%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL159-1 : 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 : n014.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 02:05:48 PM UTC 2026
% Result : Unsatisfiable 3.31s 1.18s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 65 unt; 0 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 13 ( 3 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 74 !; 0 ?; 43 :)
% 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(f10,axiom,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-2.ax',and_definition) ).
fof(f13,axiom,
! [X0,X1] : xor(X0,X1) = or(and(X0,not(X1)),and(not(X0),X1)),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',xor_definition) ).
fof(f14,axiom,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',xor_commutativity) ).
fof(f19,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/Axioms/LCL002-1.ax',false_definition) ).
fof(f20,negated_conjecture,
xor(x,xor(truth,y)) != xor(xor(x,truth),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
fof(f21,plain,
! [X0,X1] : and(X0,X1) = not(implies(not(not(X0)),not(X1))),
inference(definition_unfolding,[],[f10,f7]) ).
fof(f22,plain,
! [X0,X1] : xor(X0,X1) = implies(not(not(implies(not(not(X0)),not(not(X1))))),not(implies(not(not(not(X0))),not(X1)))),
inference(definition_unfolding,[],[f13,f7,f21,f21]) ).
fof(f25,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(definition_unfolding,[],[f9,f7,f7]) ).
fof(f28,plain,
! [X0,X1] : implies(not(not(implies(not(not(X0)),not(not(X1))))),not(implies(not(not(not(X0))),not(X1)))) = implies(not(not(implies(not(not(X1)),not(not(X0))))),not(implies(not(not(not(X1))),not(X0)))),
inference(definition_unfolding,[],[f14,f22,f22]) ).
fof(f31,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))))) != implies(not(not(implies(not(not(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(not(x))),not(truth)))))),not(not(y))))),not(implies(not(not(not(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(not(x))),not(truth))))))),not(y)))),
inference(definition_unfolding,[],[f20,f22,f22,f22,f22]) ).
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,[],[f25]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : implies(not(not(implies(not(not(X0)),not(not(X1))))),not(implies(not(not(not(X0))),not(X1)))) = implies(not(not(implies(not(not(X1)),not(not(X0))))),not(implies(not(not(not(X1))),not(X0)))),
inference(cnf_transformation,[],[f28]) ).
tcf(c_77,plain,
not(truth) = falsehood,
inference(cnf_transformation,[],[f19]) ).
tcf(c_78,negated_conjecture,
implies(not(not(implies(not(not(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(not(x))),not(truth)))))),not(not(y))))),not(implies(not(not(not(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(not(x))),not(truth))))))),not(y)))) != implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(not(truth)),not(not(y))))),not(implies(not(not(not(truth))),not(y)))))))),
inference(cnf_transformation,[],[f31]) ).
tcf(c_110,plain,
implies(not(not(implies(not(not(implies(not(not(implies(not(not(x)),not(falsehood)))),not(implies(not(not(not(x))),falsehood))))),not(not(y))))),not(implies(not(not(not(implies(not(not(implies(not(not(x)),not(falsehood)))),not(implies(not(not(not(x))),falsehood)))))),not(y)))) != implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(falsehood)),not(y)))))))),
inference(light_normalisation,[status(thm)],[c_78,c_77]) ).
tcf(c_111,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(y)),not(falsehood))))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(not(falsehood),not(not(y))))),not(implies(not(not(y)),not(falsehood)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(x)),not(falsehood))))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(not(falsehood),not(not(x))))),not(implies(not(not(x)),not(falsehood)))))))),
inference(demodulation,[status(thm)],[c_110,c_71,c_74]) ).
