%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE090-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 01:51:35 PM UTC 2026
% Result : Unsatisfiable 8.15s 7.01s
% Output : CNFRefutation 8.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 17
% Syntax : Number of clauses : 122 ( 122 unt; 0 nHn; 78 RR)
% Number of literals : 122 ( 121 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 65 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t22,axiom,
sF0 = addition(sK2_goals_X0,sK1_goals_X1),
introduced(definition) ).
cnf(t2,axiom,
addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t30,plain,
addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t2810,plain,
sF0 = sK1_goals_X1,
inference(step,[status(thm)],[t22,t30]) ).
cnf(t35,plain,
sK1_goals_X1 = sF0,
inference(orient,[status(thm)],[t2810]) ).
cnf(t23,axiom,
sF1 = antidomain(sK1_goals_X1),
introduced(definition) ).
cnf(t26,plain,
antidomain(sK1_goals_X1) = sF1,
inference(orient,[status(thm)],[t23]) ).
cnf(t2811,plain,
antidomain(sF0) = sF1,
inference(step,[status(thm)],[t26,t35]) ).
cnf(t36,plain,
antidomain(sF0) = sF1,
inference(rw,[status(thm)],[t2811]) ).
cnf(t40,plain,
antidomain(sF0) = sF1,
inference(orient,[status(thm)],[t36]) ).
cnf(t24,axiom,
sF2 = antidomain(sK2_goals_X0),
introduced(definition) ).
cnf(t27,plain,
antidomain(sK2_goals_X0) = sF2,
inference(orient,[status(thm)],[t24]) ).
cnf(t25,axiom,
sF3 = addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)),
introduced(definition) ).
cnf(t9,axiom,
addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t57,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t2814,plain,
sF3 = addition(antidomain(sK2_goals_X0),antidomain(sK1_goals_X1)),
inference(step,[status(thm)],[t25,t57]) ).
cnf(t2815,plain,
sF3 = addition(sF2,antidomain(sK1_goals_X1)),
inference(step,[status(thm)],[t2814,t27]) ).
cnf(t2816,plain,
sF3 = addition(sF2,antidomain(sF0)),
inference(step,[status(thm)],[t2815,t35]) ).
cnf(t2817,plain,
sF3 = addition(sF2,sF1),
inference(step,[status(thm)],[t2816,t40]) ).
cnf(t2818,plain,
sF3 = addition(sF1,sF2),
inference(step,[status(thm)],[t2817,t57]) ).
cnf(t72,plain,
addition(sF1,sF2) = sF3,
inference(orient,[status(thm)],[t2818]) ).
cnf(t18,axiom,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t212,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
cnf(t19,axiom,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t257,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(orient,[status(thm)],[t19]) ).
cnf(t8,axiom,
multiplication(antidomain(X1),X1) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t43,plain,
multiplication(antidomain(X1),X1) = zero,
inference(orient,[status(thm)],[t8]) ).
cnf(t263,plain,
multiplication(addition(X1,antidomain(X2)),X2) = addition(multiplication(X1,X2),zero),
inference(cp,[status(thm)],[t257,t43]) ).
cnf(t1,axiom,
addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t29,plain,
addition(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t3059,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(step,[status(thm)],[t263,t29]) ).
cnf(t2604,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(orient,[status(thm)],[t3059]) ).
cnf(t14,axiom,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t52,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t74,plain,
addition(sF1,addition(sF2,X1)) = addition(sF3,X1),
inference(cp,[status(thm)],[t52,t72]) ).
cnf(t123,plain,
addition(sF1,addition(sF2,X1)) = addition(sF3,X1),
inference(orient,[status(thm)],[t74]) ).
cnf(t12,axiom,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t2820,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(step,[status(thm)],[t12,t57]) ).
cnf(t82,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(orient,[status(thm)],[t2820]) ).
cnf(t83,plain,
one = addition(sF2,antidomain(antidomain(sK2_goals_X0))),
inference(cp,[status(thm)],[t82,t27]) ).
cnf(t2823,plain,
one = addition(sF2,antidomain(sF2)),
inference(step,[status(thm)],[t83,t27]) ).
cnf(t90,plain,
addition(sF2,antidomain(sF2)) = one,
inference(orient,[status(thm)],[t2823]) ).
cnf(t128,plain,
addition(sF3,antidomain(sF2)) = addition(sF1,one),
inference(cp,[status(thm)],[t123,t90]) ).
cnf(t0,axiom,
addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t28,plain,
addition(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t54,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(cp,[status(thm)],[t52,t28]) ).
cnf(t75,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(orient,[status(thm)],[t54]) ).
cnf(t84,plain,
one = addition(sF1,antidomain(antidomain(sF0))),
inference(cp,[status(thm)],[t82,t40]) ).
cnf(t2825,plain,
one = addition(sF1,antidomain(sF1)),
inference(step,[status(thm)],[t84,t40]) ).
cnf(t97,plain,
addition(sF1,antidomain(sF1)) = one,
inference(orient,[status(thm)],[t2825]) ).
