%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP751-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 01:28:20 PM UTC 2026
% Result : Unsatisfiable 63.51s 9.45s
% Output : CNFRefutation 63.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of clauses : 77 ( 77 unt; 0 nHn; 45 RR)
% Number of literals : 77 ( 76 equ; 7 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t7,axiom,
sF0 = rd(a,a),
introduced(definition) ).
cnf(t13,plain,
rd(a,a) = sF0,
inference(orient,[status(thm)],[t7]) ).
cnf(t8,axiom,
sF1 = mult(rd(a,a),b),
introduced(definition) ).
cnf(t22989,plain,
sF1 = mult(sF0,b),
inference(step,[status(thm)],[t8,t13]) ).
cnf(t34,plain,
mult(sF0,b) = sF1,
inference(orient,[status(thm)],[t22989]) ).
cnf(t9,axiom,
sF2 = mult(a,c),
introduced(definition) ).
cnf(t14,plain,
mult(a,c) = sF2,
inference(orient,[status(thm)],[t9]) ).
cnf(t10,axiom,
sF3 = mult(mult(rd(a,a),b),mult(a,c)),
introduced(definition) ).
cnf(t22991,plain,
sF3 = mult(mult(sF0,b),mult(a,c)),
inference(step,[status(thm)],[t10,t13]) ).
cnf(t22992,plain,
sF3 = mult(sF1,mult(a,c)),
inference(step,[status(thm)],[t22991,t34]) ).
cnf(t22993,plain,
sF3 = mult(sF1,sF2),
inference(step,[status(thm)],[t22992,t14]) ).
cnf(t296,plain,
mult(sF1,sF2) = sF3,
inference(orient,[status(thm)],[t22993]) ).
cnf(t11,axiom,
sF4 = mult(b,c),
introduced(definition) ).
cnf(t15,plain,
mult(b,c) = sF4,
inference(orient,[status(thm)],[t11]) ).
cnf(t12,axiom,
sF5 = mult(a,mult(b,c)),
introduced(definition) ).
cnf(t22990,plain,
sF5 = mult(a,sF4),
inference(step,[status(thm)],[t12,t15]) ).
cnf(t39,plain,
mult(a,sF4) = sF5,
inference(orient,[status(thm)],[t22990]) ).
cnf(t3,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t28,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t6,axiom,
mult(mult(X1,mult(X1,X1)),mult(X2,X3)) = mult(mult(X1,X2),mult(mult(X1,X1),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t189,plain,
mult(mult(X1,mult(X1,X1)),mult(X2,X3)) = mult(mult(X1,X2),mult(mult(X1,X1),X3)),
inference(orient,[status(thm)],[t6]) ).
cnf(t4,axiom,
mult(mult(X1,X2),mult(X1,X3)) = mult(mult(X1,X1),mult(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t46,plain,
mult(mult(X1,X2),mult(X1,X3)) = mult(mult(X1,X1),mult(X2,X3)),
inference(orient,[status(thm)],[t4]) ).
cnf(t50,plain,
mult(mult(b,b),mult(X1,c)) = mult(mult(b,X1),sF4),
inference(cp,[status(thm)],[t46,t15]) ).
cnf(t77,plain,
mult(mult(b,b),mult(X1,c)) = mult(mult(b,X1),sF4),
inference(orient,[status(thm)],[t50]) ).
cnf(t201,plain,
mult(mult(X1,mult(b,b)),mult(mult(X1,X1),mult(X2,c))) = mult(mult(X1,mult(X1,X1)),mult(mult(b,X2),sF4)),
inference(cp,[status(thm)],[t189,t77]) ).
cnf(t22701,plain,
mult(mult(X1,mult(b,b)),mult(mult(X1,X1),mult(X2,c))) = mult(mult(X1,mult(X1,X1)),mult(mult(b,X2),sF4)),
inference(orient,[status(thm)],[t201]) ).
