%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL156-1 : 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 : n017.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 02:05:47 PM UTC 2026
% Result : Unsatisfiable 2.04s 6.40s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?; 32 :)
% 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] : or(X0,X1) = implies(not(X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',or_definition) ).
fof(f9,axiom,
! [X0,X1] : or(X0,X1) = or(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',or_commutativity) ).
fof(f15,axiom,
! [X0,X1] : and_star(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',and_star_definition) ).
fof(f16,plain,
! [X0,X1] : not(or(not(X0),not(X1))) = and_star(X0,X1),
inference(reorient_equations,[],[f15]) ).
fof(f19,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',false_definition) ).
fof(f20,negated_conjecture,
and_star(x,truth) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
fof(f21,plain,
x != and_star(x,truth),
inference(reorient_equations,[],[f20]) ).
fof(f24,plain,
! [X0,X1] : and_star(X0,X1) = not(implies(not(not(X0)),not(X1))),
inference(definition_unfolding,[],[f16,f7]) ).
fof(f26,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(definition_unfolding,[],[f9,f7,f7]) ).
fof(f32,plain,
x != not(implies(not(not(x)),not(truth))),
inference(definition_unfolding,[],[f21,f24]) ).
tcf(c_66,plain,
! [X0: $i] : implies(truth,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,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_68,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(cnf_transformation,[],[f6]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = implies(not(X1),X0),
inference(cnf_transformation,[],[f26]) ).
tcf(c_77,plain,
not(truth) = falsehood,
inference(cnf_transformation,[],[f19]) ).
tcf(c_78,negated_conjecture,
not(implies(not(not(x)),not(truth))) != x,
inference(cnf_transformation,[],[f32]) ).
tcf(c_110,plain,
not(implies(not(not(x)),falsehood)) != x,
inference(light_normalisation,[status(thm)],[c_78,c_77]) ).
tcf(c_111,plain,
not(implies(not(falsehood),not(x))) != x,
inference(demodulation,[status(thm)],[c_110,c_71]) ).
tcf(c_185,plain,
! [X0: $i] : implies(not(X0),truth) = implies(falsehood,X0),
inference(superposition,[status(thm)],[c_77,c_71]) ).
tcf(c_197,plain,
! [X0: $i] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[status(thm)],[c_66,c_68]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] : implies(implies(X0,not(X1)),not(X1)) = implies(implies(not(X0),X1),X0),
inference(superposition,[status(thm)],[c_71,c_68]) ).
tcf(c_207,plain,
! [X0: $i] : implies(not(X0),not(X0)) = implies(implies(falsehood,X0),truth),
inference(superposition,[status(thm)],[c_185,c_197]) ).
tcf(c_223,plain,
! [X0: $i] : implies(implies(not(X0),not(truth)),X0) = truth,
inference(superposition,[status(thm)],[c_66,c_69]) ).
tcf(c_232,plain,
! [X0: $i] : implies(implies(not(X0),falsehood),X0) = truth,
inference(light_normalisation,[status(thm)],[c_223,c_77]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i] : implies(implies(truth,X0),implies(implies(X0,X1),X1)) = truth,
inference(superposition,[status(thm)],[c_66,c_67]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(light_normalisation,[status(thm)],[c_300,c_66]) ).
tcf(c_696,plain,
! [X0: $i] : implies(implies(not(falsehood),X0),X0) = truth,
inference(superposition,[status(thm)],[c_71,c_232]) ).
tcf(c_697,plain,
implies(implies(falsehood,falsehood),truth) = truth,
inference(superposition,[status(thm)],[c_77,c_232]) ).
tcf(c_780,plain,
implies(not(falsehood),not(falsehood)) = truth,
inference(demodulation,[status(thm)],[c_697,c_207]) ).
tcf(c_810,plain,
implies(truth,not(falsehood)) = truth,
inference(superposition,[status(thm)],[c_780,c_696]) ).
tcf(c_837,plain,
not(falsehood) = truth,
inference(demodulation,[status(thm)],[c_810,c_66]) ).
tcf(c_838,plain,
! [X0: $i] : implies(implies(truth,X0),X0) = truth,
inference(demodulation,[status(thm)],[c_696,c_837]) ).
tcf(c_840,plain,
not(implies(truth,not(x))) != x,
inference(demodulation,[status(thm)],[c_111,c_837]) ).
