%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL145-1 : 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 : n008.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 10.99s 2.65s
% Output : CNFRefutation 10.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 17
% Syntax : Number of formulae : 84 ( 84 unt; 10 def)
% Number of atoms : 151 ( 83 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 12 ( 10 usr; 11 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/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(f5,axiom,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL001-1.ax',big_hat_definition) ).
fof(f14,negated_conjecture,
not(big_V(x,y)) != big_hat(not(x),not(y)),
file('/export/starexec/sandbox/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,
not(implies(implies(x,y),y)) != not(implies(implies(not(not(x)),not(not(y))),not(not(y)))),
inference(definition_unfolding,[],[f14,f8,f15]) ).
tcf(c_58,plain,
! [X0: $i] : implies(truth,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_59,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_60,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(cnf_transformation,[],[f6]) ).
tcf(c_64,negated_conjecture,
not(implies(implies(not(not(x)),not(not(y))),not(not(y)))) != not(implies(implies(x,y),y)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_109,plain,
not(implies(implies(not(not(y)),not(not(x))),not(not(x)))) != not(implies(implies(y,x),x)),
inference(demodulation,[status(thm)],[c_64,c_60]) ).
tcf(c_131,definition,
iPr_def_10 = not(y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_132,definition,
iPr_def_11 = not(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_133,definition,
iPr_def_12 = not(x),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_134,definition,
iPr_def_13 = not(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_135,definition,
iPr_def_14 = implies(iPr_def_11,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_136,definition,
iPr_def_15 = implies(iPr_def_14,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_137,definition,
iPr_def_16 = not(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_138,definition,
iPr_def_17 = implies(y,x),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_139,definition,
iPr_def_18 = implies(iPr_def_17,x),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_140,definition,
iPr_def_19 = not(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_141,plain,
iPr_def_16 != iPr_def_19,
inference(demodulation,[status(thm)],[c_109,c_138,c_139,c_140,c_133,c_134,c_131,c_132,c_135,c_136,c_137]) ).
tcf(c_199,plain,
! [X0: $i] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[status(thm)],[c_58,c_60]) ).
tcf(c_220,plain,
! [X0: $i] : implies(implies(not(X0),iPr_def_10),implies(y,X0)) = truth,
inference(superposition,[status(thm)],[c_131,c_61]) ).
tcf(c_226,plain,
! [X0: $i] : implies(implies(not(X0),not(truth)),X0) = truth,
inference(superposition,[status(thm)],[c_58,c_61]) ).
tcf(c_244,plain,
implies(implies(iPr_def_10,not(truth)),y) = truth,
inference(superposition,[status(thm)],[c_131,c_226]) ).
tcf(c_245,plain,
implies(implies(iPr_def_11,not(truth)),iPr_def_10) = truth,
inference(superposition,[status(thm)],[c_132,c_226]) ).
tcf(c_307,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_61,c_59]) ).
tcf(c_320,plain,
! [X0: $i] : implies(implies(X0,implies(iPr_def_10,not(truth))),implies(truth,implies(X0,y))) = truth,
inference(superposition,[status(thm)],[c_244,c_59]) ).
tcf(c_321,plain,
! [X0: $i] : implies(implies(X0,implies(iPr_def_11,not(truth))),implies(truth,implies(X0,iPr_def_10))) = truth,
inference(superposition,[status(thm)],[c_245,c_59]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i] : implies(implies(truth,X0),implies(implies(X0,X1),X1)) = truth,
inference(superposition,[status(thm)],[c_58,c_59]) ).
tcf(c_354,plain,
! [X0: $i,X1: $i] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(light_normalisation,[status(thm)],[c_326,c_58]) ).
tcf(c_442,plain,
! [X0: $i] : implies(X0,implies(X0,X0)) = truth,
inference(superposition,[status(thm)],[c_199,c_354]) ).
tcf(c_481,plain,
! [X0: $i] : implies(implies(truth,X0),X0) = truth,
inference(superposition,[status(thm)],[c_354,c_58]) ).
tcf(c_487,plain,
! [X0: $i] : implies(X0,X0) = truth,
inference(light_normalisation,[status(thm)],[c_481,c_58]) ).
tcf(c_530,plain,
! [X0: $i] : implies(X0,truth) = truth,
inference(light_normalisation,[status(thm)],[c_442,c_487]) ).
tcf(c_542,plain,
! [X0: $i,X1: $i] : implies(truth,implies(implies(truth,X0),implies(X1,X0))) = truth,
inference(superposition,[status(thm)],[c_530,c_59]) ).
