%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG245-1 : 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 12:52:12 PM UTC 2026
% Result : Unsatisfiable 13.10s 7.11s
% Output : CNFRefutation 13.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of clauses : 63 ( 63 unt; 0 nHn; 51 RR)
% Number of literals : 63 ( 62 equ; 14 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 : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t5,axiom,
sFlat0 = mult(a,c),
introduced(definition) ).
cnf(t212,plain,
mult(a,c) = sFlat0,
inference(orient,[status(thm)],[t5]) ).
cnf(t6,axiom,
sFlat1 = mult(b,d),
introduced(definition) ).
cnf(t230,plain,
mult(b,d) = sFlat1,
inference(orient,[status(thm)],[t6]) ).
cnf(t7,axiom,
sFlat2 = mult(mult(a,c),mult(b,d)),
introduced(definition) ).
cnf(t171,plain,
mult(mult(a,c),mult(b,d)) = sFlat2,
inference(orient,[status(thm)],[t7]) ).
cnf(t1496,plain,
mult(sFlat0,mult(b,d)) = sFlat2,
inference(step,[status(thm)],[t171,t212]) ).
cnf(t229,plain,
mult(sFlat0,mult(b,d)) = sFlat2,
inference(rw,[status(thm)],[t1496]) ).
cnf(t1510,plain,
mult(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t229,t230]) ).
cnf(t349,plain,
mult(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t1510]) ).
cnf(t8,axiom,
sFlat3 = mult(a,b),
introduced(definition) ).
cnf(t194,plain,
mult(a,b) = sFlat3,
inference(orient,[status(thm)],[t8]) ).
cnf(t9,axiom,
sFlat4 = mult(c,d),
introduced(definition) ).
cnf(t247,plain,
mult(c,d) = sFlat4,
inference(orient,[status(thm)],[t9]) ).
cnf(t10,axiom,
sFlat5 = mult(mult(a,b),mult(c,d)),
introduced(definition) ).
cnf(t146,plain,
mult(mult(a,b),mult(c,d)) = sFlat5,
inference(orient,[status(thm)],[t10]) ).
cnf(t1495,plain,
mult(sFlat3,mult(c,d)) = sFlat5,
inference(step,[status(thm)],[t146,t194]) ).
cnf(t211,plain,
mult(sFlat3,mult(c,d)) = sFlat5,
inference(rw,[status(thm)],[t1495]) ).
cnf(t1509,plain,
mult(sFlat3,sFlat4) = sFlat5,
inference(step,[status(thm)],[t211,t247]) ).
cnf(t332,plain,
mult(sFlat3,sFlat4) = sFlat5,
inference(orient,[status(thm)],[t1509]) ).
cnf(t1,axiom,
mult(mult(X1,X2),mult(X1,X3)) = mult(X1,mult(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t14,plain,
mult(mult(X1,X2),mult(X1,X3)) = mult(X1,mult(X2,X3)),
inference(orient,[status(thm)],[t1]) ).
cnf(t0,axiom,
mult(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t13,plain,
mult(X1,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t15,plain,
mult(X1,mult(X2,X1)) = mult(mult(X1,X2),X1),
inference(cp,[status(thm)],[t14,t13]) ).
cnf(t366,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
inference(orient,[status(thm)],[t15]) ).
cnf(t3,axiom,
mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(X1,X3),mult(X2,X4)))) = mult(mult(X1,X3),mult(X2,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t26,plain,
mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(X1,X3),mult(X2,X4)))) = mult(mult(X1,X3),mult(X2,X4)),
inference(orient,[status(thm)],[t3]) ).
cnf(t176,plain,
mult(mult(a,b),mult(c,d)) = mult(sFlat2,mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),
inference(cp,[status(thm)],[t26,t171]) ).
cnf(t1497,plain,
sFlat5 = mult(sFlat2,mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),
inference(step,[status(thm)],[t176,t146]) ).
cnf(t1498,plain,
sFlat5 = mult(sFlat2,mult(sFlat2,mult(mult(a,b),mult(c,d)))),
inference(step,[status(thm)],[t1497,t171]) ).
cnf(t1499,plain,
sFlat5 = mult(sFlat2,mult(sFlat2,sFlat5)),
inference(step,[status(thm)],[t1498,t146]) ).
cnf(t264,plain,
mult(sFlat2,mult(sFlat2,sFlat5)) = sFlat5,
inference(orient,[status(thm)],[t1499]) ).
cnf(t265,plain,
mult(sFlat2,mult(mult(sFlat2,sFlat5),X1)) = mult(sFlat5,mult(sFlat2,X1)),
inference(cp,[status(thm)],[t14,t264]) ).
cnf(t1429,plain,
mult(sFlat2,mult(mult(sFlat2,sFlat5),X1)) = mult(sFlat5,mult(sFlat2,X1)),
inference(orient,[status(thm)],[t265]) ).
