%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP656-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 5.23s 1.13s
% Output : CNFRefutation 5.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 6 RR)
% Number of literals : 39 ( 38 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 : 77 ( 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(t5,axiom,
mult(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),mult(X3,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t13,plain,
mult(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),mult(X3,X1)),
inference(orient,[status(thm)],[t5]) ).
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(t15,plain,
mult(mult(X1,X2),mult(ld(X2,X3),X1)) = mult(mult(X1,X3),X1),
inference(cp,[status(thm)],[t13,t7]) ).
cnf(t25,plain,
mult(mult(X1,X2),mult(ld(X2,X3),X1)) = mult(mult(X1,X3),X1),
inference(orient,[status(thm)],[t15]) ).
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(t26,plain,
mult(mult(X1,X2),X1) = mult(X3,mult(ld(ld(X1,X3),X2),X1)),
inference(cp,[status(thm)],[t25,t7]) ).
cnf(t89,plain,
mult(X1,mult(ld(ld(X2,X1),X3),X2)) = mult(mult(X2,X3),X2),
inference(orient,[status(thm)],[t26]) ).
cnf(t92,plain,
mult(ld(ld(X1,X2),X3),X1) = ld(X2,mult(mult(X1,X3),X1)),
inference(cp,[status(thm)],[t11,t89]) ).
cnf(t102,plain,
ld(X1,mult(mult(X2,X3),X2)) = mult(ld(ld(X2,X1),X3),X2),
inference(orient,[status(thm)],[t92]) ).
cnf(t103,plain,
mult(ld(ld(X1,mult(X1,X2)),X2),X1) = X1,
inference(cp,[status(thm)],[t102,t11]) ).
cnf(t160,plain,
mult(ld(X2,X2),X1) = X1,
inference(step,[status(thm)],[t103,t11]) ).
cnf(t119,plain,
mult(ld(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t160]) ).
cnf(t136,plain,
mult(mult(ld(X1,X1),X2),ld(X1,X1)) = mult(X3,mult(ld(X3,X2),ld(X1,X1))),
inference(cp,[status(thm)],[t25,t119]) ).
cnf(t161,plain,
mult(X2,ld(X1,X1)) = mult(X3,mult(ld(X3,X2),ld(X1,X1))),
inference(step,[status(thm)],[t136,t119]) ).
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(t18,plain,
mult(X1,mult(X2,X3)) = rd(mult(mult(X1,X2),mult(X3,X1)),X1),
inference(cp,[status(thm)],[t9,t13]) ).
cnf(t49,plain,
rd(mult(mult(X1,X2),mult(X3,X1)),X1) = mult(X1,mult(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
cnf(t50,plain,
mult(X1,mult(ld(X1,X2),X3)) = rd(mult(X2,mult(X3,X1)),X1),
inference(cp,[status(thm)],[t49,t7]) ).
cnf(t62,plain,
mult(X1,mult(ld(X1,X2),X3)) = rd(mult(X2,mult(X3,X1)),X1),
inference(orient,[status(thm)],[t50]) ).
cnf(t162,plain,
mult(X2,ld(X1,X1)) = rd(mult(X2,mult(ld(X1,X1),X3)),X3),
inference(step,[status(thm)],[t161,t62]) ).
cnf(t163,plain,
mult(X2,ld(X1,X1)) = rd(mult(X2,X3),X3),
inference(step,[status(thm)],[t162,t119]) ).
cnf(t164,plain,
mult(X2,ld(X1,X1)) = X2,
inference(step,[status(thm)],[t163,t9]) ).
cnf(t146,plain,
mult(X1,ld(X2,X2)) = X1,
inference(orient,[status(thm)],[t164]) ).
cnf(t156,plain,
efalse = eq(tuple(mult(ld(X1,X1),x1(ld(X1,X1))),x1_2(ld(X1,X1))),tuple(x1(ld(X1,X1)),x1_2(ld(X1,X1)))),
inference(cp,[status(thm)],[t22,t146]) ).
cnf(t165,plain,
efalse = eq(tuple(x1(ld(X1,X1)),x1_2(ld(X1,X1))),tuple(x1(ld(X1,X1)),x1_2(ld(X1,X1)))),
inference(step,[status(thm)],[t156,t119]) ).
cnf(t0,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t21,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t0]) ).
cnf(t166,plain,
efalse = etrue,
inference(step,[status(thm)],[t165,t21]) ).
cnf(t157,plain,
efalse = etrue,
inference(orient,[status(thm)],[t166]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t157]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP656-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n016.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 15:35:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.23/1.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.23/1.13 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------