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_299,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_317,plain,
! [X0: $i,X1: $i] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(light_normalisation,[status(thm)],[c_299,c_66]) ).
tcf(c_664,plain,
! [X0: $i] : implies(implies(not(falsehood),X0),X0) = truth,
inference(superposition,[status(thm)],[c_71,c_232]) ).
tcf(c_665,plain,
implies(implies(falsehood,falsehood),truth) = truth,
inference(superposition,[status(thm)],[c_77,c_232]) ).
tcf(c_699,plain,
implies(not(falsehood),not(falsehood)) = truth,
inference(demodulation,[status(thm)],[c_665,c_207]) ).
tcf(c_777,plain,
implies(truth,not(falsehood)) = truth,
inference(superposition,[status(thm)],[c_699,c_664]) ).
tcf(c_802,plain,
not(falsehood) = truth,
inference(demodulation,[status(thm)],[c_777,c_66]) ).
tcf(c_803,plain,
! [X0: $i] : implies(implies(truth,X0),X0) = truth,
inference(demodulation,[status(thm)],[c_664,c_802]) ).
tcf(c_805,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(not(y)),truth)))))))),not(implies(not(not(not(x))),not(implies(not(not(implies(truth,not(not(y))))),not(implies(not(not(y)),truth))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(not(x)),truth)))))))),not(implies(not(not(not(y))),not(implies(not(not(implies(truth,not(not(x))))),not(implies(not(not(x)),truth))))))),
inference(demodulation,[status(thm)],[c_111,c_802]) ).
tcf(c_806,plain,
! [X0: $i] : implies(X0,X0) = truth,
inference(light_normalisation,[status(thm)],[c_803,c_66]) ).
tcf(c_807,plain,
! [X0: $i] : implies(implies(X0,truth),truth) = truth,
inference(demodulation,[status(thm)],[c_197,c_806]) ).
tcf(c_822,plain,
! [X0: $i] : implies(not(X0),falsehood) = implies(truth,X0),
inference(superposition,[status(thm)],[c_802,c_71]) ).
tcf(c_824,plain,
! [X0: $i] : implies(not(X0),falsehood) = X0,
inference(light_normalisation,[status(thm)],[c_822,c_66]) ).
tcf(c_852,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(not(not(x)))),not(implies(falsehood,not(x))))))))),not(implies(not(not(not(y))),not(implies(not(not(not(not(x)))),not(implies(falsehood,not(x)))))))),
inference(demodulation,[status(thm)],[c_805,c_66,c_185]) ).
tcf(c_920,plain,
! [X0: $i] : implies(implies(falsehood,X0),truth) = truth,
inference(superposition,[status(thm)],[c_185,c_807]) ).
tcf(c_1006,plain,
! [X0: $i] : implies(X0,truth) = truth,
inference(superposition,[status(thm)],[c_807,c_317]) ).
tcf(c_1018,plain,
! [X0: $i] : implies(not(X0),implies(implies(falsehood,X0),truth)) = truth,
inference(superposition,[status(thm)],[c_185,c_317]) ).
tcf(c_1040,plain,
! [X0: $i] : implies(falsehood,X0) = truth,
inference(light_normalisation,[status(thm)],[c_1018,c_185,c_920]) ).
tcf(c_1044,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(not(not(x)))),not(truth))))))),not(implies(not(not(not(y))),not(implies(not(not(not(not(x)))),not(truth)))))),
inference(demodulation,[status(thm)],[c_852,c_1040]) ).
tcf(c_1045,plain,
implies(not(not(implies(not(not(x)),not(not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y))))))))),not(implies(not(not(not(x))),not(implies(not(not(not(not(y)))),not(implies(falsehood,not(y)))))))) != implies(not(not(implies(not(not(y)),not(not(implies(not(not(not(not(x)))),falsehood)))))),not(implies(not(not(not(y))),not(implies(not(not(not(not(x)))),falsehood))))),
inference(light_normalisation,[status(thm)],[c_1044,c_77]) ).
tcf(c_1141,plain,
! [X0: $i] : implies(implies(X0,not(truth)),not(truth)) = implies(truth,X0),
inference(superposition,[status(thm)],[c_1006,c_198]) ).
