%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE169-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 01:51:46 PM UTC 2026
% Result : Unsatisfiable 32.51s 9.53s
% Output : CNFRefutation 32.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 18
% Syntax : Number of clauses : 103 ( 103 unt; 0 nHn; 67 RR)
% Number of literals : 103 ( 102 equ; 17 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-4 aty)
% Number of variables : 64 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t23,axiom,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t51,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t23]) ).
cnf(t8,axiom,
multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t34,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t53,plain,
multiplication(addition(one,X1),X2) = addition(X2,multiplication(X1,X2)),
inference(cp,[status(thm)],[t51,t34]) ).
cnf(t540,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(orient,[status(thm)],[t53]) ).
cnf(t31,axiom,
sFlat5 = multiplication(star(sigma),multiplication(a,multiplication(sigma,a))),
introduced(definition) ).
cnf(t57,plain,
multiplication(star(sigma),multiplication(a,multiplication(sigma,a))) = sFlat5,
inference(orient,[status(thm)],[t31]) ).
cnf(t30,axiom,
sFlat4 = multiplication(a,multiplication(sigma,a)),
introduced(definition) ).
cnf(t63,plain,
multiplication(a,multiplication(sigma,a)) = sFlat4,
inference(orient,[status(thm)],[t30]) ).
cnf(t810,plain,
multiplication(star(sigma),sFlat4) = sFlat5,
inference(step,[status(thm)],[t57,t63]) ).
cnf(t69,plain,
multiplication(star(sigma),sFlat4) = sFlat5,
inference(rw,[status(thm)],[t810]) ).
cnf(t28,axiom,
sFlat2 = star(sigma),
introduced(definition) ).
cnf(t120,plain,
star(sigma) = sFlat2,
inference(orient,[status(thm)],[t28]) ).
cnf(t823,plain,
multiplication(sFlat2,sFlat4) = sFlat5,
inference(step,[status(thm)],[t69,t120]) ).
cnf(t209,plain,
multiplication(sFlat2,sFlat4) = sFlat5,
inference(orient,[status(thm)],[t823]) ).
cnf(t545,plain,
multiplication(addition(one,sFlat2),sFlat4) = addition(sFlat4,sFlat5),
inference(cp,[status(thm)],[t540,t209]) ).
cnf(t10,axiom,
addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t92,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t10]) ).
cnf(t851,plain,
multiplication(addition(sFlat2,one),sFlat4) = addition(sFlat4,sFlat5),
inference(step,[status(thm)],[t545,t92]) ).
cnf(t14,axiom,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t97,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t0,axiom,
addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t35,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t100,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t97,t35]) ).
cnf(t277,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t100]) ).
cnf(hi11,axiom,
ifeq2(leq(A,B),true,addition(A,B),B) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi13,axiom,
leq(addition(one,multiplication(A,star(A))),star(A)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t20,plain,
addition(addition(one,multiplication(X1,star(X1))),star(X1)) = star(X1),
inference(hyper_resolution,[status(thm)],[hi11,hi13]) ).
cnf(t813,plain,
addition(one,addition(multiplication(X1,star(X1)),star(X1))) = star(X1),
inference(step,[status(thm)],[t20,t97]) ).
cnf(t814,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(step,[status(thm)],[t813,t92]) ).
cnf(t106,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(orient,[status(thm)],[t814]) ).
cnf(t280,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = addition(one,star(X1)),
inference(cp,[status(thm)],[t277,t106]) ).
cnf(t830,plain,
star(X1) = addition(one,star(X1)),
inference(step,[status(thm)],[t280,t106]) ).
cnf(t292,plain,
addition(one,star(X1)) = star(X1),
inference(orient,[status(thm)],[t830]) ).
cnf(t293,plain,
star(sigma) = addition(one,sFlat2),
inference(cp,[status(thm)],[t292,t120]) ).
cnf(t831,plain,
sFlat2 = addition(one,sFlat2),
inference(step,[status(thm)],[t293,t120]) ).
cnf(t832,plain,
sFlat2 = addition(sFlat2,one),
inference(step,[status(thm)],[t831,t92]) ).
cnf(t297,plain,
addition(sFlat2,one) = sFlat2,
inference(orient,[status(thm)],[t832]) ).
cnf(t852,plain,
multiplication(sFlat2,sFlat4) = addition(sFlat4,sFlat5),
inference(step,[status(thm)],[t851,t297]) ).
