%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL109-6 : 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 : n009.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 02:05:40 PM UTC 2026
% Result : Unsatisfiable 223.82s 33.45s
% Output : CNFRefutation 223.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 60 ( 60 unt; 0 def)
% Number of atoms : 60 ( 59 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 12 ( 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; 4 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 86 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : xor(X0,falsehood) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_2) ).
fof(f3,axiom,
! [X0] : xor(X0,X0) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_3) ).
fof(f4,plain,
! [X0] : falsehood = xor(X0,X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0] : and_star(X0,truth) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_4) ).
fof(f6,axiom,
! [X0] : and_star(X0,falsehood) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_5) ).
fof(f7,plain,
! [X0] : falsehood = and_star(X0,falsehood),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0] : and_star(xor(truth,X0),X0) = falsehood,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_6) ).
fof(f9,plain,
! [X0] : falsehood = and_star(xor(truth,X0),X0),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0,X1] : xor(X0,xor(truth,X1)) = xor(xor(X0,truth),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_7) ).
fof(f11,axiom,
! [X0,X1] : and_star(xor(and_star(xor(truth,X0),X1),truth),X1) = and_star(xor(and_star(xor(truth,X1),X0),truth),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL002-0.ax',axiom_8) ).
fof(f12,axiom,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutativity) ).
fof(f13,axiom,
! [X2,X0,X1] : and_star(and_star(X0,X1),X2) = and_star(X0,and_star(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_associativity) ).
fof(f14,axiom,
! [X0,X1] : and_star(X0,X1) = and_star(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).
fof(f17,axiom,
! [X0,X1] : implies(X0,X1) = xor(truth,and_star(X0,xor(truth,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
fof(f18,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
fof(f19,plain,
truth != implies(implies(implies(a,b),implies(b,a)),implies(b,a)),
inference(reorient_equations,[],[f18]) ).
fof(f21,plain,
truth != xor(truth,and_star(xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))),
inference(definition_unfolding,[],[f19,f17,f17,f17,f17,f17]) ).
tcf(c_63,plain,
! [X0: $i] : xor(X0,falsehood) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_64,plain,
! [X0: $i] : xor(X0,X0) = falsehood,
inference(cnf_transformation,[],[f4]) ).
tcf(c_65,plain,
! [X0: $i] : and_star(X0,truth) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,plain,
! [X0: $i] : and_star(X0,falsehood) = falsehood,
inference(cnf_transformation,[],[f7]) ).
tcf(c_67,plain,
! [X0: $i] : and_star(xor(truth,X0),X0) = falsehood,
inference(cnf_transformation,[],[f9]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : xor(xor(X0,truth),X1) = xor(X0,xor(truth,X1)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : and_star(xor(and_star(xor(truth,X0),X1),truth),X1) = and_star(xor(and_star(xor(truth,X1),X0),truth),X0),
inference(cnf_transformation,[],[f11]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : xor(X0,X1) = xor(X1,X0),
inference(cnf_transformation,[],[f12]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] : and_star(and_star(X0,X1),X2) = and_star(X0,and_star(X1,X2)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : and_star(X0,X1) = and_star(X1,X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_74,negated_conjecture,
xor(truth,and_star(xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))) != truth,
inference(cnf_transformation,[],[f21]) ).
tcf(c_84,plain,
! [X0: $i] : and_star(X0,xor(truth,X0)) = falsehood,
inference(theory_normalisation,[status(thm)],[c_67,c_71,c_72]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] : and_star(X0,xor(and_star(xor(truth,X1),X0),truth)) = and_star(X1,xor(and_star(xor(truth,X0),X1),truth)),
inference(theory_normalisation,[status(thm)],[c_69,c_71,c_72]) ).
tcf(c_86,negated_conjecture,
xor(truth,and_star(xor(truth,xor(truth,and_star(b,xor(truth,a)))),xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))))) != truth,
inference(theory_normalisation,[status(thm)],[c_74,c_71,c_72]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] : and_star(X0,xor(truth,and_star(xor(truth,X1),X0))) = and_star(X1,xor(truth,and_star(xor(truth,X0),X1))),
inference(demodulation,[status(thm)],[c_85,c_70]) ).
tcf(c_112,plain,
xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,xor(truth,xor(truth,and_star(b,xor(truth,a))))))))))) != truth,
inference(demodulation,[status(thm)],[c_86,c_71,c_72,c_111]) ).
tcf(c_194,plain,
! [X0: $i] : xor(falsehood,X0) = X0,
inference(superposition,[status(thm)],[c_63,c_70]) ).
