%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP659-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 01:27:56 PM UTC 2026
% Result : Unsatisfiable 3.33s 0.82s
% Output : CNFRefutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 8
% Syntax : Number of clauses : 99 ( 99 unt; 0 nHn; 6 RR)
% Number of literals : 99 ( 98 equ; 3 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 : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 203 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(eg0,negated_conjecture,
tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t6,plain,
eq(tuple(mult(X1,x1(X1)),mult(x1_2(X1),X1)),tuple(x1(X1),x1_2(X1))) = efalse,
inference(equality_encoding,[status(esa)],[eg0]) ).
cnf(t22,plain,
eq(tuple(mult(X1,x1(X1)),mult(x1_2(X1),X1)),tuple(x1(X1),x1_2(X1))) = efalse,
inference(orient,[status(thm)],[t6]) ).
cnf(t4,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t2,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t10,plain,
X1 = rd(X2,ld(X1,X2)),
inference(cp,[status(thm)],[t9,t7]) ).
cnf(t23,plain,
rd(X1,ld(X2,X1)) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t1,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t11,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t5,axiom,
mult(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),mult(X3,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t13,plain,
mult(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),mult(X3,X2)),
inference(orient,[status(thm)],[t5]) ).
cnf(t15,plain,
mult(mult(X1,X2),mult(ld(X2,X3),X2)) = mult(mult(X1,X3),X2),
inference(cp,[status(thm)],[t13,t7]) ).
cnf(t25,plain,
mult(mult(X1,X2),mult(ld(X2,X3),X2)) = mult(mult(X1,X3),X2),
inference(orient,[status(thm)],[t15]) ).
cnf(t30,plain,
mult(ld(X1,X2),X1) = ld(mult(X3,X1),mult(mult(X3,X2),X1)),
inference(cp,[status(thm)],[t11,t25]) ).
cnf(t123,plain,
ld(mult(X1,X2),mult(mult(X1,X3),X2)) = mult(ld(X2,X3),X2),
inference(orient,[status(thm)],[t30]) ).
cnf(t136,plain,
mult(ld(X1,ld(X2,X3)),X1) = ld(mult(X2,X1),mult(X3,X1)),
inference(cp,[status(thm)],[t123,t7]) ).
cnf(t145,plain,
ld(mult(X1,X2),mult(X3,X2)) = mult(ld(X2,ld(X1,X3)),X2),
inference(orient,[status(thm)],[t136]) ).
cnf(t3,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,plain,
mult(rd(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t153,plain,
mult(ld(X1,ld(rd(X2,X1),X3)),X1) = ld(X2,mult(X3,X1)),
inference(cp,[status(thm)],[t145,t8]) ).
cnf(t211,plain,
mult(ld(X1,ld(rd(X2,X1),X3)),X1) = ld(X2,mult(X3,X1)),
inference(orient,[status(thm)],[t153]) ).
cnf(t222,plain,
ld(X1,ld(rd(X2,X1),X3)) = rd(ld(X2,mult(X3,X1)),X1),
inference(cp,[status(thm)],[t9,t211]) ).
cnf(t232,plain,
ld(X1,ld(rd(X2,X1),X3)) = rd(ld(X2,mult(X3,X1)),X1),
inference(orient,[status(thm)],[t222]) ).
cnf(t239,plain,
ld(rd(X1,X2),X3) = mult(X2,rd(ld(X1,mult(X3,X2)),X2)),
inference(cp,[status(thm)],[t7,t232]) ).
cnf(t379,plain,
mult(X1,rd(ld(X2,mult(X3,X1)),X1)) = ld(rd(X2,X1),X3),
inference(orient,[status(thm)],[t239]) ).
cnf(t12,plain,
X1 = ld(rd(X2,X1),X2),
inference(cp,[status(thm)],[t11,t8]) ).
cnf(t24,plain,
ld(rd(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t380,plain,
ld(rd(rd(mult(X1,X2),X3),X2),X1) = mult(X2,rd(X3,X2)),
inference(cp,[status(thm)],[t379,t24]) ).
cnf(t407,plain,
ld(rd(rd(mult(X1,X2),X3),X2),X1) = mult(X2,rd(X3,X2)),
inference(orient,[status(thm)],[t380]) ).
cnf(t28,plain,
mult(mult(rd(X1,X2),X3),X2) = mult(X1,mult(ld(X2,X3),X2)),
inference(cp,[status(thm)],[t25,t8]) ).
cnf(t35,plain,
mult(mult(rd(X1,X2),X3),X2) = mult(X1,mult(ld(X2,X3),X2)),
inference(orient,[status(thm)],[t28]) ).
cnf(t37,plain,
mult(X1,mult(ld(X2,X2),X2)) = mult(X1,X2),
inference(cp,[status(thm)],[t35,t8]) ).
cnf(t45,plain,
mult(X1,mult(ld(X2,X2),X2)) = mult(X1,X2),
inference(orient,[status(thm)],[t37]) ).