cnf(t100,plain,
addition(sF1,antidomain(sF1)) = addition(sF1,one),
inference(cp,[status(thm)],[t75,t97]) ).
cnf(t2826,plain,
one = addition(sF1,one),
inference(step,[status(thm)],[t100,t97]) ).
cnf(t101,plain,
addition(sF1,one) = one,
inference(orient,[status(thm)],[t2826]) ).
cnf(t2839,plain,
addition(sF3,antidomain(sF2)) = one,
inference(step,[status(thm)],[t128,t101]) ).
cnf(t158,plain,
addition(sF3,antidomain(sF2)) = one,
inference(orient,[status(thm)],[t2839]) ).
cnf(t2606,plain,
multiplication(sF3,sF2) = multiplication(one,sF2),
inference(cp,[status(thm)],[t2604,t158]) ).
cnf(t5,axiom,
multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t33,plain,
multiplication(one,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t3060,plain,
multiplication(sF3,sF2) = sF2,
inference(step,[status(thm)],[t2606,t33]) ).
cnf(t2622,plain,
multiplication(sF3,sF2) = sF2,
inference(orient,[status(thm)],[t3060]) ).
cnf(t2624,plain,
multiplication(sF3,addition(sF2,X1)) = addition(sF2,multiplication(sF3,X1)),
inference(cp,[status(thm)],[t212,t2622]) ).
cnf(t2687,plain,
addition(sF2,multiplication(sF3,X1)) = multiplication(sF3,addition(sF2,X1)),
inference(orient,[status(thm)],[t2624]) ).
cnf(t20,axiom,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t304,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(orient,[status(thm)],[t20]) ).
cnf(t44,plain,
zero = multiplication(sF2,sK2_goals_X0),
inference(cp,[status(thm)],[t43,t27]) ).
cnf(t48,plain,
multiplication(sF2,sK2_goals_X0) = zero,
inference(orient,[status(thm)],[t44]) ).
cnf(t265,plain,
multiplication(addition(X1,sF2),sK2_goals_X0) = addition(multiplication(X1,sK2_goals_X0),zero),
inference(cp,[status(thm)],[t257,t48]) ).
cnf(t2873,plain,
multiplication(addition(X1,sF2),sK2_goals_X0) = multiplication(X1,sK2_goals_X0),
inference(step,[status(thm)],[t265,t29]) ).
cnf(t673,plain,
multiplication(addition(X1,sF2),sK2_goals_X0) = multiplication(X1,sK2_goals_X0),
inference(orient,[status(thm)],[t2873]) ).
cnf(t674,plain,
multiplication(sF1,sK2_goals_X0) = multiplication(sF3,sK2_goals_X0),
inference(cp,[status(thm)],[t673,t72]) ).
cnf(t46,plain,
zero = multiplication(sF1,sF0),
inference(cp,[status(thm)],[t43,t40]) ).
cnf(t49,plain,
multiplication(sF1,sF0) = zero,
inference(orient,[status(thm)],[t46]) ).
cnf(t221,plain,
multiplication(sF1,addition(sF0,X1)) = addition(zero,multiplication(sF1,X1)),
inference(cp,[status(thm)],[t212,t49]) ).
cnf(t59,plain,
addition(zero,X1) = X1,
inference(cp,[status(thm)],[t57,t29]) ).
cnf(t65,plain,
addition(zero,X1) = X1,
inference(orient,[status(thm)],[t59]) ).
cnf(t2861,plain,
multiplication(sF1,addition(sF0,X1)) = multiplication(sF1,X1),
inference(step,[status(thm)],[t221,t65]) ).
cnf(t429,plain,
multiplication(sF1,addition(sF0,X1)) = multiplication(sF1,X1),
inference(orient,[status(thm)],[t2861]) ).
cnf(t37,plain,
addition(sK2_goals_X0,sF0) = sK1_goals_X1,
inference(rw,[status(thm)],[t30]) ).
cnf(t2812,plain,
addition(sK2_goals_X0,sF0) = sF0,
inference(step,[status(thm)],[t37,t35]) ).
cnf(t42,plain,
addition(sK2_goals_X0,sF0) = sF0,
inference(orient,[status(thm)],[t2812]) ).
cnf(t2813,plain,
addition(sF0,sK2_goals_X0) = sF0,
inference(step,[status(thm)],[t42,t57]) ).
cnf(t58,plain,
addition(sF0,sK2_goals_X0) = sF0,
inference(rw,[status(thm)],[t2813]) ).
cnf(t62,plain,
addition(sF0,sK2_goals_X0) = sF0,
inference(orient,[status(thm)],[t58]) ).
cnf(t430,plain,
multiplication(sF1,sK2_goals_X0) = multiplication(sF1,sF0),
inference(cp,[status(thm)],[t429,t62]) ).
cnf(t2862,plain,
multiplication(sF1,sK2_goals_X0) = zero,
inference(step,[status(thm)],[t430,t49]) ).
cnf(t439,plain,
multiplication(sF1,sK2_goals_X0) = zero,
inference(orient,[status(thm)],[t2862]) ).