tcf(c_209,plain,
! [X0: $i] : and_star(truth,X0) = X0,
inference(superposition,[status(thm)],[c_72,c_65]) ).
tcf(c_210,plain,
! [X0: $i] : and_star(falsehood,X0) = falsehood,
inference(superposition,[status(thm)],[c_72,c_66]) ).
tcf(c_223,plain,
! [X0: $i] : xor(truth,xor(truth,X0)) = xor(falsehood,X0),
inference(superposition,[status(thm)],[c_64,c_68]) ).
tcf(c_231,plain,
! [X0: $i] : xor(truth,xor(truth,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_223,c_194]) ).
tcf(c_232,plain,
xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(b,xor(truth,a))))))))) != truth,
inference(demodulation,[status(thm)],[c_112,c_231]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] : and_star(X0,and_star(xor(truth,X0),X1)) = and_star(falsehood,X1),
inference(superposition,[status(thm)],[c_84,c_71]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] : and_star(X0,and_star(X1,xor(truth,and_star(X0,X1)))) = falsehood,
inference(superposition,[status(thm)],[c_71,c_84]) ).
tcf(c_282,plain,
! [X0: $i,X1: $i] : and_star(xor(truth,and_star(xor(truth,X0),xor(truth,X1))),xor(truth,and_star(X0,xor(truth,and_star(xor(truth,xor(truth,X1)),X0))))) = and_star(X1,xor(truth,and_star(xor(truth,xor(truth,and_star(xor(truth,X0),xor(truth,X1)))),X1))),
inference(superposition,[status(thm)],[c_111,c_111]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i] : and_star(xor(truth,and_star(xor(truth,X0),xor(truth,X1))),xor(truth,and_star(X0,xor(truth,and_star(xor(truth,xor(truth,X1)),X0))))) = and_star(X1,xor(truth,and_star(X1,xor(truth,xor(truth,and_star(xor(truth,X0),xor(truth,X1))))))),
inference(theory_normalisation,[status(thm)],[c_282,c_71,c_72]) ).
tcf(c_579,plain,
! [X0: $i,X1: $i] : and_star(X0,and_star(xor(truth,X0),X1)) = falsehood,
inference(demodulation,[status(thm)],[c_243,c_210]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i] : and_star(xor(truth,X0),and_star(X0,X1)) = falsehood,
inference(superposition,[status(thm)],[c_231,c_579]) ).
tcf(c_605,plain,
! [X0: $i,X1: $i] : and_star(X0,xor(truth,and_star(xor(truth,and_star(xor(truth,xor(truth,X0)),X1)),X0))) = and_star(and_star(xor(truth,xor(truth,X0)),X1),xor(truth,falsehood)),
inference(superposition,[status(thm)],[c_579,c_111]) ).
tcf(c_612,plain,
! [X0: $i,X1: $i] : and_star(X0,and_star(X1,xor(truth,X0))) = falsehood,
inference(theory_normalisation,[status(thm)],[c_600,c_71,c_72]) ).
tcf(c_616,plain,
! [X0: $i,X1: $i] : and_star(X0,xor(truth,and_star(X0,xor(truth,and_star(xor(truth,xor(truth,X0)),X1))))) = and_star(xor(truth,falsehood),and_star(X1,xor(truth,xor(truth,X0)))),
inference(theory_normalisation,[status(thm)],[c_605,c_71,c_72]) ).
tcf(c_617,plain,
! [X0: $i,X1: $i] : and_star(X0,xor(truth,and_star(X0,xor(truth,and_star(X0,X1))))) = and_star(xor(truth,falsehood),and_star(X1,X0)),
inference(light_normalisation,[status(thm)],[c_616,c_231]) ).
tcf(c_4276,plain,
! [X0: $i,X1: $i] : and_star(xor(truth,and_star(xor(truth,X0),xor(truth,X1))),xor(truth,and_star(X0,xor(truth,and_star(X1,X0))))) = X1,
inference(demodulation,[status(thm)],[c_299,c_63,c_65,c_231,c_612]) ).
tcf(c_14443,plain,
! [X0: $i,X1: $i] : and_star(X0,xor(truth,and_star(X0,xor(truth,and_star(X0,X1))))) = and_star(X1,X0),
inference(demodulation,[status(thm)],[c_617,c_63,c_209]) ).
tcf(c_14462,plain,
! [X0: $i,X1: $i] : and_star(X0,xor(truth,and_star(X0,xor(truth,and_star(X1,X0))))) = and_star(X1,X0),
inference(superposition,[status(thm)],[c_72,c_14443]) ).