cnf(t49,plain,
mult(ld(X1,X1),X1) = ld(X2,mult(X2,X1)),
inference(cp,[status(thm)],[t11,t45]) ).
cnf(t974,plain,
mult(ld(X1,X1),X1) = X1,
inference(step,[status(thm)],[t49,t11]) ).
cnf(t58,plain,
mult(ld(X1,X1),X1) = X1,
inference(orient,[status(thm)],[t974]) ).
cnf(t60,plain,
ld(X1,X1) = rd(X1,X1),
inference(cp,[status(thm)],[t9,t58]) ).
cnf(t64,plain,
ld(X1,X1) = rd(X1,X1),
inference(orient,[status(thm)],[t60]) ).
cnf(t146,plain,
mult(ld(X1,ld(X2,X2)),X1) = rd(mult(X2,X1),mult(X2,X1)),
inference(cp,[status(thm)],[t145,t64]) ).
cnf(t975,plain,
mult(ld(X1,rd(X2,X2)),X1) = rd(mult(X2,X1),mult(X2,X1)),
inference(step,[status(thm)],[t146,t64]) ).
cnf(t165,plain,
mult(ld(X1,rd(X2,X2)),X1) = rd(mult(X2,X1),mult(X2,X1)),
inference(orient,[status(thm)],[t975]) ).
cnf(t172,plain,
ld(X1,rd(X2,X2)) = rd(rd(mult(X2,X1),mult(X2,X1)),X1),
inference(cp,[status(thm)],[t9,t165]) ).
cnf(t277,plain,
rd(rd(mult(X1,X2),mult(X1,X2)),X2) = ld(X2,rd(X1,X1)),
inference(orient,[status(thm)],[t172]) ).
cnf(t408,plain,
mult(X1,rd(mult(X2,X1),X1)) = ld(ld(X1,rd(X2,X2)),X2),
inference(cp,[status(thm)],[t407,t277]) ).
cnf(t979,plain,
mult(X1,X2) = ld(ld(X1,rd(X2,X2)),X2),
inference(step,[status(thm)],[t408,t9]) ).
cnf(t428,plain,
ld(ld(X1,rd(X2,X2)),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t979]) ).
cnf(t434,plain,
ld(X1,rd(X2,X2)) = rd(X2,mult(X1,X2)),
inference(cp,[status(thm)],[t23,t428]) ).
cnf(t441,plain,
ld(X1,rd(X2,X2)) = rd(X2,mult(X1,X2)),
inference(orient,[status(thm)],[t434]) ).
cnf(t18,plain,
mult(X1,mult(X2,X3)) = rd(mult(mult(X1,X2),mult(X3,X2)),X2),
inference(cp,[status(thm)],[t9,t13]) ).
cnf(t73,plain,
rd(mult(mult(X1,X2),mult(X3,X2)),X2) = mult(X1,mult(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
cnf(t86,plain,
mult(X1,mult(X2,rd(X3,X2))) = rd(mult(mult(X1,X2),X3),X2),
inference(cp,[status(thm)],[t73,t8]) ).
cnf(t105,plain,
mult(X1,mult(X2,rd(X3,X2))) = rd(mult(mult(X1,X2),X3),X2),
inference(orient,[status(thm)],[t86]) ).
cnf(t113,plain,
mult(X1,rd(X2,X1)) = ld(X3,rd(mult(mult(X3,X1),X2),X1)),
inference(cp,[status(thm)],[t11,t105]) ).
cnf(t193,plain,
ld(X1,rd(mult(mult(X1,X2),X3),X2)) = mult(X2,rd(X3,X2)),
inference(orient,[status(thm)],[t113]) ).
cnf(t197,plain,
mult(X1,rd(ld(mult(X2,X1),X3),X1)) = ld(X2,rd(X3,X1)),
inference(cp,[status(thm)],[t193,t7]) ).
cnf(t300,plain,
mult(X1,rd(ld(mult(X2,X1),X3),X1)) = ld(X2,rd(X3,X1)),
inference(orient,[status(thm)],[t197]) ).
cnf(t311,plain,
ld(rd(X1,X2),rd(X3,X2)) = mult(X2,rd(ld(X1,X3),X2)),
inference(cp,[status(thm)],[t300,t8]) ).
cnf(t328,plain,
ld(rd(X1,X2),rd(X3,X2)) = mult(X2,rd(ld(X1,X3),X2)),
inference(orient,[status(thm)],[t311]) ).
cnf(t446,plain,
rd(X1,mult(rd(X2,X1),X1)) = mult(X1,rd(ld(X2,X1),X1)),
inference(cp,[status(thm)],[t441,t328]) ).
cnf(t985,plain,
rd(X1,X2) = mult(X1,rd(ld(X2,X1),X1)),
inference(step,[status(thm)],[t446,t8]) ).
cnf(t470,plain,
mult(X1,rd(ld(X2,X1),X1)) = rd(X1,X2),
inference(orient,[status(thm)],[t985]) ).
