%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : KLE151-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 01:51:45 PM UTC 2026
% Result : Unsatisfiable 46.25s 12.19s
% Output : CNFRefutation 46.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of clauses : 87 ( 87 unt; 0 nHn; 60 RR)
% Number of literals : 87 ( 86 equ; 9 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 : 52 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t25,axiom,
sFlat0 = multiplication(sK1_goals_X1,sK2_goals_X0),
introduced(definition) ).
cnf(t73,plain,
multiplication(sK1_goals_X1,sK2_goals_X0) = sFlat0,
inference(orient,[status(thm)],[t25]) ).
cnf(t26,axiom,
sFlat1 = strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0)),
introduced(definition) ).
cnf(t9480,plain,
sFlat1 = strong_iteration(sFlat0),
inference(step,[status(thm)],[t26,t73]) ).
cnf(t177,plain,
strong_iteration(sFlat0) = sFlat1,
inference(orient,[status(thm)],[t9480]) ).
cnf(t27,axiom,
sFlat2 = multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),
introduced(definition) ).
cnf(t53,plain,
multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))) = sFlat2,
inference(orient,[status(thm)],[t27]) ).
cnf(t9476,plain,
multiplication(sK2_goals_X0,strong_iteration(sFlat0)) = sFlat2,
inference(step,[status(thm)],[t53,t73]) ).
cnf(t79,plain,
multiplication(sK2_goals_X0,strong_iteration(sFlat0)) = sFlat2,
inference(rw,[status(thm)],[t9476]) ).
cnf(t9489,plain,
multiplication(sK2_goals_X0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t79,t177]) ).
cnf(t204,plain,
multiplication(sK2_goals_X0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t9489]) ).
cnf(t28,axiom,
sFlat3 = multiplication(sK2_goals_X0,sK1_goals_X1),
introduced(definition) ).
cnf(t59,plain,
multiplication(sK2_goals_X0,sK1_goals_X1) = sFlat3,
inference(orient,[status(thm)],[t28]) ).
cnf(t29,axiom,
sFlat4 = strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),
introduced(definition) ).
cnf(t9478,plain,
sFlat4 = strong_iteration(sFlat3),
inference(step,[status(thm)],[t29,t59]) ).
cnf(t172,plain,
strong_iteration(sFlat3) = sFlat4,
inference(orient,[status(thm)],[t9478]) ).
cnf(t30,axiom,
sFlat5 = multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0),
introduced(definition) ).
cnf(t9475,plain,
sFlat5 = multiplication(strong_iteration(sFlat3),sK2_goals_X0),
inference(step,[status(thm)],[t30,t59]) ).
cnf(t65,plain,
multiplication(strong_iteration(sFlat3),sK2_goals_X0) = sFlat5,
inference(orient,[status(thm)],[t9475]) ).
cnf(t9479,plain,
multiplication(sFlat4,sK2_goals_X0) = sFlat5,
inference(step,[status(thm)],[t65,t172]) ).
cnf(t176,plain,
multiplication(sFlat4,sK2_goals_X0) = sFlat5,
inference(rw,[status(thm)],[t9479]) ).
cnf(t193,plain,
multiplication(sFlat4,sK2_goals_X0) = sFlat5,
inference(orient,[status(thm)],[t176]) ).
cnf(t31,axiom,
sFlat6 = leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)),
introduced(definition) ).
cnf(t9481,plain,
sFlat6 = leq(multiplication(sK2_goals_X0,strong_iteration(sFlat0)),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)),
inference(step,[status(thm)],[t31,t73]) ).
cnf(t9482,plain,
sFlat6 = leq(multiplication(sK2_goals_X0,sFlat1),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)),
inference(step,[status(thm)],[t9481,t177]) ).
cnf(t9483,plain,
sFlat6 = leq(multiplication(sK2_goals_X0,sFlat1),multiplication(strong_iteration(sFlat3),sK2_goals_X0)),
inference(step,[status(thm)],[t9482,t59]) ).
cnf(t9484,plain,
sFlat6 = leq(multiplication(sK2_goals_X0,sFlat1),multiplication(sFlat4,sK2_goals_X0)),
inference(step,[status(thm)],[t9483,t172]) ).
cnf(t181,plain,
leq(multiplication(sK2_goals_X0,sFlat1),multiplication(sFlat4,sK2_goals_X0)) = sFlat6,
inference(orient,[status(thm)],[t9484]) ).