tcf(c_1159,plain,
! [X0: $i] : implies(implies(X0,falsehood),falsehood) = X0,
inference(light_normalisation,[status(thm)],[c_1141,c_77,c_66]) ).
tcf(c_1187,plain,
! [X0: $i] : implies(implies(not(falsehood),X0),falsehood) = implies(truth,not(X0)),
inference(superposition,[status(thm)],[c_1040,c_198]) ).
tcf(c_1190,plain,
! [X0: $i] : implies(truth,not(X0)) = implies(X0,falsehood),
inference(light_normalisation,[status(thm)],[c_1187,c_66,c_802]) ).
tcf(c_1205,plain,
! [X0: $i] : implies(X0,falsehood) = not(X0),
inference(superposition,[status(thm)],[c_824,c_1159]) ).
tcf(c_1220,plain,
! [X0: $i] : not(not(X0)) = X0,
inference(demodulation,[status(thm)],[c_824,c_1205]) ).
tcf(c_1239,plain,
implies(implies(x,not(y)),not(implies(not(x),y))) != implies(implies(y,not(x)),not(implies(not(x),y))),
inference(demodulation,[status(thm)],[c_1045,c_77,c_71,c_802,c_1040,c_1190,c_1205,c_1220]) ).
tcf(c_1248,plain,
! [X0: $i,X1: $i] : implies(not(X0),not(X1)) = implies(X1,X0),
inference(superposition,[status(thm)],[c_1220,c_71]) ).
tcf(c_1495,plain,
! [X0: $i,X1: $i] : implies(X0,not(X1)) = implies(X1,not(X0)),
inference(superposition,[status(thm)],[c_1220,c_1248]) ).
tcf(c_1518,plain,
implies(implies(x,not(y)),not(implies(not(x),y))) != implies(implies(x,not(y)),not(implies(not(x),y))),
inference(demodulation,[status(thm)],[c_1239,c_1495]) ).
tcf(c_1520,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1518]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL159-1 : 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 : n014.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 22:06:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running UEQ theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.31/1.18 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.31/1.18 % SZS status Started for theBenchmark.p
% 3.31/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.31/1.18
% 3.31/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.31/1.18
% 3.31/1.18 % ------ iProver source info
% 3.31/1.18
% 3.31/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.31/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.31/1.18 % git: non_committed_changes: false
% 3.31/1.18
% 3.31/1.18 % ------ Parsing...% successful
% 3.31/1.18
% 3.31/1.18
% 3.31/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.31/1.18
% 3.31/1.18 % ------ 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 %
% 3.31/1.18
% 3.31/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.31/1.18
% 3.31/1.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.31/1.18 % ------ Proving...
% 3.31/1.18 % ------ Problem Properties
% 3.31/1.18
% 3.31/1.18 %
% 3.31/1.18 % clauses 10
% 3.31/1.18 % conjectures 0
% 3.31/1.18 % EPR 0
% 3.31/1.18 % Horn 10
% 3.31/1.18 % unary 10
% 3.31/1.18 % binary 0
% 3.31/1.18 % lits 10
% 3.31/1.18 % lits eq 10
% 3.31/1.18 % fd_pure 0
% 3.31/1.18 % fd_pseudo 0
% 3.31/1.18 % fd_cond 0
% 3.31/1.18 % fd_pseudo_cond 0
% 3.31/1.18 % AC symbols 0
% 3.31/1.18
% 3.31/1.18 % ------ Input Options Time Limit: Unbounded
% 3.31/1.18
% 3.31/1.18
% 3.31/1.18 % ------
% 3.31/1.18 % Current options:
% 3.31/1.18 % ------
% 3.31/1.18
% 3.31/1.18
% 3.31/1.18 %
% 3.31/1.18
% 3.31/1.18 % ------ Proving...
% 3.31/1.18 %
% 3.31/1.18
% 3.31/1.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.31/1.18
% 3.31/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.31/1.18
% 3.31/1.18
%------------------------------------------------------------------------------