%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP201-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 01:25:40 PM UTC 2026
% Result : Unsatisfiable 9.90s 2.14s
% Output : CNFRefutation 9.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 9
% Syntax : Number of clauses : 123 ( 123 unt; 0 nHn; 4 RR)
% Number of literals : 123 ( 122 equ; 3 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 248 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
multiply(multiply(multiply(X1,X2),X3),X2) = multiply(X1,multiply(X2,multiply(X3,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t23,plain,
multiply(multiply(multiply(X1,X2),X3),X2) = multiply(X1,multiply(X2,multiply(X3,X2))),
inference(orient,[status(thm)],[t8]) ).
cnf(t1,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t11,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t28,plain,
multiply(identity,multiply(X1,multiply(X2,X1))) = multiply(multiply(X1,X2),X1),
inference(cp,[status(thm)],[t23,t11]) ).
cnf(t9749,plain,
multiply(X1,multiply(X2,X1)) = multiply(multiply(X1,X2),X1),
inference(step,[status(thm)],[t28,t11]) ).
cnf(t83,plain,
multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)),
inference(orient,[status(thm)],[t9749]) ).
cnf(t7,axiom,
right_division(multiply(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t15,plain,
right_division(multiply(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t5,axiom,
multiply(X1,left_division(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
multiply(X1,left_division(X1,X2)) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t16,plain,
X1 = right_division(X2,left_division(X1,X2)),
inference(cp,[status(thm)],[t15,t9]) ).
cnf(t54,plain,
right_division(X1,left_division(X2,X1)) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t4,axiom,
left_division(X1,multiply(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
left_division(X1,multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t2,axiom,
multiply(X1,right_inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t33,plain,
multiply(X1,right_inverse(X1)) = identity,
inference(orient,[status(thm)],[t2]) ).
cnf(t84,plain,
multiply(X1,multiply(right_inverse(X1),X1)) = multiply(identity,X1),
inference(cp,[status(thm)],[t83,t33]) ).
cnf(t9750,plain,
multiply(X1,multiply(right_inverse(X1),X1)) = X1,
inference(step,[status(thm)],[t84,t11]) ).
cnf(t98,plain,
multiply(X1,multiply(right_inverse(X1),X1)) = X1,
inference(orient,[status(thm)],[t9750]) ).
cnf(t102,plain,
multiply(right_inverse(X1),X1) = left_division(X1,X1),
inference(cp,[status(thm)],[t19,t98]) ).
cnf(t0,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t10,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t20,plain,
identity = left_division(X1,X1),
inference(cp,[status(thm)],[t19,t10]) ).
cnf(t49,plain,
left_division(X1,X1) = identity,
inference(orient,[status(thm)],[t20]) ).
cnf(t9751,plain,
multiply(right_inverse(X1),X1) = identity,
inference(step,[status(thm)],[t102,t49]) ).
cnf(t106,plain,
multiply(right_inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t9751]) ).
cnf(t111,plain,
multiply(right_inverse(X1),multiply(X1,multiply(X2,X1))) = multiply(multiply(identity,X2),X1),
inference(cp,[status(thm)],[t23,t106]) ).
cnf(t9783,plain,
multiply(right_inverse(X1),multiply(X1,multiply(X2,X1))) = multiply(X2,X1),
inference(step,[status(thm)],[t111,t11]) ).
cnf(t468,plain,
multiply(right_inverse(X1),multiply(X1,multiply(X2,X1))) = multiply(X2,X1),
inference(orient,[status(thm)],[t9783]) ).
cnf(t6,axiom,
multiply(right_division(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t13,plain,
multiply(right_division(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t483,plain,
multiply(right_division(X1,X2),X2) = multiply(right_inverse(X2),multiply(X2,X1)),
inference(cp,[status(thm)],[t468,t13]) ).
cnf(t9784,plain,
X1 = multiply(right_inverse(X2),multiply(X2,X1)),
inference(step,[status(thm)],[t483,t13]) ).