tcf(c_553,plain,
! [X0: $i,X1: $i] : implies(truth,implies(X0,implies(X1,X0))) = truth,
inference(light_normalisation,[status(thm)],[c_542,c_58]) ).
tcf(c_699,plain,
! [X0: $i,X1: $i] : implies(X0,implies(X1,X0)) = truth,
inference(demodulation,[status(thm)],[c_553,c_58]) ).
tcf(c_9111,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_307,c_58]) ).
tcf(c_9118,plain,
! [X0: $i,X1: $i] : implies(truth,implies(not(X0),implies(X0,X1))) = truth,
inference(superposition,[status(thm)],[c_699,c_9111]) ).
tcf(c_10104,plain,
! [X0: $i,X1: $i] : implies(not(X0),implies(X0,X1)) = truth,
inference(demodulation,[status(thm)],[c_9118,c_58]) ).
tcf(c_10107,plain,
! [X0: $i] : implies(iPr_def_11,implies(iPr_def_10,X0)) = truth,
inference(superposition,[status(thm)],[c_132,c_10104]) ).
tcf(c_10112,plain,
! [X0: $i] : implies(not(truth),X0) = truth,
inference(superposition,[status(thm)],[c_58,c_10104]) ).
tcf(c_10451,plain,
! [X0: $i] : implies(implies(X0,not(truth)),not(truth)) = implies(truth,X0),
inference(superposition,[status(thm)],[c_10112,c_60]) ).
tcf(c_10544,plain,
! [X0: $i] : implies(implies(X0,not(truth)),not(truth)) = X0,
inference(light_normalisation,[status(thm)],[c_10451,c_58]) ).
tcf(c_11118,plain,
! [X0: $i] : implies(not(implies(X0,not(truth))),X0) = truth,
inference(superposition,[status(thm)],[c_10544,c_10104]) ).
tcf(c_12171,plain,
! [X0: $i] : implies(truth,implies(X0,implies(not(X0),not(truth)))) = truth,
inference(superposition,[status(thm)],[c_11118,c_61]) ).
tcf(c_13649,plain,
! [X0: $i] : implies(implies(X0,implies(iPr_def_10,not(truth))),implies(X0,y)) = truth,
inference(demodulation,[status(thm)],[c_320,c_58]) ).
tcf(c_13659,plain,
implies(truth,implies(iPr_def_11,y)) = truth,
inference(superposition,[status(thm)],[c_10107,c_13649]) ).
tcf(c_13800,plain,
implies(iPr_def_11,y) = truth,
inference(demodulation,[status(thm)],[c_13659,c_58]) ).
tcf(c_14111,plain,
! [X0: $i] : implies(implies(X0,implies(iPr_def_11,not(truth))),implies(X0,iPr_def_10)) = truth,
inference(demodulation,[status(thm)],[c_321,c_58]) ).
tcf(c_14120,plain,
implies(truth,implies(not(iPr_def_11),iPr_def_10)) = truth,
inference(superposition,[status(thm)],[c_10104,c_14111]) ).
tcf(c_14218,plain,
! [X0: $i] : implies(X0,implies(not(X0),not(truth))) = truth,
inference(demodulation,[status(thm)],[c_12171,c_58]) ).
tcf(c_14248,plain,
! [X0: $i] : implies(implies(implies(not(X0),not(truth)),X0),X0) = implies(truth,implies(not(X0),not(truth))),
inference(superposition,[status(thm)],[c_14218,c_60]) ).
tcf(c_14405,plain,
! [X0: $i] : implies(truth,implies(not(X0),not(truth))) = X0,
inference(light_normalisation,[status(thm)],[c_14248,c_58,c_226]) ).
tcf(c_14435,plain,
implies(not(iPr_def_11),iPr_def_10) = truth,
inference(demodulation,[status(thm)],[c_14120,c_58]) ).
tcf(c_14456,plain,
implies(truth,implies(y,iPr_def_11)) = truth,
inference(superposition,[status(thm)],[c_14435,c_220]) ).
tcf(c_14463,plain,
implies(y,iPr_def_11) = truth,
inference(demodulation,[status(thm)],[c_14456,c_58]) ).
tcf(c_14480,plain,
implies(implies(iPr_def_11,y),y) = implies(truth,iPr_def_11),
inference(superposition,[status(thm)],[c_14463,c_60]) ).
tcf(c_14493,plain,
implies(truth,y) = implies(truth,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_14480,c_13800]) ).
