%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP657-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 01:27:55 PM UTC 2026
% Result : Unsatisfiable 4.53s 1.12s
% Output : CNFRefutation 4.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 8 RR)
% Number of literals : 38 ( 37 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 : 61 ( 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/sandbox2/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(t23,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(t3,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t8,plain,
mult(rd(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t4,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t9,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t1,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t11,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t5,axiom,
mult(mult(X1,X2),mult(X3,X1)) = mult(X1,mult(mult(X2,X3),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t13,plain,
mult(mult(X1,X2),mult(X3,X1)) = mult(X1,mult(mult(X2,X3),X1)),
inference(orient,[status(thm)],[t5]) ).
cnf(t2,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t7,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t14,plain,
mult(X1,mult(mult(ld(X1,X2),X3),X1)) = mult(X2,mult(X3,X1)),
inference(cp,[status(thm)],[t13,t7]) ).
cnf(t26,plain,
mult(X1,mult(mult(ld(X1,X2),X3),X1)) = mult(X2,mult(X3,X1)),
inference(orient,[status(thm)],[t14]) ).
cnf(t31,plain,
mult(mult(ld(X1,X2),X3),X1) = ld(X1,mult(X2,mult(X3,X1))),
inference(cp,[status(thm)],[t11,t26]) ).
cnf(t34,plain,
ld(X1,mult(X2,mult(X3,X1))) = mult(mult(ld(X1,X2),X3),X1),
inference(orient,[status(thm)],[t31]) ).
cnf(t35,plain,
mult(mult(ld(X1,X1),X2),X1) = mult(X2,X1),
inference(cp,[status(thm)],[t34,t11]) ).
cnf(t45,plain,
mult(mult(ld(X1,X1),X2),X1) = mult(X2,X1),
inference(orient,[status(thm)],[t35]) ).
cnf(t51,plain,
mult(ld(X1,X1),X2) = rd(mult(X2,X1),X1),
inference(cp,[status(thm)],[t9,t45]) ).
cnf(t109,plain,
mult(ld(X1,X1),X2) = X2,
inference(step,[status(thm)],[t51,t9]) ).
cnf(t54,plain,
mult(ld(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t109]) ).
cnf(t60,plain,
ld(X1,X1) = rd(X2,X2),
inference(cp,[status(thm)],[t9,t54]) ).
cnf(t68,plain,
ld(X1,X1) = rd(X2,X2),
inference(orient,[status(thm)],[t60]) ).
cnf(t74,plain,
X1 = mult(ld(X2,X2),X1),
inference(cp,[status(thm)],[t8,t68]) ).
cnf(t111,plain,
X1 = mult(rd(etrue,etrue),X1),
inference(step,[status(thm)],[t74,t68]) ).
cnf(t99,plain,
mult(rd(etrue,etrue),X1) = X1,
inference(orient,[status(thm)],[t111]) ).
cnf(t105,plain,
efalse = eq(tuple(x1(rd(etrue,etrue)),mult(x1_2(rd(etrue,etrue)),rd(etrue,etrue))),tuple(x1(rd(etrue,etrue)),x1_2(rd(etrue,etrue)))),
inference(cp,[status(thm)],[t23,t99]) ).
cnf(t69,plain,
X1 = mult(X1,rd(X2,X2)),
inference(cp,[status(thm)],[t7,t68]) ).
cnf(t78,plain,
mult(X1,rd(X2,X2)) = X1,
inference(orient,[status(thm)],[t69]) ).
cnf(t112,plain,
efalse = eq(tuple(x1(rd(etrue,etrue)),x1_2(rd(etrue,etrue))),tuple(x1(rd(etrue,etrue)),x1_2(rd(etrue,etrue)))),
inference(step,[status(thm)],[t105,t78]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t22,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t113,plain,
efalse = etrue,
inference(step,[status(thm)],[t112,t22]) ).
cnf(t106,plain,
efalse = etrue,
inference(orient,[status(thm)],[t113]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t106]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP657-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 15:31:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.53/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.53/1.12 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------