cnf(t496,plain,
multiply(right_inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t9784]) ).
cnf(t503,plain,
left_division(X1,X2) = multiply(right_inverse(X1),X2),
inference(cp,[status(thm)],[t496,t9]) ).
cnf(t520,plain,
multiply(right_inverse(X1),X2) = left_division(X1,X2),
inference(orient,[status(thm)],[t503]) ).
cnf(t109,plain,
X1 = left_division(right_inverse(X1),identity),
inference(cp,[status(thm)],[t19,t106]) ).
cnf(t35,plain,
right_inverse(X1) = left_division(X1,identity),
inference(cp,[status(thm)],[t19,t33]) ).
cnf(t50,plain,
left_division(X1,identity) = right_inverse(X1),
inference(orient,[status(thm)],[t35]) ).
cnf(t9761,plain,
X1 = right_inverse(right_inverse(X1)),
inference(step,[status(thm)],[t109,t50]) ).
cnf(t121,plain,
right_inverse(right_inverse(X1)) = X1,
inference(orient,[status(thm)],[t9761]) ).
cnf(t527,plain,
left_division(right_inverse(X1),X2) = multiply(X1,X2),
inference(cp,[status(thm)],[t520,t121]) ).
cnf(t545,plain,
left_division(right_inverse(X1),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t527]) ).
cnf(t550,plain,
right_inverse(X1) = right_division(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t54,t545]) ).
cnf(t587,plain,
right_division(X1,multiply(X2,X1)) = right_inverse(X2),
inference(orient,[status(thm)],[t550]) ).
cnf(t26,plain,
multiply(X1,multiply(left_division(X1,X2),multiply(X3,left_division(X1,X2)))) = multiply(multiply(X2,X3),left_division(X1,X2)),
inference(cp,[status(thm)],[t23,t9]) ).
cnf(t1267,plain,
multiply(X1,multiply(left_division(X1,X2),multiply(X3,left_division(X1,X2)))) = multiply(multiply(X2,X3),left_division(X1,X2)),
inference(orient,[status(thm)],[t26]) ).
cnf(t1284,plain,
multiply(multiply(X1,X2),left_division(X2,X1)) = multiply(X2,multiply(left_division(X2,X1),X1)),
inference(cp,[status(thm)],[t1267,t9]) ).
cnf(t25,plain,
multiply(X1,multiply(X2,multiply(identity,X2))) = multiply(multiply(X1,X2),X2),
inference(cp,[status(thm)],[t23,t10]) ).
cnf(t9747,plain,
multiply(X1,multiply(X2,X2)) = multiply(multiply(X1,X2),X2),
inference(step,[status(thm)],[t25,t11]) ).
cnf(t56,plain,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
inference(orient,[status(thm)],[t9747]) ).
cnf(t534,plain,
multiply(right_inverse(X1),multiply(X2,X2)) = multiply(left_division(X1,X2),X2),
inference(cp,[status(thm)],[t56,t520]) ).
cnf(t9786,plain,
left_division(X1,multiply(X2,X2)) = multiply(left_division(X1,X2),X2),
inference(step,[status(thm)],[t534,t520]) ).
cnf(t601,plain,
left_division(X1,multiply(X2,X2)) = multiply(left_division(X1,X2),X2),
inference(orient,[status(thm)],[t9786]) ).
cnf(t606,plain,
multiply(X1,X1) = multiply(X2,multiply(left_division(X2,X1),X1)),
inference(cp,[status(thm)],[t9,t601]) ).
cnf(t699,plain,
multiply(X1,multiply(left_division(X1,X2),X2)) = multiply(X2,X2),
inference(orient,[status(thm)],[t606]) ).
cnf(t9797,plain,
multiply(multiply(X1,X2),left_division(X2,X1)) = multiply(X1,X1),
inference(step,[status(thm)],[t1284,t699]) ).
cnf(t1329,plain,
multiply(multiply(X1,X2),left_division(X2,X1)) = multiply(X1,X1),
inference(orient,[status(thm)],[t9797]) ).