cnf(t4,axiom,
mult(mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(X1,X3),mult(X2,X4))),mult(mult(X1,X3),mult(X2,X4))) = mult(mult(X1,X2),mult(X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t52,plain,
mult(mult(mult(mult(X1,X2),mult(X3,X4)),mult(mult(X1,X3),mult(X2,X4))),mult(mult(X1,X3),mult(X2,X4))) = mult(mult(X1,X2),mult(X3,X4)),
inference(orient,[status(thm)],[t4]) ).
cnf(t185,plain,
mult(mult(a,c),mult(b,d)) = mult(mult(sFlat2,mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))),
inference(cp,[status(thm)],[t52,t171]) ).
cnf(t1503,plain,
sFlat2 = mult(mult(sFlat2,mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))),
inference(step,[status(thm)],[t185,t171]) ).
cnf(t1504,plain,
sFlat2 = mult(mult(sFlat2,sFlat5),mult(mult(a,b),mult(c,d))),
inference(step,[status(thm)],[t1503,t146]) ).
cnf(t1505,plain,
sFlat2 = mult(mult(sFlat2,sFlat5),sFlat5),
inference(step,[status(thm)],[t1504,t146]) ).
cnf(t298,plain,
mult(mult(sFlat2,sFlat5),sFlat5) = sFlat2,
inference(orient,[status(thm)],[t1505]) ).
cnf(t1430,plain,
mult(sFlat5,mult(sFlat2,sFlat5)) = mult(sFlat2,sFlat2),
inference(cp,[status(thm)],[t1429,t298]) ).
cnf(t1529,plain,
mult(sFlat5,mult(sFlat2,sFlat5)) = sFlat2,
inference(step,[status(thm)],[t1430,t13]) ).
cnf(t1452,plain,
mult(sFlat5,mult(sFlat2,sFlat5)) = sFlat2,
inference(orient,[status(thm)],[t1529]) ).
cnf(t1455,plain,
mult(sFlat5,mult(mult(sFlat2,sFlat5),sFlat5)) = mult(sFlat2,sFlat5),
inference(cp,[status(thm)],[t366,t1452]) ).
cnf(t1531,plain,
mult(sFlat5,sFlat2) = mult(sFlat2,sFlat5),
inference(step,[status(thm)],[t1455,t298]) ).
cnf(t1474,plain,
mult(sFlat5,sFlat2) = mult(sFlat2,sFlat5),
inference(orient,[status(thm)],[t1531]) ).
cnf(goal_0,negated_conjecture,
mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))) != mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
mult(mult(sFlat0,mult(b,d)),mult(mult(a,b),mult(c,d))) != mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),
inference(rw,[status(thm)],[goal_0,t212]) ).
cnf(g0_1,plain,
mult(mult(sFlat0,sFlat1),mult(mult(a,b),mult(c,d))) != mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),
inference(rw,[status(thm)],[g0_0,t230]) ).
cnf(g0_2,plain,
mult(sFlat2,mult(mult(a,b),mult(c,d))) != mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),
inference(rw,[status(thm)],[g0_1,t349]) ).
cnf(g0_3,plain,
mult(sFlat2,mult(sFlat3,mult(c,d))) != mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),
inference(rw,[status(thm)],[g0_2,t194]) ).
cnf(g0_4,plain,
mult(sFlat2,mult(sFlat3,sFlat4)) != mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),
inference(rw,[status(thm)],[g0_3,t247]) ).
cnf(g0_5,plain,
mult(sFlat2,sFlat5) != mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))),
inference(rw,[status(thm)],[g0_4,t332]) ).
cnf(g0_6,plain,
mult(sFlat2,sFlat5) != mult(mult(sFlat3,mult(c,d)),mult(mult(a,c),mult(b,d))),
inference(rw,[status(thm)],[g0_5,t194]) ).
cnf(g0_7,plain,
mult(sFlat2,sFlat5) != mult(mult(sFlat3,sFlat4),mult(mult(a,c),mult(b,d))),
inference(rw,[status(thm)],[g0_6,t247]) ).
cnf(g0_8,plain,
mult(sFlat2,sFlat5) != mult(sFlat5,mult(mult(a,c),mult(b,d))),
inference(rw,[status(thm)],[g0_7,t332]) ).
cnf(g0_9,plain,
mult(sFlat2,sFlat5) != mult(sFlat5,mult(sFlat0,mult(b,d))),
inference(rw,[status(thm)],[g0_8,t212]) ).
cnf(g0_10,plain,
mult(sFlat2,sFlat5) != mult(sFlat5,mult(sFlat0,sFlat1)),
inference(rw,[status(thm)],[g0_9,t230]) ).
cnf(g0_11,plain,
mult(sFlat2,sFlat5) != mult(sFlat5,sFlat2),
inference(rw,[status(thm)],[g0_10,t349]) ).
cnf(g0_12,plain,
mult(sFlat2,sFlat5) != mult(sFlat2,sFlat5),
inference(rw,[status(thm)],[g0_11,t1474]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG245-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n015.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 05:19:16 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 13.10/7.11 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.10/7.11 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------