cnf(t9487,plain,
leq(multiplication(sK2_goals_X0,sFlat1),sFlat5) = sFlat6,
inference(step,[status(thm)],[t181,t193]) ).
cnf(t202,plain,
leq(multiplication(sK2_goals_X0,sFlat1),sFlat5) = sFlat6,
inference(rw,[status(thm)],[t9487]) ).
cnf(t9494,plain,
leq(sFlat2,sFlat5) = sFlat6,
inference(step,[status(thm)],[t202,t204]) ).
cnf(t231,plain,
leq(sFlat2,sFlat5) = sFlat6,
inference(orient,[status(thm)],[t9494]) ).
cnf(t22,axiom,
ifeq(leq(X1,addition(multiplication(X2,X1),X3)),true,leq(X1,multiplication(strong_iteration(X2),X3)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t114,plain,
ifeq(leq(X1,addition(multiplication(X2,X1),X3)),true,leq(X1,multiplication(strong_iteration(X2),X3)),true) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t8,axiom,
addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t80,plain,
addition(X1,X2) = addition(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t119,plain,
true = ifeq(leq(X1,addition(X2,multiplication(X3,X1))),true,leq(X1,multiplication(strong_iteration(X3),X2)),true),
inference(cp,[status(thm)],[t114,t80]) ).
cnf(t8225,plain,
ifeq(leq(X1,addition(X2,multiplication(X3,X1))),true,leq(X1,multiplication(strong_iteration(X3),X2)),true) = true,
inference(orient,[status(thm)],[t119]) ).
cnf(t20,axiom,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t43,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(orient,[status(thm)],[t20]) ).
cnf(t5,axiom,
multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t32,plain,
multiplication(X1,one) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t44,plain,
multiplication(X1,addition(one,X2)) = addition(X1,multiplication(X1,X2)),
inference(cp,[status(thm)],[t43,t32]) ).
cnf(t622,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(orient,[status(thm)],[t44]) ).
cnf(t19,axiom,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t42,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(orient,[status(thm)],[t19]) ).
cnf(t64,plain,
multiplication(sK2_goals_X0,multiplication(sK1_goals_X1,X1)) = multiplication(sFlat3,X1),
inference(cp,[status(thm)],[t42,t59]) ).
cnf(t234,plain,
multiplication(sK2_goals_X0,multiplication(sK1_goals_X1,X1)) = multiplication(sFlat3,X1),
inference(orient,[status(thm)],[t64]) ).
cnf(t78,plain,
multiplication(sK1_goals_X1,multiplication(sK2_goals_X0,X1)) = multiplication(sFlat0,X1),
inference(cp,[status(thm)],[t42,t73]) ).
cnf(t252,plain,
multiplication(sK1_goals_X1,multiplication(sK2_goals_X0,X1)) = multiplication(sFlat0,X1),
inference(orient,[status(thm)],[t78]) ).
cnf(t256,plain,
multiplication(sFlat0,sFlat1) = multiplication(sK1_goals_X1,sFlat2),
inference(cp,[status(thm)],[t252,t204]) ).
cnf(t275,plain,
multiplication(sK1_goals_X1,sFlat2) = multiplication(sFlat0,sFlat1),
inference(orient,[status(thm)],[t256]) ).
cnf(t276,plain,
multiplication(sFlat3,sFlat2) = multiplication(sK2_goals_X0,multiplication(sFlat0,sFlat1)),
inference(cp,[status(thm)],[t234,t275]) ).
cnf(t450,plain,
multiplication(sK2_goals_X0,multiplication(sFlat0,sFlat1)) = multiplication(sFlat3,sFlat2),
inference(orient,[status(thm)],[t276]) ).
cnf(t638,plain,
multiplication(sK2_goals_X0,addition(one,multiplication(sFlat0,sFlat1))) = addition(sK2_goals_X0,multiplication(sFlat3,sFlat2)),
inference(cp,[status(thm)],[t622,t450]) ).
cnf(t12,axiom,
addition(multiplication(X1,strong_iteration(X1)),one) = strong_iteration(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t9477,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(step,[status(thm)],[t12,t80]) ).
cnf(t94,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(orient,[status(thm)],[t9477]) ).