cnf(t1365,plain,
right_inverse(multiply(X1,X2)) = right_division(left_division(X2,X1),multiply(X1,X1)),
inference(cp,[status(thm)],[t587,t1329]) ).
cnf(t62,plain,
multiply(right_division(X1,X2),multiply(X2,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t56,t13]) ).
cnf(t133,plain,
multiply(right_division(X1,X2),multiply(X2,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t62]) ).
cnf(t141,plain,
right_division(X1,X2) = right_division(multiply(X1,X2),multiply(X2,X2)),
inference(cp,[status(thm)],[t15,t133]) ).
cnf(t368,plain,
right_division(multiply(X1,X2),multiply(X2,X2)) = right_division(X1,X2),
inference(orient,[status(thm)],[t141]) ).
cnf(t528,plain,
right_division(right_inverse(X1),X2) = right_division(left_division(X1,X2),multiply(X2,X2)),
inference(cp,[status(thm)],[t368,t520]) ).
cnf(t868,plain,
right_division(left_division(X1,X2),multiply(X2,X2)) = right_division(right_inverse(X1),X2),
inference(orient,[status(thm)],[t528]) ).
cnf(t9806,plain,
right_inverse(multiply(X1,X2)) = right_division(right_inverse(X2),X1),
inference(step,[status(thm)],[t1365,t868]) ).
cnf(t1451,plain,
right_inverse(multiply(X1,X2)) = right_division(right_inverse(X2),X1),
inference(orient,[status(thm)],[t9806]) ).
cnf(t1465,plain,
right_division(right_inverse(X1),right_inverse(X2)) = right_inverse(left_division(X2,X1)),
inference(cp,[status(thm)],[t1451,t520]) ).
cnf(t1371,plain,
multiply(X1,X2) = right_division(multiply(X1,X1),left_division(X2,X1)),
inference(cp,[status(thm)],[t15,t1329]) ).
cnf(t536,plain,
right_inverse(X1) = right_division(left_division(X1,X2),X2),
inference(cp,[status(thm)],[t15,t520]) ).
cnf(t553,plain,
right_division(left_division(X1,X2),X2) = right_inverse(X1),
inference(orient,[status(thm)],[t536]) ).
cnf(t21,plain,
X1 = left_division(right_division(X2,X1),X2),
inference(cp,[status(thm)],[t19,t13]) ).
cnf(t55,plain,
left_division(right_division(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t21]) ).
cnf(t559,plain,
right_inverse(right_division(X1,X2)) = right_division(X2,X1),
inference(cp,[status(thm)],[t553,t55]) ).
cnf(t567,plain,
right_inverse(right_division(X1,X2)) = right_division(X2,X1),
inference(orient,[status(thm)],[t559]) ).
cnf(t377,plain,
right_division(right_division(X1,X2),X2) = right_division(X1,multiply(X2,X2)),
inference(cp,[status(thm)],[t368,t13]) ).
cnf(t383,plain,
right_division(right_division(X1,X2),X2) = right_division(X1,multiply(X2,X2)),
inference(orient,[status(thm)],[t377]) ).
cnf(t568,plain,
right_division(X1,right_division(X2,X1)) = right_inverse(right_division(X2,multiply(X1,X1))),
inference(cp,[status(thm)],[t567,t383]) ).
cnf(t9787,plain,
right_division(X1,right_division(X2,X1)) = right_division(multiply(X1,X1),X2),
inference(step,[status(thm)],[t568,t567]) ).
cnf(t610,plain,
right_division(multiply(X1,X1),X2) = right_division(X1,right_division(X2,X1)),
inference(orient,[status(thm)],[t9787]) ).
cnf(t9798,plain,
multiply(X1,X2) = right_division(X1,right_division(left_division(X2,X1),X1)),
inference(step,[status(thm)],[t1371,t610]) ).
cnf(t9799,plain,
multiply(X1,X2) = right_division(X1,right_inverse(X2)),
inference(step,[status(thm)],[t9798,t553]) ).
