%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP756-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 01:28:21 PM UTC 2026
% Result : Unsatisfiable 5.68s 6.18s
% Output : CNFRefutation 5.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 6
% Syntax : Number of clauses : 75 ( 75 unt; 0 nHn; 3 RR)
% Number of literals : 75 ( 74 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 180 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t4,axiom,
mult(mult(X1,X2),mult(X2,X3)) = mult(X1,mult(mult(X2,X2),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t11,plain,
mult(mult(X1,X2),mult(X2,X3)) = mult(X1,mult(mult(X2,X2),X3)),
inference(orient,[status(thm)],[t4]) ).
cnf(t2,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t6,plain,
mult(rd(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t13,plain,
mult(rd(X1,X2),mult(mult(X2,X2),X3)) = mult(X1,mult(X2,X3)),
inference(cp,[status(thm)],[t11,t6]) ).
cnf(t22,plain,
mult(rd(X1,X2),mult(mult(X2,X2),X3)) = mult(X1,mult(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t1,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t5,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t25,plain,
mult(X1,mult(X2,ld(mult(X2,X2),X3))) = mult(rd(X1,X2),X3),
inference(cp,[status(thm)],[t22,t5]) ).
cnf(t43,plain,
mult(X1,mult(X2,ld(mult(X2,X2),X3))) = mult(rd(X1,X2),X3),
inference(orient,[status(thm)],[t25]) ).
cnf(t49,plain,
mult(X1,mult(mult(X2,X2),mult(X3,ld(mult(X3,X3),Y3)))) = mult(mult(X1,X2),mult(rd(X2,X3),Y3)),
inference(cp,[status(thm)],[t11,t43]) ).
cnf(t1292,plain,
mult(X1,mult(rd(mult(X2,X2),X3),Y3)) = mult(mult(X1,X2),mult(rd(X2,X3),Y3)),
inference(step,[status(thm)],[t49,t43]) ).
cnf(t240,plain,
mult(mult(X1,X2),mult(rd(X2,X3),Y3)) = mult(X1,mult(rd(mult(X2,X2),X3),Y3)),
inference(orient,[status(thm)],[t1292]) ).
cnf(t0,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t9,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t250,plain,
mult(X1,mult(rd(mult(X2,X2),X3),X3)) = mult(mult(X1,X2),X2),
inference(cp,[status(thm)],[t240,t6]) ).
cnf(t1293,plain,
mult(X1,mult(X2,X2)) = mult(mult(X1,X2),X2),
inference(step,[status(thm)],[t250,t6]) ).
cnf(t290,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t1293]) ).
cnf(t300,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(cp,[status(thm)],[t290,t6]) ).
cnf(t324,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(orient,[status(thm)],[t300]) ).
cnf(t3,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t7,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t8,plain,
X1 = rd(X2,ld(X1,X2)),
inference(cp,[status(thm)],[t7,t5]) ).
cnf(t20,plain,
rd(X1,ld(X2,X1)) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t29,plain,
mult(mult(X1,X1),X2) = ld(rd(X3,X1),mult(X3,mult(X1,X2))),
inference(cp,[status(thm)],[t9,t22]) ).
cnf(t56,plain,
ld(rd(X1,X2),mult(X1,mult(X2,X3))) = mult(mult(X2,X2),X3),
inference(orient,[status(thm)],[t29]) ).
cnf(t60,plain,
mult(mult(X1,X1),X2) = ld(rd(rd(X3,mult(X1,X2)),X1),X3),
inference(cp,[status(thm)],[t56,t6]) ).
cnf(t69,plain,
ld(rd(rd(X1,mult(X2,X3)),X2),X1) = mult(mult(X2,X2),X3),
inference(orient,[status(thm)],[t60]) ).
cnf(t76,plain,
rd(rd(X1,mult(X2,X3)),X2) = rd(X1,mult(mult(X2,X2),X3)),
inference(cp,[status(thm)],[t20,t69]) ).