tcf(c_15217,plain,
! [X0: $i,X1: $i,X2: $i] : and_star(X0,and_star(xor(truth,and_star(X0,xor(truth,and_star(X1,X0)))),X2)) = and_star(and_star(X1,X0),X2),
inference(superposition,[status(thm)],[c_14462,c_71]) ).
tcf(c_15282,plain,
! [X0: $i,X1: $i,X2: $i] : and_star(X0,and_star(xor(truth,and_star(X0,xor(truth,and_star(X1,X0)))),X2)) = and_star(X1,and_star(X0,X2)),
inference(theory_normalisation,[status(thm)],[c_15217,c_71,c_72]) ).
tcf(c_104341,plain,
! [X0: $i,X1: $i,X2: $i] : and_star(X0,and_star(X1,xor(truth,and_star(X0,xor(truth,and_star(X2,X0)))))) = and_star(X2,and_star(X0,X1)),
inference(superposition,[status(thm)],[c_72,c_15282]) ).
tcf(c_209834,plain,
! [X0: $i,X1: $i] : and_star(X0,and_star(X1,xor(truth,and_star(xor(truth,X1),xor(truth,X0))))) = and_star(X1,X0),
inference(superposition,[status(thm)],[c_4276,c_104341]) ).
tcf(c_281834,plain,
! [X0: $i,X1: $i] : and_star(X0,and_star(xor(truth,X1),xor(truth,and_star(X1,xor(truth,X0))))) = and_star(xor(truth,X1),X0),
inference(superposition,[status(thm)],[c_231,c_209834]) ).
tcf(c_282433,plain,
xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(xor(truth,b),a))))) != truth,
inference(demodulation,[status(thm)],[c_232,c_281834]) ).
tcf(c_282434,plain,
xor(truth,and_star(a,and_star(xor(truth,b),xor(truth,and_star(a,xor(truth,b)))))) != truth,
inference(theory_normalisation,[status(thm)],[c_282433,c_71,c_72]) ).
tcf(c_282435,plain,
$false,
inference(ground_joinability,[status(thm)],[c_282434,c_63,c_246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 21:57:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running UEQ theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 223.82/33.45 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 223.82/33.45 % SZS status Started for theBenchmark.p
% 223.82/33.45 % SZS status Unsatisfiable for theBenchmark.p
% 223.82/33.45
% 223.82/33.45 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 223.82/33.45
% 223.82/33.45 % ------ iProver source info
% 223.82/33.45
% 223.82/33.45 % git: date: 2026-07-19 20:42:38 +0200
% 223.82/33.45 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 223.82/33.45 % git: non_committed_changes: false
% 223.82/33.45
% 223.82/33.45 % ------ Parsing...% successful
% 223.82/33.45
% 223.82/33.45
% 223.82/33.45 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 223.82/33.45
% 223.82/33.45 % ------ 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 %
% 223.82/33.45
% 223.82/33.45 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 223.82/33.45
% 223.82/33.45 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 223.82/33.45 % ------ Proving...
% 223.82/33.45 % ------ Problem Properties
% 223.82/33.45
% 223.82/33.45 %
% 223.82/33.45 % clauses 11
% 223.82/33.45 % conjectures 0
% 223.82/33.45 % EPR 0
% 223.82/33.45 % Horn 11
% 223.82/33.45 % unary 11
% 223.82/33.45 % binary 0
% 223.82/33.45 % lits 11
% 223.82/33.45 % lits eq 11
% 223.82/33.45 % fd_pure 0
% 223.82/33.45 % fd_pseudo 0
% 223.82/33.45 % fd_cond 0
% 223.82/33.45 % fd_pseudo_cond 0
% 223.82/33.45 % AC symbols 1
% 223.82/33.45
% 223.82/33.45 % ------ Input Options Time Limit: Unbounded
% 223.82/33.45
% 223.82/33.45
% 223.82/33.45 % ------
% 223.82/33.45 % Current options:
% 223.82/33.45 % ------
% 223.82/33.45
% 223.82/33.45
% 223.82/33.45 %
% 223.82/33.45
% 223.82/33.45 % ------ Proving...
% 223.82/33.45 %
% 223.82/33.45
% 223.82/33.45 % SZS status Unsatisfiable for theBenchmark.p
% 223.82/33.45
% 223.82/33.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 223.82/33.45
% 223.82/33.45
%------------------------------------------------------------------------------