cnf(t2874,plain,
zero = multiplication(sF3,sK2_goals_X0),
inference(step,[status(thm)],[t674,t439]) ).
cnf(t681,plain,
multiplication(sF3,sK2_goals_X0) = zero,
inference(orient,[status(thm)],[t2874]) ).
cnf(t687,plain,
antidomain(multiplication(sF3,antidomain(antidomain(sK2_goals_X0)))) = addition(antidomain(zero),antidomain(multiplication(sF3,antidomain(antidomain(sK2_goals_X0))))),
inference(cp,[status(thm)],[t304,t681]) ).
cnf(t2918,plain,
antidomain(multiplication(sF3,antidomain(sF2))) = addition(antidomain(zero),antidomain(multiplication(sF3,antidomain(antidomain(sK2_goals_X0))))),
inference(step,[status(thm)],[t687,t27]) ).
cnf(t3,axiom,
multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t31,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t45,plain,
zero = antidomain(one),
inference(cp,[status(thm)],[t43,t31]) ).
cnf(t47,plain,
antidomain(one) = zero,
inference(orient,[status(thm)],[t45]) ).
cnf(t85,plain,
one = addition(zero,antidomain(antidomain(one))),
inference(cp,[status(thm)],[t82,t47]) ).
cnf(t2821,plain,
one = antidomain(antidomain(one)),
inference(step,[status(thm)],[t85,t65]) ).
cnf(t2822,plain,
one = antidomain(zero),
inference(step,[status(thm)],[t2821,t47]) ).
cnf(t89,plain,
antidomain(zero) = one,
inference(orient,[status(thm)],[t2822]) ).
cnf(t2919,plain,
antidomain(multiplication(sF3,antidomain(sF2))) = addition(one,antidomain(multiplication(sF3,antidomain(antidomain(sK2_goals_X0))))),
inference(step,[status(thm)],[t2918,t89]) ).
cnf(t88,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = addition(antidomain(X1),one),
inference(cp,[status(thm)],[t75,t82]) ).
cnf(t2827,plain,
one = addition(antidomain(X1),one),
inference(step,[status(thm)],[t88,t82]) ).
cnf(t2828,plain,
one = addition(one,antidomain(X1)),
inference(step,[status(thm)],[t2827,t57]) ).
cnf(t104,plain,
addition(one,antidomain(X1)) = one,
inference(orient,[status(thm)],[t2828]) ).
cnf(t2920,plain,
antidomain(multiplication(sF3,antidomain(sF2))) = one,
inference(step,[status(thm)],[t2919,t104]) ).
cnf(t1076,plain,
antidomain(multiplication(sF3,antidomain(sF2))) = one,
inference(orient,[status(thm)],[t2920]) ).
cnf(t1077,plain,
zero = multiplication(one,multiplication(sF3,antidomain(sF2))),
inference(cp,[status(thm)],[t43,t1076]) ).
cnf(t2921,plain,
zero = multiplication(sF3,antidomain(sF2)),
inference(step,[status(thm)],[t1077,t33]) ).
cnf(t1081,plain,
multiplication(sF3,antidomain(sF2)) = zero,
inference(orient,[status(thm)],[t2921]) ).
cnf(t2693,plain,
multiplication(sF3,addition(sF2,antidomain(sF2))) = addition(sF2,zero),
inference(cp,[status(thm)],[t2687,t1081]) ).
cnf(t3070,plain,
multiplication(sF3,one) = addition(sF2,zero),
inference(step,[status(thm)],[t2693,t90]) ).
cnf(t3071,plain,
sF3 = addition(sF2,zero),
inference(step,[status(thm)],[t3070,t31]) ).
cnf(t3072,plain,
sF3 = sF2,
inference(step,[status(thm)],[t3071,t29]) ).
cnf(t2715,plain,
sF3 = sF2,
inference(orient,[status(thm)],[t3072]) ).
cnf(t3073,plain,
addition(sF1,sF2) = sF2,
inference(step,[status(thm)],[t72,t2715]) ).
cnf(t2716,plain,
addition(sF1,sF2) = sF2,
inference(orient,[status(thm)],[t3073]) ).
cnf(goal_0,negated_conjecture,
addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) != antidomain(sK2_goals_X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
addition(antidomain(sF0),antidomain(sK2_goals_X0)) != antidomain(sK2_goals_X0),
inference(rw,[status(thm)],[goal_0,t35]) ).
cnf(g0_1,plain,
addition(sF1,antidomain(sK2_goals_X0)) != antidomain(sK2_goals_X0),
inference(rw,[status(thm)],[g0_0,t40]) ).
cnf(g0_2,plain,
addition(sF1,sF2) != antidomain(sK2_goals_X0),
inference(rw,[status(thm)],[g0_1,t27]) ).
cnf(g0_3,plain,
sF2 != antidomain(sK2_goals_X0),
inference(rw,[status(thm)],[g0_2,t2716]) ).
cnf(g0_4,plain,
sF2 != sF2,
inference(rw,[status(thm)],[g0_3,t27]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE090-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n004.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 18:54:14 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.15/7.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.15/7.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------