cnf(t853,plain,
sFlat5 = addition(sFlat4,sFlat5),
inference(step,[status(thm)],[t852,t209]) ).
cnf(t578,plain,
addition(sFlat4,sFlat5) = sFlat5,
inference(orient,[status(thm)],[t853]) ).
cnf(t22,axiom,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t44,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t22]) ).
cnf(t29,axiom,
sFlat3 = multiplication(sigma,a),
introduced(definition) ).
cnf(t78,plain,
multiplication(sigma,a) = sFlat3,
inference(orient,[status(thm)],[t29]) ).
cnf(t811,plain,
multiplication(a,sFlat3) = sFlat4,
inference(step,[status(thm)],[t63,t78]) ).
cnf(t84,plain,
multiplication(a,sFlat3) = sFlat4,
inference(rw,[status(thm)],[t811]) ).
cnf(t188,plain,
multiplication(a,sFlat3) = sFlat4,
inference(orient,[status(thm)],[t84]) ).
cnf(t191,plain,
multiplication(a,addition(sFlat3,X1)) = addition(sFlat4,multiplication(a,X1)),
inference(cp,[status(thm)],[t44,t188]) ).
cnf(t785,plain,
addition(sFlat4,multiplication(a,X1)) = multiplication(a,addition(sFlat3,X1)),
inference(orient,[status(thm)],[t191]) ).
cnf(t27,axiom,
sFlat1 = multiplication(a,multiplication(b,a)),
introduced(definition) ).
cnf(t70,plain,
multiplication(a,multiplication(b,a)) = sFlat1,
inference(orient,[status(thm)],[t27]) ).
cnf(t26,axiom,
sFlat0 = multiplication(b,a),
introduced(definition) ).
cnf(t85,plain,
multiplication(b,a) = sFlat0,
inference(orient,[status(thm)],[t26]) ).
cnf(t812,plain,
multiplication(a,sFlat0) = sFlat1,
inference(step,[status(thm)],[t70,t85]) ).
cnf(t91,plain,
multiplication(a,sFlat0) = sFlat1,
inference(rw,[status(thm)],[t812]) ).
cnf(t197,plain,
multiplication(a,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t91]) ).
cnf(t789,plain,
multiplication(a,addition(sFlat3,sFlat0)) = addition(sFlat4,sFlat1),
inference(cp,[status(thm)],[t785,t197]) ).
cnf(t872,plain,
multiplication(a,addition(sFlat0,sFlat3)) = addition(sFlat4,sFlat1),
inference(step,[status(thm)],[t789,t92]) ).
cnf(t79,plain,
multiplication(addition(sigma,X1),a) = addition(sFlat3,multiplication(X1,a)),
inference(cp,[status(thm)],[t51,t78]) ).
cnf(t666,plain,
addition(sFlat3,multiplication(X1,a)) = multiplication(addition(sigma,X1),a),
inference(orient,[status(thm)],[t79]) ).
cnf(t669,plain,
multiplication(addition(sigma,b),a) = addition(sFlat3,sFlat0),
inference(cp,[status(thm)],[t666,t85]) ).
cnf(t2,axiom,
addition(a,b) = sigma,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t817,plain,
addition(b,a) = sigma,
inference(step,[status(thm)],[t2,t92]) ).
cnf(t117,plain,
addition(b,a) = sigma,
inference(orient,[status(thm)],[t817]) ).
cnf(t279,plain,
addition(b,a) = addition(b,sigma),
inference(cp,[status(thm)],[t277,t117]) ).
cnf(t828,plain,
sigma = addition(b,sigma),
inference(step,[status(thm)],[t279,t117]) ).
cnf(t829,plain,
sigma = addition(sigma,b),
inference(step,[status(thm)],[t828,t92]) ).
cnf(t288,plain,
addition(sigma,b) = sigma,
inference(orient,[status(thm)],[t829]) ).
cnf(t861,plain,
multiplication(sigma,a) = addition(sFlat3,sFlat0),
inference(step,[status(thm)],[t669,t288]) ).
cnf(t862,plain,
sFlat3 = addition(sFlat3,sFlat0),
inference(step,[status(thm)],[t861,t78]) ).
cnf(t863,plain,
sFlat3 = addition(sFlat0,sFlat3),
inference(step,[status(thm)],[t862,t92]) ).
cnf(t677,plain,
addition(sFlat0,sFlat3) = sFlat3,
inference(orient,[status(thm)],[t863]) ).
