]) ).
tcf(c_37250,plain,
! [X0: $i,X1: $i] : implies(implies(implies(implies(iPr_def_10,X0),implies(x,X0)),X1),implies(iPr_def_11,X1)) = truth,
inference(superposition,[status(thm)],[c_34570,c_35143]) ).
tcf(c_38024,plain,
! [X0: $i,X1: $i] : implies(implies(implies(implies(iPr_def_12,X0),implies(y,X0)),X1),implies(iPr_def_13,X1)) = truth,
inference(superposition,[status(thm)],[c_34571,c_35143]) ).
tcf(c_39203,plain,
implies(truth,implies(iPr_def_11,implies(y,implies(x,z)))) = truth,
inference(superposition,[status(thm)],[c_35051,c_37250]) ).
tcf(c_39210,plain,
implies(iPr_def_11,iPr_def_13) = truth,
inference(demodulation,[status(thm)],[c_39203,c_84,c_78,c_79]) ).
tcf(c_39289,plain,
implies(truth,implies(iPr_def_13,implies(x,implies(y,z)))) = truth,
inference(superposition,[status(thm)],[c_35071,c_38024]) ).
tcf(c_39296,plain,
implies(iPr_def_13,iPr_def_11) = truth,
inference(demodulation,[status(thm)],[c_39289,c_84,c_76,c_77]) ).
tcf(c_39473,plain,
implies(implies(iPr_def_11,iPr_def_13),iPr_def_13) = implies(truth,iPr_def_11),
inference(superposition,[status(thm)],[c_39296,c_82]) ).
tcf(c_39485,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_39473,c_84,c_39210]) ).
tcf(c_39486,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_39485,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL138-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.58 % Computer : n003.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Wed Sep 23 22:05:27 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.62 Running UEQ theorem proving
% 0.15/5.62 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.63
% 0.15/5.63 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.63
% 0.15/5.63 % Detected problem language: tptp
% 0.15/5.64 % Proving...
% 34.23/10.52 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 34.23/10.52 % SZS status Started for theBenchmark.p
% 34.23/10.52 % SZS status Unsatisfiable for theBenchmark.p
% 34.23/10.52
% 34.23/10.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 34.23/10.52
% 34.23/10.52 % ------ iProver source info
% 34.23/10.52
% 34.23/10.52 % git: date: 2026-07-19 20:42:38 +0200
% 34.23/10.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 34.23/10.52 % git: non_committed_changes: false
% 34.23/10.52
% 34.23/10.52 % ------ Parsing...% successful
% 34.23/10.52
% 34.23/10.52
% 34.23/10.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 34.23/10.52
% 34.23/10.52 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 34.23/10.52
% 34.23/10.52 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 34.23/10.52
% 34.23/10.52 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 34.23/10.52 % ------ Proving...
% 34.23/10.52 % ------ Problem Properties
% 34.23/10.52
% 34.23/10.52 %
% 34.23/10.52 % clauses 9
% 34.23/10.52 % conjectures 1
% 34.23/10.52 % EPR 1
% 34.23/10.52 % Horn 9
% 34.23/10.52 % unary 9
% 34.23/10.52 % binary 0
% 34.23/10.52 % lits 9
% 34.23/10.52 % lits eq 9
% 34.23/10.52 % fd_pure 0
% 34.23/10.52 % fd_pseudo 0
% 34.23/10.52 % fd_cond 0
% 34.23/10.52 % fd_pseudo_cond 0
% 34.23/10.52 % AC symbols 0
% 34.23/10.52
% 34.23/10.52 % ------ Input Options Time Limit: Unbounded
% 34.23/10.52
% 34.23/10.52
% 34.23/10.52 % ------
% 34.23/10.52 % Current options:
% 34.23/10.52 % ------
% 34.23/10.52
% 34.23/10.52
% 34.23/10.52 %
% 34.23/10.52
% 34.23/10.52 % ------ Proving...
% 34.23/10.52 %
% 34.23/10.52
% 34.23/10.52 % SZS status Unsatisfiable for theBenchmark.p
% 34.23/10.52
% 34.23/10.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 34.23/10.52
% 34.23/10.52
%------------------------------------------------------------------------------