%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 01:28:02 PM UTC 2026
% Result : Unsatisfiable 4.38s 6.32s
% Output : CNFRefutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 3 RR)
% Number of literals : 51 ( 50 equ; 2 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t6,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t9,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
inference(orient,[status(thm)],[t6]) ).
cnf(t1,axiom,
rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t7,plain,
rd(mult(X1,X1),X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t10,plain,
mult(X1,rd(mult(X2,X3),X3)) = rd(mult(mult(X1,X2),X3),rd(mult(X3,X3),X3)),
inference(cp,[status(thm)],[t9,t7]) ).
cnf(t190,plain,
mult(X1,rd(mult(X2,X3),X3)) = rd(mult(mult(X1,X2),X3),X3),
inference(step,[status(thm)],[t10,t7]) ).
cnf(t57,plain,
mult(X1,rd(mult(X2,X3),X3)) = rd(mult(mult(X1,X2),X3),X3),
inference(orient,[status(thm)],[t190]) ).
cnf(t191,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = rd(mult(mult(X1,X2),X4),X4),
inference(step,[status(thm)],[t9,t57]) ).
cnf(t58,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = rd(mult(mult(X1,X2),X4),X4),
inference(orient,[status(thm)],[t191]) ).
cnf(t3,axiom,
rd(mult(X1,X2),X2) = mult(rd(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t16,plain,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
inference(orient,[status(thm)],[t3]) ).
cnf(t4,axiom,
rd(mult(rd(X1,X1),X2),X2) = ld(X1,mult(X1,ld(X2,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t2,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t14,plain,
ld(X1,mult(X1,X2)) = mult(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t2]) ).
cnf(t183,plain,
rd(mult(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(step,[status(thm)],[t4,t14]) ).
cnf(t29,plain,
mult(X1,ld(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(orient,[status(thm)],[t183]) ).
cnf(t0,axiom,
ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t8,plain,
ld(X1,mult(X1,X1)) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t180,plain,
mult(X1,ld(X1,X1)) = X1,
inference(step,[status(thm)],[t8,t14]) ).
cnf(t15,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[t180]) ).
cnf(t33,plain,
mult(X1,ld(X1,X1)) = X1,
inference(orient,[status(thm)],[t15]) ).
cnf(t35,plain,
mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
inference(cp,[status(thm)],[t14,t33]) ).
cnf(t184,plain,
rd(mult(rd(X1,X1),X1),X1) = ld(X1,X1),
inference(step,[status(thm)],[t35,t29]) ).
cnf(t185,plain,
rd(rd(mult(X1,X1),X1),X1) = ld(X1,X1),
inference(step,[status(thm)],[t184,t16]) ).
cnf(t186,plain,
rd(X1,X1) = ld(X1,X1),
inference(step,[status(thm)],[t185,t7]) ).
cnf(t38,plain,
ld(X1,X1) = rd(X1,X1),
inference(orient,[status(thm)],[t186]) ).
cnf(t188,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(step,[status(thm)],[t29,t38]) ).
cnf(t42,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(rw,[status(thm)],[t188]) ).
cnf(t86,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(orient,[status(thm)],[t42]) ).
cnf(t87,plain,
rd(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1) = mult(rd(X1,X1),rd(rd(X1,X1),rd(X1,X1))),
inference(cp,[status(thm)],[t86,t38]) ).
cnf(t187,plain,
mult(X1,rd(X1,X1)) = X1,
inference(step,[status(thm)],[t33,t38]) ).
cnf(t41,plain,
mult(X1,rd(X1,X1)) = X1,
inference(rw,[status(thm)],[t187]) ).
cnf(t43,plain,
mult(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t41]) ).
cnf(t195,plain,
rd(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1) = rd(X1,X1),
inference(step,[status(thm)],[t87,t43]) ).
cnf(t109,plain,
rd(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1) = rd(X1,X1),
inference(orient,[status(thm)],[t195]) ).
cnf(t111,plain,
rd(mult(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1),X1) = mult(rd(X1,X1),X1),
inference(cp,[status(thm)],[t16,t109]) ).
cnf(t61,plain,
rd(mult(mult(X1,X2),X2),X2) = mult(X1,X2),
inference(cp,[status(thm)],[t57,t7]) ).
cnf(t75,plain,
rd(mult(mult(X1,X2),X2),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t61]) ).
cnf(t196,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = mult(rd(X1,X1),X1),
inference(step,[status(thm)],[t111,t75]) ).
cnf(t197,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = rd(mult(X1,X1),X1),
inference(step,[status(thm)],[t196,t16]) ).
cnf(t198,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = X1,
inference(step,[status(thm)],[t197,t7]) ).
cnf(t115,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = X1,
inference(orient,[status(thm)],[t198]) ).
cnf(t118,plain,
rd(mult(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X2),X2) = rd(mult(X1,rd(X3,X2)),rd(X3,X2)),
inference(cp,[status(thm)],[t58,t115]) ).
cnf(t201,plain,
rd(mult(X1,X2),X2) = rd(mult(X1,rd(X3,X2)),rd(X3,X2)),
inference(step,[status(thm)],[t118,t115]) ).
cnf(t128,plain,
rd(mult(X1,rd(X2,X3)),rd(X2,X3)) = rd(mult(X1,X3),X3),
inference(orient,[status(thm)],[t201]) ).
cnf(t136,plain,
rd(mult(X1,X2),X2) = rd(mult(X1,mult(X3,X2)),rd(mult(mult(X3,X2),X2),X2)),
inference(cp,[status(thm)],[t128,t75]) ).
cnf(t203,plain,
rd(mult(X1,X2),X2) = rd(mult(X1,mult(X3,X2)),mult(X3,X2)),
inference(step,[status(thm)],[t136,t75]) ).
cnf(t163,plain,
rd(mult(X1,mult(X2,X3)),mult(X2,X3)) = rd(mult(X1,X3),X3),
inference(orient,[status(thm)],[t203]) ).
cnf(goal_0,negated_conjecture,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
rd(mult(a,c),c) != rd(mult(a,c),c),
inference(rw,[status(thm)],[goal_0,t163]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.59 % Computer : n017.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.59 % DateTime : Wed Sep 23 15:37:36 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.38/6.32 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.38/6.32 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------