tcf(c_841,plain,
! [X0: $i] : implies(X0,X0) = truth,
inference(light_normalisation,[status(thm)],[c_838,c_66]) ).
tcf(c_842,plain,
! [X0: $i] : implies(implies(X0,truth),truth) = truth,
inference(demodulation,[status(thm)],[c_197,c_841]) ).
tcf(c_857,plain,
! [X0: $i] : implies(not(X0),falsehood) = implies(truth,X0),
inference(superposition,[status(thm)],[c_837,c_71]) ).
tcf(c_859,plain,
! [X0: $i] : implies(not(X0),falsehood) = X0,
inference(light_normalisation,[status(thm)],[c_857,c_66]) ).
tcf(c_886,plain,
not(not(x)) != x,
inference(demodulation,[status(thm)],[c_840,c_66]) ).
tcf(c_1057,plain,
! [X0: $i] : implies(X0,truth) = truth,
inference(superposition,[status(thm)],[c_842,c_318]) ).
tcf(c_1187,plain,
! [X0: $i] : implies(implies(X0,not(truth)),not(truth)) = implies(truth,X0),
inference(superposition,[status(thm)],[c_1057,c_198]) ).
tcf(c_1205,plain,
! [X0: $i] : implies(implies(X0,falsehood),falsehood) = X0,
inference(light_normalisation,[status(thm)],[c_1187,c_77,c_66]) ).
tcf(c_1251,plain,
! [X0: $i] : implies(X0,falsehood) = not(X0),
inference(superposition,[status(thm)],[c_859,c_1205]) ).
tcf(c_1266,plain,
! [X0: $i] : not(not(X0)) = X0,
inference(demodulation,[status(thm)],[c_859,c_1251]) ).
tcf(c_1267,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_886,c_1266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL156-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.59 % Computer : n017.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.59 % DateTime : Wed Sep 23 22:01:37 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.60 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.63 Running UEQ theorem proving
% 0.16/5.63 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
% 0.16/5.64
% 0.16/5.64 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.64
% 0.16/5.64 % Detected problem language: tptp
% 0.16/5.65 % Proving...
% 2.04/6.40 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.04/6.40 % SZS status Started for theBenchmark.p
% 2.04/6.40 % SZS status Unsatisfiable for theBenchmark.p
% 2.04/6.40
% 2.04/6.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.04/6.40
% 2.04/6.40 % ------ iProver source info
% 2.04/6.40
% 2.04/6.40 % git: date: 2026-07-19 20:42:38 +0200
% 2.04/6.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.04/6.40 % git: non_committed_changes: false
% 2.04/6.40
% 2.04/6.40 % ------ Parsing...% successful
% 2.04/6.40
% 2.04/6.40
% 2.04/6.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.04/6.40
% 2.04/6.40 % ------ Preprocessing... sup_sim: 2 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.04/6.40
% 2.04/6.40 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.04/6.40
% 2.04/6.40 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.04/6.40 % ------ Proving...
% 2.04/6.40 % ------ Problem Properties
% 2.04/6.40
% 2.04/6.40 %
% 2.04/6.40 % clauses 10
% 2.04/6.40 % conjectures 0
% 2.04/6.40 % EPR 0
% 2.04/6.40 % Horn 10
% 2.04/6.40 % unary 10
% 2.04/6.40 % binary 0
% 2.04/6.40 % lits 10
% 2.04/6.40 % lits eq 10
% 2.04/6.40 % fd_pure 0
% 2.04/6.40 % fd_pseudo 0
% 2.04/6.40 % fd_cond 0
% 2.04/6.40 % fd_pseudo_cond 0
% 2.04/6.40 % AC symbols 0
% 2.04/6.40
% 2.04/6.40 % ------ Input Options Time Limit: Unbounded
% 2.04/6.40
% 2.04/6.40
% 2.04/6.40 % ------
% 2.04/6.40 % Current options:
% 2.04/6.40 % ------
% 2.04/6.40
% 2.04/6.40
% 2.04/6.40 %
% 2.04/6.40
% 2.04/6.40 % ------ Proving...
% 2.04/6.40 %
% 2.04/6.40
% 2.04/6.40 % SZS status Unsatisfiable for theBenchmark.p
% 2.04/6.40
% 2.04/6.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.04/6.40
% 2.04/6.40
%------------------------------------------------------------------------------