cnf(t78,plain,
rd(rd(X1,mult(X2,X3)),X2) = rd(X1,mult(mult(X2,X2),X3)),
inference(orient,[status(thm)],[t76]) ).
cnf(t87,plain,
rd(X1,mult(X2,X3)) = mult(rd(X1,mult(mult(X2,X2),X3)),X2),
inference(cp,[status(thm)],[t6,t78]) ).
cnf(t102,plain,
mult(rd(X1,mult(mult(X2,X2),X3)),X2) = rd(X1,mult(X2,X3)),
inference(orient,[status(thm)],[t87]) ).
cnf(t108,plain,
rd(X1,mult(X2,ld(mult(X2,X2),X3))) = mult(rd(X1,X3),X2),
inference(cp,[status(thm)],[t102,t5]) ).
cnf(t120,plain,
rd(X1,mult(X2,ld(mult(X2,X2),X3))) = mult(rd(X1,X3),X2),
inference(orient,[status(thm)],[t108]) ).
cnf(t327,plain,
mult(X1,mult(X2,ld(mult(X2,X2),X3))) = mult(mult(rd(X1,X3),X2),mult(mult(X2,ld(mult(X2,X2),X3)),mult(X2,ld(mult(X2,X2),X3)))),
inference(cp,[status(thm)],[t324,t120]) ).
cnf(t1301,plain,
mult(rd(X1,X2),X3) = mult(mult(rd(X1,X3),X2),mult(mult(X2,ld(mult(X2,X2),X3)),mult(X2,ld(mult(X2,X2),X3)))),
inference(step,[status(thm)],[t327,t43]) ).
cnf(t14,plain,
mult(X1,mult(mult(X2,X2),ld(X2,X3))) = mult(mult(X1,X2),X3),
inference(cp,[status(thm)],[t11,t5]) ).
cnf(t31,plain,
mult(X1,mult(mult(X2,X2),ld(X2,X3))) = mult(mult(X1,X2),X3),
inference(orient,[status(thm)],[t14]) ).
cnf(t37,plain,
mult(X1,mult(mult(X2,X2),mult(mult(X3,X3),ld(X3,Y3)))) = mult(mult(X1,X2),mult(mult(X2,X3),Y3)),
inference(cp,[status(thm)],[t11,t31]) ).
cnf(t1291,plain,
mult(X1,mult(mult(mult(X2,X2),X3),Y3)) = mult(mult(X1,X2),mult(mult(X2,X3),Y3)),
inference(step,[status(thm)],[t37,t31]) ).
cnf(t191,plain,
mult(mult(X1,X2),mult(mult(X2,X3),Y3)) = mult(X1,mult(mult(mult(X2,X2),X3),Y3)),
inference(orient,[status(thm)],[t1291]) ).
cnf(t1302,plain,
mult(rd(X1,X2),X3) = mult(rd(X1,X3),mult(mult(mult(X2,X2),ld(mult(X2,X2),X3)),mult(X2,ld(mult(X2,X2),X3)))),
inference(step,[status(thm)],[t1301,t191]) ).
cnf(t1303,plain,
mult(rd(X1,X2),X3) = mult(rd(X1,X3),mult(rd(mult(mult(X2,X2),ld(mult(X2,X2),X3)),X2),X3)),
inference(step,[status(thm)],[t1302,t43]) ).
cnf(t1304,plain,
mult(rd(X1,X2),X3) = mult(rd(X1,X3),mult(rd(X3,X2),X3)),
inference(step,[status(thm)],[t1303,t5]) ).
cnf(t789,plain,
mult(rd(X1,X2),mult(rd(X2,X3),X2)) = mult(rd(X1,X3),X2),
inference(orient,[status(thm)],[t1304]) ).
cnf(t306,plain,
mult(X1,X2) = rd(mult(X1,mult(X2,X2)),X2),
inference(cp,[status(thm)],[t7,t290]) ).
cnf(t352,plain,
rd(mult(X1,mult(X2,X2)),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t306]) ).