cnf(t1383,plain,
right_division(X1,right_inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t9799]) ).
cnf(t9811,plain,
multiply(right_inverse(X1),X2) = right_inverse(left_division(X2,X1)),
inference(step,[status(thm)],[t1465,t1383]) ).
cnf(t9812,plain,
left_division(X1,X2) = right_inverse(left_division(X2,X1)),
inference(step,[status(thm)],[t9811,t520]) ).
cnf(t1486,plain,
right_inverse(left_division(X1,X2)) = left_division(X2,X1),
inference(orient,[status(thm)],[t9812]) ).
cnf(t537,plain,
multiply(right_inverse(X1),multiply(X2,multiply(X3,X2))) = multiply(multiply(left_division(X1,X2),X3),X2),
inference(cp,[status(thm)],[t23,t520]) ).
cnf(t9878,plain,
left_division(X1,multiply(X2,multiply(X3,X2))) = multiply(multiply(left_division(X1,X2),X3),X2),
inference(step,[status(thm)],[t537,t520]) ).
cnf(t3170,plain,
left_division(X1,multiply(X2,multiply(X3,X2))) = multiply(multiply(left_division(X1,X2),X3),X2),
inference(orient,[status(thm)],[t9878]) ).
cnf(t3178,plain,
multiply(multiply(left_division(X1,right_inverse(X2)),X3),right_inverse(X2)) = left_division(X1,left_division(X2,multiply(X3,right_inverse(X2)))),
inference(cp,[status(thm)],[t3170,t520]) ).
cnf(t1395,plain,
multiply(X1,right_inverse(X2)) = right_division(X1,X2),
inference(cp,[status(thm)],[t1383,t121]) ).
cnf(t1408,plain,
multiply(X1,right_inverse(X2)) = right_division(X1,X2),
inference(orient,[status(thm)],[t1395]) ).
cnf(t9947,plain,
right_division(multiply(left_division(X1,right_inverse(X2)),X3),X2) = left_division(X1,left_division(X2,multiply(X3,right_inverse(X2)))),
inference(step,[status(thm)],[t3178,t1408]) ).
cnf(t1416,plain,
right_division(right_inverse(X1),X2) = left_division(X1,right_inverse(X2)),
inference(cp,[status(thm)],[t1408,t520]) ).
cnf(t1509,plain,
left_division(X1,right_inverse(X2)) = right_division(right_inverse(X1),X2),
inference(orient,[status(thm)],[t1416]) ).
cnf(t9948,plain,
right_division(multiply(right_division(right_inverse(X1),X2),X3),X2) = left_division(X1,left_division(X2,multiply(X3,right_inverse(X2)))),
inference(step,[status(thm)],[t9947,t1509]) ).
cnf(t573,plain,
multiply(right_division(X1,X2),X3) = left_division(right_division(X2,X1),X3),
inference(cp,[status(thm)],[t545,t567]) ).
cnf(t621,plain,
left_division(right_division(X1,X2),X3) = multiply(right_division(X2,X1),X3),
inference(orient,[status(thm)],[t573]) ).
cnf(t1398,plain,
multiply(right_division(right_inverse(X1),X2),X3) = left_division(multiply(X2,X1),X3),
inference(cp,[status(thm)],[t621,t1383]) ).
cnf(t2007,plain,
multiply(right_division(right_inverse(X1),X2),X3) = left_division(multiply(X2,X1),X3),
inference(orient,[status(thm)],[t1398]) ).
cnf(t9949,plain,
right_division(left_division(multiply(X2,X1),X3),X2) = left_division(X1,left_division(X2,multiply(X3,right_inverse(X2)))),
inference(step,[status(thm)],[t9948,t2007]) ).
cnf(t533,plain,
multiply(right_inverse(X1),multiply(X2,right_inverse(X1))) = multiply(left_division(X1,X2),right_inverse(X1)),
inference(cp,[status(thm)],[t83,t520]) ).