cnf(t5,axiom,
mult(mult(X1,X2),mult(X3,X3)) = mult(mult(X1,X3),mult(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t113,plain,
mult(mult(X1,X2),mult(X3,X3)) = mult(mult(X1,X3),mult(X2,X3)),
inference(orient,[status(thm)],[t5]) ).
cnf(t1,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t21,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t116,plain,
mult(mult(X1,X2),mult(ld(X1,X3),X2)) = mult(X3,mult(X2,X2)),
inference(cp,[status(thm)],[t113,t21]) ).
cnf(t1984,plain,
mult(mult(X1,X2),mult(ld(X1,X3),X2)) = mult(X3,mult(X2,X2)),
inference(orient,[status(thm)],[t116]) ).
cnf(t1985,plain,
mult(X1,mult(c,c)) = mult(sF2,mult(ld(a,X1),c)),
inference(cp,[status(thm)],[t1984,t14]) ).
cnf(t2108,plain,
mult(sF2,mult(ld(a,X1),c)) = mult(X1,mult(c,c)),
inference(orient,[status(thm)],[t1985]) ).
cnf(t0,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t16,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t2109,plain,
mult(mult(a,X1),mult(c,c)) = mult(sF2,mult(X1,c)),
inference(cp,[status(thm)],[t2108,t16]) ).
cnf(t2377,plain,
mult(mult(a,X1),mult(c,c)) = mult(sF2,mult(X1,c)),
inference(orient,[status(thm)],[t2109]) ).
cnf(t22719,plain,
mult(mult(a,mult(a,a)),mult(mult(b,c),sF4)) = mult(mult(a,mult(b,b)),mult(sF2,mult(a,c))),
inference(cp,[status(thm)],[t22701,t2377]) ).
cnf(t23108,plain,
mult(mult(a,mult(b,c)),mult(mult(a,a),sF4)) = mult(mult(a,mult(b,b)),mult(sF2,mult(a,c))),
inference(step,[status(thm)],[t22719,t189]) ).
cnf(t23109,plain,
mult(mult(a,sF4),mult(mult(a,a),sF4)) = mult(mult(a,mult(b,b)),mult(sF2,mult(a,c))),
inference(step,[status(thm)],[t23108,t15]) ).
cnf(t23110,plain,
mult(sF5,mult(mult(a,a),sF4)) = mult(mult(a,mult(b,b)),mult(sF2,mult(a,c))),
inference(step,[status(thm)],[t23109,t39]) ).
cnf(t48,plain,
mult(mult(a,a),mult(X1,c)) = mult(mult(a,X1),sF2),
inference(cp,[status(thm)],[t46,t14]) ).
cnf(t65,plain,
mult(mult(a,a),mult(X1,c)) = mult(mult(a,X1),sF2),
inference(orient,[status(thm)],[t48]) ).
cnf(t66,plain,
mult(mult(a,b),sF2) = mult(mult(a,a),sF4),
inference(cp,[status(thm)],[t65,t15]) ).
cnf(t72,plain,
mult(mult(a,a),sF4) = mult(mult(a,b),sF2),
inference(orient,[status(thm)],[t66]) ).
cnf(t23111,plain,
mult(sF5,mult(mult(a,b),sF2)) = mult(mult(a,mult(b,b)),mult(sF2,mult(a,c))),
inference(step,[status(thm)],[t23110,t72]) ).
cnf(t2,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t22,plain,
mult(rd(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t23,plain,
a = mult(sF0,a),
inference(cp,[status(thm)],[t22,t13]) ).
cnf(t25,plain,
mult(sF0,a) = a,
inference(orient,[status(thm)],[t23]) ).
cnf(t118,plain,
mult(mult(sF0,X1),mult(a,X1)) = mult(a,mult(X1,X1)),
inference(cp,[status(thm)],[t113,t25]) ).