cnf(t873,plain,
multiplication(a,sFlat3) = addition(sFlat4,sFlat1),
inference(step,[status(thm)],[t872,t677]) ).
cnf(t874,plain,
sFlat4 = addition(sFlat4,sFlat1),
inference(step,[status(thm)],[t873,t188]) ).
cnf(t875,plain,
sFlat4 = addition(sFlat1,sFlat4),
inference(step,[status(thm)],[t874,t92]) ).
cnf(t803,plain,
addition(sFlat1,sFlat4) = sFlat4,
inference(orient,[status(thm)],[t875]) ).
cnf(t16,axiom,
ifeq3(addition(X1,X2),X2,leq(X1,X2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t174,plain,
ifeq3(addition(X1,X2),X2,leq(X1,X2),true) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t285,plain,
true = ifeq3(addition(X1,X2),addition(X1,X2),leq(X1,addition(X1,X2)),true),
inference(cp,[status(thm)],[t174,t277]) ).
cnf(t13,axiom,
ifeq3(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t42,plain,
ifeq3(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t834,plain,
true = leq(X1,addition(X1,X2)),
inference(step,[status(thm)],[t285,t42]) ).
cnf(t307,plain,
leq(X1,addition(X1,X2)) = true,
inference(orient,[status(thm)],[t834]) ).
cnf(goal_0,negated_conjecture,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
leq(multiplication(a,multiplication(b,a)),sFlat5) != true,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
leq(multiplication(a,multiplication(b,a)),addition(sFlat4,sFlat5)) != true,
inference(rw,[status(thm)],[g0_0,t578]) ).
cnf(g0_2,plain,
leq(multiplication(a,multiplication(b,a)),addition(sFlat5,sFlat4)) != true,
inference(rw,[status(thm)],[g0_1,t92]) ).
cnf(g0_3,plain,
leq(multiplication(a,multiplication(b,a)),addition(sFlat5,addition(sFlat1,sFlat4))) != true,
inference(rw,[status(thm)],[g0_2,t803]) ).
cnf(g0_4,plain,
leq(multiplication(a,multiplication(b,a)),addition(sFlat5,addition(sFlat4,sFlat1))) != true,
inference(rw,[status(thm)],[g0_3,t92]) ).
cnf(g0_5,plain,
leq(multiplication(a,multiplication(b,a)),addition(addition(sFlat4,sFlat1),sFlat5)) != true,
inference(rw,[status(thm)],[g0_4,t92]) ).
cnf(g0_6,plain,
leq(multiplication(a,multiplication(b,a)),addition(sFlat4,addition(sFlat1,sFlat5))) != true,
inference(rw,[status(thm)],[g0_5,t97]) ).
cnf(g0_7,plain,
leq(multiplication(a,multiplication(b,a)),addition(sFlat4,addition(sFlat5,sFlat1))) != true,
inference(rw,[status(thm)],[g0_6,t92]) ).
cnf(g0_8,plain,
leq(multiplication(a,multiplication(b,a)),addition(addition(sFlat5,sFlat1),sFlat4)) != true,
inference(rw,[status(thm)],[g0_7,t92]) ).
cnf(g0_9,plain,
leq(multiplication(a,sFlat0),addition(addition(sFlat5,sFlat1),sFlat4)) != true,
inference(rw,[status(thm)],[g0_8,t85]) ).
cnf(g0_10,plain,
leq(multiplication(a,sFlat0),addition(addition(sFlat1,sFlat5),sFlat4)) != true,
inference(rw,[status(thm)],[g0_9,t92]) ).
cnf(g0_11,plain,
leq(multiplication(a,sFlat0),addition(sFlat1,addition(sFlat5,sFlat4))) != true,
inference(rw,[status(thm)],[g0_10,t97]) ).
cnf(g0_12,plain,
leq(multiplication(a,sFlat0),addition(sFlat1,addition(sFlat4,sFlat5))) != true,
inference(rw,[status(thm)],[g0_11,t92]) ).
cnf(g0_13,plain,
leq(multiplication(a,sFlat0),addition(sFlat1,sFlat5)) != true,
inference(rw,[status(thm)],[g0_12,t578]) ).
cnf(g0_14,plain,
leq(sFlat1,addition(sFlat1,sFlat5)) != true,
inference(rw,[status(thm)],[g0_13,t197]) ).
cnf(g0_15,plain,
true != true,
inference(rw,[status(thm)],[g0_14,t307]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE169-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n007.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 19:09:27 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 32.51/9.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.51/9.53 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------