cnf(t361,plain,
mult(rd(X1,mult(X2,X2)),X2) = rd(X1,X2),
inference(cp,[status(thm)],[t352,t6]) ).
cnf(t434,plain,
mult(rd(X1,mult(X2,X2)),X2) = rd(X1,X2),
inference(orient,[status(thm)],[t361]) ).
cnf(t806,plain,
mult(rd(X1,mult(X2,X2)),X2) = mult(rd(X1,X2),rd(X2,X2)),
inference(cp,[status(thm)],[t789,t434]) ).
cnf(t1307,plain,
rd(X1,X2) = mult(rd(X1,X2),rd(X2,X2)),
inference(step,[status(thm)],[t806,t434]) ).
cnf(t890,plain,
mult(rd(X1,X2),rd(X2,X2)) = rd(X1,X2),
inference(orient,[status(thm)],[t1307]) ).
cnf(t897,plain,
rd(mult(X1,X2),X2) = mult(X1,rd(X2,X2)),
inference(cp,[status(thm)],[t890,t7]) ).
cnf(t1308,plain,
X1 = mult(X1,rd(X2,X2)),
inference(step,[status(thm)],[t897,t7]) ).
cnf(t927,plain,
mult(X1,rd(X2,X2)) = X1,
inference(orient,[status(thm)],[t1308]) ).
cnf(t932,plain,
rd(X1,X1) = ld(X2,X2),
inference(cp,[status(thm)],[t9,t927]) ).
cnf(t946,plain,
rd(X1,X1) = ld(X2,X2),
inference(orient,[status(thm)],[t932]) ).
cnf(t959,plain,
X1 = mult(ld(X2,X2),X1),
inference(cp,[status(thm)],[t6,t946]) ).
cnf(t1310,plain,
X1 = mult(rd(c,c),X1),
inference(step,[status(thm)],[t959,t946]) ).
cnf(t992,plain,
mult(rd(c,c),X1) = X1,
inference(orient,[status(thm)],[t1310]) ).
cnf(t10,plain,
X1 = ld(rd(X2,X1),X2),
inference(cp,[status(thm)],[t9,t6]) ).
cnf(t21,plain,
ld(rd(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t928,plain,
rd(X1,rd(X2,X2)) = X1,
inference(cp,[status(thm)],[t927,t6]) ).
cnf(t941,plain,
rd(X1,rd(X2,X2)) = X1,
inference(orient,[status(thm)],[t928]) ).
cnf(t944,plain,
rd(X1,X1) = ld(X2,X2),
inference(cp,[status(thm)],[t21,t941]) ).
cnf(t1311,plain,
rd(X1,X1) = rd(c,c),
inference(step,[status(thm)],[t944,t946]) ).
cnf(t1012,plain,
rd(X1,X1) = rd(c,c),
inference(orient,[status(thm)],[t1311]) ).
cnf(t1027,plain,
X1 = mult(rd(X2,X2),X1),
inference(cp,[status(thm)],[t992,t1012]) ).
cnf(t1100,plain,
mult(rd(X1,X1),X2) = X2,
inference(orient,[status(thm)],[t1027]) ).
cnf(t1121,plain,
mult(X1,mult(rd(mult(X2,X2),X2),X3)) = mult(mult(X1,X2),X3),
inference(cp,[status(thm)],[t240,t1100]) ).
cnf(t1331,plain,
mult(X1,mult(X2,X3)) = mult(mult(X1,X2),X3),
inference(step,[status(thm)],[t1121,t7]) ).
cnf(t1249,plain,
mult(mult(X1,X2),X3) = mult(X1,mult(X2,X3)),
inference(orient,[status(thm)],[t1331]) ).
cnf(goal_0,negated_conjecture,
mult(mult(a,b),c) != mult(a,mult(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
mult(a,mult(b,c)) != mult(a,mult(b,c)),
inference(rw,[status(thm)],[goal_0,t1249]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP756-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.36 % Computer : n010.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Wed Sep 23 15:57:33 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.68/6.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.68/6.18 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------