cnf(t178,plain,
strong_iteration(sFlat0) = addition(one,multiplication(sFlat0,sFlat1)),
inference(cp,[status(thm)],[t94,t177]) ).
cnf(t9493,plain,
sFlat1 = addition(one,multiplication(sFlat0,sFlat1)),
inference(step,[status(thm)],[t178,t177]) ).
cnf(t227,plain,
addition(one,multiplication(sFlat0,sFlat1)) = sFlat1,
inference(orient,[status(thm)],[t9493]) ).
cnf(t9529,plain,
multiplication(sK2_goals_X0,sFlat1) = addition(sK2_goals_X0,multiplication(sFlat3,sFlat2)),
inference(step,[status(thm)],[t638,t227]) ).
cnf(t9530,plain,
sFlat2 = addition(sK2_goals_X0,multiplication(sFlat3,sFlat2)),
inference(step,[status(thm)],[t9529,t204]) ).
cnf(t654,plain,
addition(sK2_goals_X0,multiplication(sFlat3,sFlat2)) = sFlat2,
inference(orient,[status(thm)],[t9530]) ).
cnf(t8247,plain,
true = ifeq(leq(sFlat2,sFlat2),true,leq(sFlat2,multiplication(strong_iteration(sFlat3),sK2_goals_X0)),true),
inference(cp,[status(thm)],[t8225,t654]) ).
cnf(hi18,axiom,
ifeq3(addition(A,B),B,leq(A,B),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi3,axiom,
addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t3,plain,
leq(X1,X1) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi3]) ).
cnf(t113,plain,
leq(X1,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t9812,plain,
true = ifeq(true,true,leq(sFlat2,multiplication(strong_iteration(sFlat3),sK2_goals_X0)),true),
inference(step,[status(thm)],[t8247,t113]) ).
cnf(t9,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t36,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t9813,plain,
true = leq(sFlat2,multiplication(strong_iteration(sFlat3),sK2_goals_X0)),
inference(step,[status(thm)],[t9812,t36]) ).
cnf(t9814,plain,
true = leq(sFlat2,multiplication(sFlat4,sK2_goals_X0)),
inference(step,[status(thm)],[t9813,t172]) ).
cnf(t9815,plain,
true = leq(sFlat2,sFlat5),
inference(step,[status(thm)],[t9814,t193]) ).
cnf(t9816,plain,
true = sFlat6,
inference(step,[status(thm)],[t9815,t231]) ).
cnf(t8392,plain,
true = sFlat6,
inference(orient,[status(thm)],[t9816]) ).
cnf(goal_0,negated_conjecture,
leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
leq(multiplication(sK2_goals_X0,strong_iteration(sFlat0)),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) != true,
inference(rw,[status(thm)],[goal_0,t73]) ).
cnf(g0_1,plain,
leq(multiplication(sK2_goals_X0,sFlat1),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) != true,
inference(rw,[status(thm)],[g0_0,t177]) ).
cnf(g0_2,plain,
leq(sFlat2,multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) != true,
inference(rw,[status(thm)],[g0_1,t204]) ).
cnf(g0_3,plain,
leq(sFlat2,multiplication(strong_iteration(sFlat3),sK2_goals_X0)) != true,
inference(rw,[status(thm)],[g0_2,t59]) ).
cnf(g0_4,plain,
leq(sFlat2,multiplication(sFlat4,sK2_goals_X0)) != true,
inference(rw,[status(thm)],[g0_3,t172]) ).
cnf(g0_5,plain,
leq(sFlat2,sFlat5) != true,
inference(rw,[status(thm)],[g0_4,t193]) ).
cnf(g0_6,plain,
sFlat6 != true,
inference(rw,[status(thm)],[g0_5,t231]) ).
cnf(g0_7,plain,
sFlat6 != sFlat6,
inference(rw,[status(thm)],[g0_6,t8392]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE151-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.41 % Computer : n009.cluster.edu
% 0.08/5.41 % Model : x86_64 x86_64
% 0.08/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.41 % Memory : 8046.5625MB
% 0.08/5.41 % OS : Linux 6.8.0-71-generic
% 0.08/5.41 % CPULimit : 300
% 0.08/5.41 % WCLimit : 300
% 0.08/5.41 % DateTime : Wed Sep 23 19:06:34 UTC 2026
% 0.08/5.41 % CPUTime :
% 0.08/5.41 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 46.25/12.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.25/12.19 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------