cnf(t9793,plain,
left_division(X1,multiply(X2,right_inverse(X1))) = multiply(left_division(X1,X2),right_inverse(X1)),
inference(step,[status(thm)],[t533,t520]) ).
cnf(t785,plain,
left_division(X1,multiply(X2,right_inverse(X1))) = multiply(left_division(X1,X2),right_inverse(X1)),
inference(orient,[status(thm)],[t9793]) ).
cnf(t9950,plain,
right_division(left_division(multiply(X2,X1),X3),X2) = left_division(X1,multiply(left_division(X2,X3),right_inverse(X2))),
inference(step,[status(thm)],[t9949,t785]) ).
cnf(t9951,plain,
right_division(left_division(multiply(X2,X1),X3),X2) = left_division(X1,right_division(left_division(X2,X3),X2)),
inference(step,[status(thm)],[t9950,t1408]) ).
cnf(t5775,plain,
left_division(X1,right_division(left_division(X2,X3),X2)) = right_division(left_division(multiply(X2,X1),X3),X2),
inference(orient,[status(thm)],[t9951]) ).
cnf(t5817,plain,
left_division(right_division(left_division(X1,X2),X1),X3) = right_inverse(right_division(left_division(multiply(X1,X3),X2),X1)),
inference(cp,[status(thm)],[t1486,t5775]) ).
cnf(t10021,plain,
multiply(right_division(X1,left_division(X1,X2)),X3) = right_inverse(right_division(left_division(multiply(X1,X3),X2),X1)),
inference(step,[status(thm)],[t5817,t621]) ).
cnf(t10022,plain,
multiply(right_division(X1,left_division(X1,X2)),X3) = right_division(X1,left_division(multiply(X1,X3),X2)),
inference(step,[status(thm)],[t10021,t567]) ).
cnf(t7884,plain,
multiply(right_division(X1,left_division(X1,X2)),X3) = right_division(X1,left_division(multiply(X1,X3),X2)),
inference(orient,[status(thm)],[t10022]) ).
cnf(t7905,plain,
right_division(X1,left_division(multiply(X1,X2),right_inverse(X3))) = multiply(right_division(X1,right_division(right_inverse(X1),X3)),X2),
inference(cp,[status(thm)],[t7884,t1509]) ).
cnf(t10072,plain,
right_division(X1,right_division(right_inverse(multiply(X1,X2)),X3)) = multiply(right_division(X1,right_division(right_inverse(X1),X3)),X2),
inference(step,[status(thm)],[t7905,t1509]) ).
cnf(t1476,plain,
multiply(X1,multiply(X2,X3)) = right_division(X1,right_division(right_inverse(X3),X2)),
inference(cp,[status(thm)],[t1383,t1451]) ).
cnf(t2039,plain,
right_division(X1,right_division(right_inverse(X2),X3)) = multiply(X1,multiply(X3,X2)),
inference(orient,[status(thm)],[t1476]) ).
cnf(t10073,plain,
multiply(X1,multiply(X3,multiply(X1,X2))) = multiply(right_division(X1,right_division(right_inverse(X1),X3)),X2),
inference(step,[status(thm)],[t10072,t2039]) ).
cnf(t10074,plain,
multiply(X1,multiply(X3,multiply(X1,X2))) = multiply(multiply(X1,multiply(X3,X1)),X2),
inference(step,[status(thm)],[t10073,t2039]) ).
cnf(t9620,plain,
multiply(multiply(X1,multiply(X2,X1)),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
inference(orient,[status(thm)],[t10074]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(multiply(a,multiply(b,a)),c) != multiply(a,multiply(b,multiply(a,c))),
inference(rw,[status(thm)],[goal_0,t83]) ).
cnf(g0_1,plain,
multiply(a,multiply(b,multiply(a,c))) != multiply(a,multiply(b,multiply(a,c))),
inference(rw,[status(thm)],[g0_0,t9620]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP201-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.38 % Computer : n011.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Wed Sep 23 14:07:26 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.90/2.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.90/2.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------