cnf(t478,plain,
rd(X1,rd(X1,X2)) = mult(X1,rd(X2,X1)),
inference(cp,[status(thm)],[t470,t24]) ).
cnf(t498,plain,
mult(X1,rd(X2,X1)) = rd(X1,rd(X1,X2)),
inference(orient,[status(thm)],[t478]) ).
cnf(t509,plain,
rd(X1,rd(X1,mult(X2,X1))) = mult(X1,X2),
inference(cp,[status(thm)],[t498,t9]) ).
cnf(t562,plain,
rd(X1,rd(X1,mult(X2,X1))) = mult(X1,X2),
inference(orient,[status(thm)],[t509]) ).
cnf(t448,plain,
rd(X1,X1) = mult(X2,rd(X1,mult(X2,X1))),
inference(cp,[status(thm)],[t7,t441]) ).
cnf(t531,plain,
mult(X1,rd(X2,mult(X1,X2))) = rd(X2,X2),
inference(orient,[status(thm)],[t448]) ).
cnf(t537,plain,
rd(X1,X1) = mult(rd(X2,X1),rd(X1,X2)),
inference(cp,[status(thm)],[t531,t8]) ).
cnf(t630,plain,
mult(rd(X1,X2),rd(X2,X1)) = rd(X2,X2),
inference(orient,[status(thm)],[t537]) ).
cnf(t646,plain,
rd(X1,X2) = rd(rd(X2,X2),rd(X2,X1)),
inference(cp,[status(thm)],[t9,t630]) ).
cnf(t790,plain,
rd(rd(X1,X1),rd(X1,X2)) = rd(X2,X1),
inference(orient,[status(thm)],[t646]) ).
cnf(t574,plain,
rd(X1,mult(X2,X1)) = ld(mult(X1,X2),X1),
inference(cp,[status(thm)],[t24,t562]) ).
cnf(t580,plain,
ld(mult(X1,X2),X1) = rd(X1,mult(X2,X1)),
inference(orient,[status(thm)],[t574]) ).
cnf(t583,plain,
rd(X1,mult(ld(X1,X2),X1)) = ld(X2,X1),
inference(cp,[status(thm)],[t580,t7]) ).
cnf(t657,plain,
rd(X1,mult(ld(X1,X2),X1)) = ld(X2,X1),
inference(orient,[status(thm)],[t583]) ).
cnf(t791,plain,
rd(mult(ld(X1,X2),X1),X1) = rd(rd(X1,X1),ld(X2,X1)),
inference(cp,[status(thm)],[t790,t657]) ).
cnf(t1001,plain,
ld(X1,X2) = rd(rd(X1,X1),ld(X2,X1)),
inference(step,[status(thm)],[t791,t9]) ).
cnf(t886,plain,
rd(rd(X1,X1),ld(X2,X1)) = ld(X1,X2),
inference(orient,[status(thm)],[t1001]) ).
cnf(t887,plain,
ld(rd(X1,X1),X2) = rd(rd(X1,X1),ld(X2,rd(X1,X1))),
inference(cp,[status(thm)],[t886,t790]) ).
cnf(t1002,plain,
ld(rd(X1,X1),X2) = X2,
inference(step,[status(thm)],[t887,t23]) ).
cnf(t909,plain,
ld(rd(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t1002]) ).
cnf(t916,plain,
mult(rd(X1,X1),X2) = X2,
inference(cp,[status(thm)],[t909,t11]) ).
cnf(t928,plain,
mult(rd(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t916]) ).
cnf(t938,plain,
mult(X1,rd(X2,X2)) = rd(X1,rd(X1,X1)),
inference(cp,[status(thm)],[t562,t928]) ).
cnf(t66,plain,
X1 = rd(X1,rd(X1,X1)),
inference(cp,[status(thm)],[t23,t64]) ).
cnf(t71,plain,
rd(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t66]) ).
cnf(t1003,plain,
mult(X1,rd(X2,X2)) = X1,
inference(step,[status(thm)],[t938,t71]) ).
cnf(t952,plain,
mult(X1,rd(X2,X2)) = X1,
inference(orient,[status(thm)],[t1003]) ).
cnf(t966,plain,
efalse = eq(tuple(mult(rd(X1,X1),x1(rd(X1,X1))),x1_2(rd(X1,X1))),tuple(x1(rd(X1,X1)),x1_2(rd(X1,X1)))),
inference(cp,[status(thm)],[t22,t952]) ).
cnf(t1004,plain,
efalse = eq(tuple(x1(rd(X1,X1)),x1_2(rd(X1,X1))),tuple(x1(rd(X1,X1)),x1_2(rd(X1,X1)))),
inference(step,[status(thm)],[t966,t928]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t21,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t1005,plain,
efalse = etrue,
inference(step,[status(thm)],[t1004,t21]) ).
cnf(t971,plain,
efalse = etrue,
inference(orient,[status(thm)],[t1005]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t971]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP659-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 15:34:38 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.33/0.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.33/0.82 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------