%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 02:05:46 PM UTC 2026
% Result : Unsatisfiable 4.41s 6.31s
% Output : CNFRefutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 57 unt; 6 def)
% Number of atoms : 77 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 72 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
fof(f5,axiom,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_4) ).
fof(f6,plain,
! [X0,X1] : truth = implies(implies(not(X0),not(X1)),implies(X1,X0)),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0,X1] : big_V(X0,X1) = implies(implies(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-1.ax',big_V_definition) ).
fof(f8,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = big_V(X0,X1),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0,X1] : big_hat(X0,X1) = not(big_V(not(X0),not(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-1.ax',big_hat_definition) ).
fof(f14,negated_conjecture,
not(big_hat(x,y)) != big_V(not(x),not(y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
fof(f15,plain,
! [X0,X1] : big_hat(X0,X1) = not(implies(implies(not(X0),not(X1)),not(X1))),
inference(definition_unfolding,[],[f9,f8]) ).
fof(f16,plain,
implies(implies(not(x),not(y)),not(y)) != not(not(implies(implies(not(x),not(y)),not(y)))),
inference(definition_unfolding,[],[f14,f15,f8]) ).
tcf(c_58,negated_conjecture,
not(not(implies(implies(not(x),not(y)),not(y)))) != implies(implies(not(x),not(y)),not(y)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(cnf_transformation,[],[f6]) ).
tcf(c_61,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_62,plain,
! [X0: $i] : implies(truth,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_77,plain,
not(not(implies(implies(not(y),not(x)),not(x)))) != implies(implies(not(y),not(x)),not(x)),
inference(demodulation,[status(thm)],[c_58,c_59]) ).
tcf(c_82,definition,
iPr_def_10 = not(y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_83,definition,
iPr_def_11 = not(x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_84,definition,
iPr_def_12 = implies(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_85,definition,
iPr_def_13 = implies(iPr_def_12,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_86,definition,
iPr_def_14 = not(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_87,definition,
iPr_def_15 = not(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_88,plain,
iPr_def_15 != iPr_def_13,
inference(demodulation,[status(thm)],[c_77,c_83,c_82,c_84,c_85,c_86,c_87]) ).
tcf(c_138,plain,
! [X0: $i] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[status(thm)],[c_62,c_59]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i,X2: $i] : implies(truth,implies(implies(implies(X0,X1),X2),implies(implies(not(X1),not(X0)),X2))) = truth,
inference(superposition,[status(thm)],[c_60,c_61]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,implies(not(X1),not(X2))),implies(truth,implies(X0,implies(X2,X1)))) = truth,
inference(superposition,[status(thm)],[c_60,c_61]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] : implies(implies(truth,X0),implies(implies(X0,X1),X1)) = truth,
inference(superposition,[status(thm)],[c_62,c_61]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(light_normalisation,[status(thm)],[c_172,c_62]) ).
tcf(c_314,plain,
! [X0: $i] : implies(X0,implies(X0,X0)) = truth,
inference(superposition,[status(thm)],[c_138,c_185]) ).
tcf(c_345,plain,
! [X0: $i] : implies(implies(truth,X0),X0) = truth,
inference(superposition,[status(thm)],[c_185,c_62]) ).
tcf(c_351,plain,
! [X0: $i] : implies(X0,X0) = truth,
inference(light_normalisation,[status(thm)],[c_345,c_62]) ).
tcf(c_379,plain,
! [X0: $i] : implies(X0,truth) = truth,
inference(light_normalisation,[status(thm)],[c_314,c_351]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i] : implies(truth,implies(implies(truth,X0),implies(X1,X0))) = truth,
inference(superposition,[status(thm)],[c_379,c_61]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i] : implies(truth,implies(X0,implies(X1,X0))) = truth,
inference(light_normalisation,[status(thm)],[c_389,c_62]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i] : implies(X0,implies(X1,X0)) = truth,
inference(demodulation,[status(thm)],[c_400,c_62]) ).
tcf(c_1498,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(implies(X0,X1),X2),implies(implies(not(X1),not(X0)),X2)) = truth,
inference(demodulation,[status(thm)],[c_159,c_62]) ).
tcf(c_2464,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,implies(not(X1),not(X2))),implies(X0,implies(X2,X1))) = truth,
inference(demodulation,[status(thm)],[c_168,c_62]) ).
tcf(c_2471,plain,
! [X0: $i,X1: $i] : implies(truth,implies(not(X0),implies(X0,X1))) = truth,
inference(superposition,[status(thm)],[c_526,c_2464]) ).
tcf(c_2947,plain,
! [X0: $i,X1: $i] : implies(not(X0),implies(X0,X1)) = truth,
inference(demodulation,[status(thm)],[c_2471,c_62]) ).
tcf(c_2953,plain,
! [X0: $i] : implies(not(truth),X0) = truth,
inference(superposition,[status(thm)],[c_62,c_2947]) ).