cnf(t259,plain,
mult(mult(sF0,X1),mult(a,X1)) = mult(a,mult(X1,X1)),
inference(orient,[status(thm)],[t118]) ).
cnf(t263,plain,
mult(a,mult(b,b)) = mult(sF1,mult(a,b)),
inference(cp,[status(thm)],[t259,t34]) ).
cnf(t279,plain,
mult(a,mult(b,b)) = mult(sF1,mult(a,b)),
inference(orient,[status(thm)],[t263]) ).
cnf(t23112,plain,
mult(sF5,mult(mult(a,b),sF2)) = mult(mult(sF1,mult(a,b)),mult(sF2,mult(a,c))),
inference(step,[status(thm)],[t23111,t279]) ).
cnf(t23113,plain,
mult(sF5,mult(mult(a,b),sF2)) = mult(mult(sF1,mult(a,b)),mult(sF2,sF2)),
inference(step,[status(thm)],[t23112,t14]) ).
cnf(t2020,plain,
mult(X1,mult(sF2,sF2)) = mult(sF3,mult(ld(sF1,X1),sF2)),
inference(cp,[status(thm)],[t1984,t296]) ).
cnf(t2247,plain,
mult(sF3,mult(ld(sF1,X1),sF2)) = mult(X1,mult(sF2,sF2)),
inference(orient,[status(thm)],[t2020]) ).
cnf(t2248,plain,
mult(mult(sF1,X1),mult(sF2,sF2)) = mult(sF3,mult(X1,sF2)),
inference(cp,[status(thm)],[t2247,t16]) ).
cnf(t2541,plain,
mult(mult(sF1,X1),mult(sF2,sF2)) = mult(sF3,mult(X1,sF2)),
inference(orient,[status(thm)],[t2248]) ).
cnf(t23114,plain,
mult(sF5,mult(mult(a,b),sF2)) = mult(sF3,mult(mult(a,b),sF2)),
inference(step,[status(thm)],[t23113,t2541]) ).
cnf(t22802,plain,
mult(sF5,mult(mult(a,b),sF2)) = mult(sF3,mult(mult(a,b),sF2)),
inference(orient,[status(thm)],[t23114]) ).
cnf(t22804,plain,
sF5 = rd(mult(sF3,mult(mult(a,b),sF2)),mult(mult(a,b),sF2)),
inference(cp,[status(thm)],[t28,t22802]) ).
cnf(t23115,plain,
sF5 = sF3,
inference(step,[status(thm)],[t22804,t28]) ).
cnf(t22843,plain,
sF5 = sF3,
inference(orient,[status(thm)],[t23115]) ).
cnf(t23116,plain,
mult(a,sF4) = sF3,
inference(step,[status(thm)],[t39,t22843]) ).
cnf(t22844,plain,
mult(a,sF4) = sF3,
inference(orient,[status(thm)],[t23116]) ).
cnf(goal_0,negated_conjecture,
mult(mult(rd(a,a),b),mult(a,c)) != mult(a,mult(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
mult(mult(sF0,b),mult(a,c)) != mult(a,mult(b,c)),
inference(rw,[status(thm)],[goal_0,t13]) ).
cnf(g0_1,plain,
mult(sF1,mult(a,c)) != mult(a,mult(b,c)),
inference(rw,[status(thm)],[g0_0,t34]) ).
cnf(g0_2,plain,
mult(sF1,sF2) != mult(a,mult(b,c)),
inference(rw,[status(thm)],[g0_1,t14]) ).
cnf(g0_3,plain,
sF3 != mult(a,mult(b,c)),
inference(rw,[status(thm)],[g0_2,t296]) ).
cnf(g0_4,plain,
sF3 != mult(a,sF4),
inference(rw,[status(thm)],[g0_3,t15]) ).
cnf(g0_5,plain,
sF3 != sF3,
inference(rw,[status(thm)],[g0_4,t22844]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP751-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 15:59:54 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 63.51/9.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.51/9.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------