tcf(c_14580,plain,
y = iPr_def_11,
inference(demodulation,[status(thm)],[c_14493,c_58]) ).
tcf(c_14623,plain,
implies(iPr_def_11,x) = iPr_def_17,
inference(demodulation,[status(thm)],[c_138,c_14580]) ).
tcf(c_15373,plain,
! [X0: $i] : implies(not(X0),not(truth)) = X0,
inference(demodulation,[status(thm)],[c_14405,c_58]) ).
tcf(c_15379,plain,
implies(iPr_def_12,not(truth)) = x,
inference(superposition,[status(thm)],[c_133,c_15373]) ).
tcf(c_15410,plain,
! [X0: $i] : implies(X0,not(truth)) = not(X0),
inference(superposition,[status(thm)],[c_15373,c_10544]) ).
tcf(c_15452,plain,
! [X0: $i] : not(not(X0)) = X0,
inference(demodulation,[status(thm)],[c_15373,c_15410]) ).
tcf(c_15458,plain,
x = iPr_def_13,
inference(demodulation,[status(thm)],[c_15379,c_134,c_15410]) ).
tcf(c_15463,plain,
implies(iPr_def_11,iPr_def_13) = iPr_def_17,
inference(demodulation,[status(thm)],[c_14623,c_15458]) ).
tcf(c_15504,plain,
implies(iPr_def_17,iPr_def_13) = iPr_def_18,
inference(demodulation,[status(thm)],[c_139,c_15458]) ).
tcf(c_15506,plain,
iPr_def_14 = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_15463,c_135]) ).
tcf(c_15578,plain,
not(iPr_def_16) = iPr_def_15,
inference(superposition,[status(thm)],[c_137,c_15452]) ).
tcf(c_15599,plain,
not(iPr_def_15) = iPr_def_16,
inference(superposition,[status(thm)],[c_15578,c_15452]) ).
tcf(c_15774,plain,
iPr_def_15 = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_15504,c_136,c_15506]) ).
tcf(c_15793,plain,
not(iPr_def_15) = iPr_def_19,
inference(demodulation,[status(thm)],[c_140,c_15774]) ).
tcf(c_15794,plain,
iPr_def_16 = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_15793,c_15599]) ).
tcf(c_15795,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15794,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL145-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 22:05:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 10.99/2.65 % SZS status Started for theBenchmark.p
% 10.99/2.65 % SZS status Unsatisfiable for theBenchmark.p
% 10.99/2.65
% 10.99/2.65 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.99/2.65
% 10.99/2.65 % ------ iProver source info
% 10.99/2.65
% 10.99/2.65 % git: date: 2026-07-19 20:42:38 +0200
% 10.99/2.65 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.99/2.65 % git: non_committed_changes: false
% 10.99/2.65
% 10.99/2.65 % ------ Parsing...% successful
% 10.99/2.65
% 10.99/2.65
% 10.99/2.65 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.99/2.65
% 10.99/2.65 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 10.99/2.65
% 10.99/2.65 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 10.99/2.65 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.99/2.65
% 10.99/2.65 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.99/2.65 % ------ Proving...
% 10.99/2.65 % ------ Problem Properties
% 10.99/2.65
% 10.99/2.65 %
% 10.99/2.65 % clauses 15
% 10.99/2.65 % conjectures 0
% 10.99/2.65 % EPR 1
% 10.99/2.65 % Horn 15
% 10.99/2.65 % unary 15
% 10.99/2.65 % binary 0
% 10.99/2.65 % lits 15
% 10.99/2.65 % lits eq 15
% 10.99/2.65 % fd_pure 0
% 10.99/2.65 % fd_pseudo 0
% 10.99/2.65 % fd_cond 0
% 10.99/2.65 % fd_pseudo_cond 0
% 10.99/2.65 % AC symbols 0
% 10.99/2.65
% 10.99/2.65 % ------ Schedule UEQ
% 10.99/2.65
% 10.99/2.65 % ------ Option_UEQ Time Limit: 10.
% 10.99/2.65
% 10.99/2.65
% 10.99/2.65 % ------
% 10.99/2.65 % Current options:
% 10.99/2.65 % ------
% 10.99/2.65
% 10.99/2.65
% 10.99/2.65 %
% 10.99/2.65
% 10.99/2.65 % ------ Proving...
% 10.99/2.65 %
% 10.99/2.65
% 10.99/2.65 % SZS status Unsatisfiable for theBenchmark.p
% 10.99/2.65
% 10.99/2.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.99/2.65
% 10.99/2.65
%------------------------------------------------------------------------------