tcf(c_3106,plain,
! [X0: $i] : implies(implies(X0,not(truth)),not(truth)) = implies(truth,X0),
inference(superposition,[status(thm)],[c_2953,c_59]) ).
tcf(c_3145,plain,
! [X0: $i] : implies(implies(X0,not(truth)),not(truth)) = X0,
inference(light_normalisation,[status(thm)],[c_3106,c_62]) ).
tcf(c_4028,plain,
! [X0: $i] : implies(not(implies(X0,not(truth))),X0) = truth,
inference(superposition,[status(thm)],[c_3145,c_2947]) ).
tcf(c_4057,plain,
! [X0: $i] : implies(implies(implies(truth,X0),not(truth)),not(X0)) = truth,
inference(superposition,[status(thm)],[c_3145,c_1498]) ).
tcf(c_4063,plain,
! [X0: $i] : implies(implies(X0,not(truth)),not(X0)) = truth,
inference(light_normalisation,[status(thm)],[c_4057,c_62]) ).
tcf(c_4375,plain,
! [X0: $i] : implies(X0,not(implies(X0,not(truth)))) = truth,
inference(superposition,[status(thm)],[c_3145,c_4063]) ).
tcf(c_5276,plain,
! [X0: $i] : implies(implies(not(implies(X0,not(truth))),X0),X0) = implies(truth,not(implies(X0,not(truth)))),
inference(superposition,[status(thm)],[c_4375,c_59]) ).
tcf(c_5333,plain,
! [X0: $i] : implies(truth,not(implies(X0,not(truth)))) = X0,
inference(light_normalisation,[status(thm)],[c_5276,c_62,c_4028]) ).
tcf(c_5354,plain,
! [X0: $i] : not(implies(X0,not(truth))) = X0,
inference(demodulation,[status(thm)],[c_5333,c_62]) ).
tcf(c_5361,plain,
! [X0: $i] : implies(X0,not(truth)) = not(X0),
inference(superposition,[status(thm)],[c_3145,c_5354]) ).
tcf(c_5388,plain,
! [X0: $i] : not(not(X0)) = X0,
inference(demodulation,[status(thm)],[c_5354,c_5361]) ).
tcf(c_5420,plain,
not(iPr_def_14) = iPr_def_13,
inference(superposition,[status(thm)],[c_86,c_5388]) ).
tcf(c_5442,plain,
iPr_def_13 = iPr_def_15,
inference(demodulation,[status(thm)],[c_87,c_5420]) ).
tcf(c_5452,plain,
iPr_def_13 != iPr_def_13,
inference(demodulation,[status(thm)],[c_88,c_5442]) ).
tcf(c_5453,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_5452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n013.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 22:04:27 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 4.41/6.31 % SZS status Started for theBenchmark.p
% 4.41/6.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.41/6.31
% 4.41/6.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.41/6.31
% 4.41/6.31 % ------ iProver source info
% 4.41/6.31
% 4.41/6.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.41/6.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.41/6.31 % git: non_committed_changes: false
% 4.41/6.31
% 4.41/6.31 % ------ Parsing...% successful
% 4.41/6.31
% 4.41/6.31
% 4.41/6.31 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 4.41/6.31 %
% 4.41/6.31
% 4.41/6.31 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.41/6.31
% 4.41/6.31 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 4.41/6.31 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.41/6.31
% 4.41/6.31 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.41/6.31 % ------ Proving...
% 4.41/6.31 % ------ Problem Properties
% 4.41/6.31
% 4.41/6.31 %
% 4.41/6.31 % clauses 11
% 4.41/6.31 % conjectures 0
% 4.41/6.31 % EPR 1
% 4.41/6.31 % Horn 11
% 4.41/6.31 % unary 11
% 4.41/6.31 % binary 0
% 4.41/6.31 % lits 11
% 4.41/6.31 % lits eq 11
% 4.41/6.31 % fd_pure 0
% 4.41/6.31 % fd_pseudo 0
% 4.41/6.31 % fd_cond 0
% 4.41/6.31 % fd_pseudo_cond 0
% 4.41/6.31 % AC symbols 0
% 4.41/6.31
% 4.41/6.31 % ------ Schedule UEQ
% 4.41/6.31
% 4.41/6.31 % ------ Option_UEQ Time Limit: 10.
% 4.41/6.31
% 4.41/6.31
% 4.41/6.31 % ------
% 4.41/6.31 % Current options:
% 4.41/6.31 % ------
% 4.41/6.31
% 4.41/6.31
% 4.41/6.31 %
% 4.41/6.31
% 4.41/6.31 % ------ Proving...
% 4.41/6.31 %
% 4.41/6.31
% 4.41/6.31 % SZS status Unsatisfiable for theBenchmark.p
% 4.41/6.31
% 4.41/6.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.41/6.31
% 4.41/6.31
%------------------------------------------------------------------------------