%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG240-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 12:52:12 PM UTC 2026
% Result : Unsatisfiable 20.97s 3.33s
% Output : CNFRefutation 20.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of clauses : 84 ( 84 unt; 0 nHn; 57 RR)
% Number of literals : 84 ( 83 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 : 57 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t4,axiom,
sFlat0 = mult(a,c),
introduced(definition) ).
cnf(t225,plain,
mult(a,c) = sFlat0,
inference(orient,[status(thm)],[t4]) ).
cnf(t5,axiom,
sFlat1 = mult(b,d),
introduced(definition) ).
cnf(t243,plain,
mult(b,d) = sFlat1,
inference(orient,[status(thm)],[t5]) ).
cnf(t6,axiom,
sFlat2 = mult(mult(a,c),mult(b,d)),
introduced(definition) ).
cnf(t184,plain,
mult(mult(a,c),mult(b,d)) = sFlat2,
inference(orient,[status(thm)],[t6]) ).
cnf(t2593,plain,
mult(sFlat0,mult(b,d)) = sFlat2,
inference(step,[status(thm)],[t184,t225]) ).
cnf(t242,plain,
mult(sFlat0,mult(b,d)) = sFlat2,
inference(rw,[status(thm)],[t2593]) ).
cnf(t2607,plain,
mult(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t242,t243]) ).
cnf(t362,plain,
mult(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t2607]) ).
cnf(t7,axiom,
sFlat3 = mult(a,b),
introduced(definition) ).
cnf(t207,plain,
mult(a,b) = sFlat3,
inference(orient,[status(thm)],[t7]) ).
cnf(t8,axiom,
sFlat4 = mult(c,d),
introduced(definition) ).
cnf(t260,plain,
mult(c,d) = sFlat4,
inference(orient,[status(thm)],[t8]) ).
cnf(t9,axiom,
sFlat5 = mult(mult(a,b),mult(c,d)),
introduced(definition) ).
cnf(t159,plain,
mult(mult(a,b),mult(c,d)) = sFlat5,
inference(orient,[status(thm)],[t9]) ).
cnf(t2592,plain,
mult(sFlat3,mult(c,d)) = sFlat5,
inference(step,[status(thm)],[t159,t207]) ).
cnf(t224,plain,
mult(sFlat3,mult(c,d)) = sFlat5,
inference(rw,[status(thm)],[t2592]) ).
cnf(t2606,plain,
mult(sFlat3,sFlat4) = sFlat5,
inference(step,[status(thm)],[t224,t260]) ).
cnf(t345,plain,
mult(sFlat3,sFlat4) = sFlat5,
inference(orient,[status(thm)],[t2606]) ).
cnf(t1,axiom,
mult(mult(X1,X2),mult(X3,X2)) = mult(mult(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t15,plain,
mult(mult(X1,X2),mult(X3,X2)) = mult(mult(X1,X3),X2),
inference(orient,[status(thm)],[t1]) ).
cnf(t0,axiom,
mult(mult(X1,X2),mult(X1,X3)) = mult(X1,mult(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t12,plain,
mult(mult(X1,X2),mult(X1,X3)) = mult(X1,mult(X2,X3)),
inference(orient,[status(thm)],[t0]) ).
cnf(t16,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X2,X2)),
inference(cp,[status(thm)],[t15,t12]) ).
cnf(t379,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t16]) ).
cnf(t405,plain,
mult(mult(X1,X1),mult(X2,X3)) = mult(X1,mult(X2,mult(X3,X3))),
inference(cp,[status(thm)],[t379,t12]) ).
cnf(t2060,plain,
mult(mult(X1,X1),mult(X2,X3)) = mult(X1,mult(X2,mult(X3,X3))),
inference(orient,[status(thm)],[t405]) ).
cnf(t3,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(t57,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)],[t3]) ).
cnf(t201,plain,
mult(mult(a,b),mult(c,d)) = mult(mult(mult(mult(a,b),mult(c,d)),sFlat2),mult(mult(a,c),mult(b,d))),
inference(cp,[status(thm)],[t57,t184]) ).
cnf(t2603,plain,
sFlat5 = mult(mult(mult(mult(a,b),mult(c,d)),sFlat2),mult(mult(a,c),mult(b,d))),
inference(step,[status(thm)],[t201,t159]) ).
cnf(t2604,plain,
sFlat5 = mult(mult(sFlat5,sFlat2),mult(mult(a,c),mult(b,d))),
inference(step,[status(thm)],[t2603,t159]) ).
cnf(t2605,plain,
sFlat5 = mult(mult(sFlat5,sFlat2),sFlat2),
inference(step,[status(thm)],[t2604,t184]) ).
cnf(t328,plain,
mult(mult(sFlat5,sFlat2),sFlat2) = sFlat5,
inference(orient,[status(thm)],[t2605]) ).
cnf(t2113,plain,
mult(X1,mult(mult(sFlat5,sFlat2),mult(sFlat2,sFlat2))) = mult(mult(X1,X1),sFlat5),
inference(cp,[status(thm)],[t2060,t328]) ).
cnf(t2634,plain,
mult(X1,mult(mult(sFlat5,sFlat2),sFlat2)) = mult(mult(X1,X1),sFlat5),
inference(step,[status(thm)],[t2113,t15]) ).
cnf(t2635,plain,
mult(X1,sFlat5) = mult(mult(X1,X1),sFlat5),
inference(step,[status(thm)],[t2634,t328]) ).
cnf(t2636,plain,
mult(X1,sFlat5) = mult(X1,mult(sFlat5,sFlat5)),
inference(step,[status(thm)],[t2635,t379]) ).
cnf(t2224,plain,
mult(X1,mult(sFlat5,sFlat5)) = mult(X1,sFlat5),
inference(orient,[status(thm)],[t2636]) ).
cnf(t2227,plain,
mult(mult(sFlat5,X1),sFlat5) = mult(sFlat5,mult(X1,sFlat5)),
inference(cp,[status(thm)],[t2224,t12]) ).
cnf(t2256,plain,
mult(mult(sFlat5,X1),sFlat5) = mult(sFlat5,mult(X1,sFlat5)),
inference(orient,[status(thm)],[t2227]) ).
cnf(t2,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(t23,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)],[t2]) ).
cnf(t189,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)],[t23,t184]) ).
cnf(t2594,plain,
sFlat5 = mult(sFlat2,mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d)))),
inference(step,[status(thm)],[t189,t159]) ).
cnf(t2595,plain,
sFlat5 = mult(sFlat2,mult(sFlat2,mult(mult(a,b),mult(c,d)))),
inference(step,[status(thm)],[t2594,t184]) ).
cnf(t2596,plain,
sFlat5 = mult(sFlat2,mult(sFlat2,sFlat5)),
inference(step,[status(thm)],[t2595,t159]) ).
cnf(t277,plain,
mult(sFlat2,mult(sFlat2,sFlat5)) = sFlat5,
inference(orient,[status(thm)],[t2596]) ).
cnf(t278,plain,
mult(sFlat2,mult(mult(sFlat2,sFlat5),X1)) = mult(sFlat5,mult(sFlat2,X1)),
inference(cp,[status(thm)],[t12,t277]) ).
cnf(t2500,plain,
mult(sFlat2,mult(mult(sFlat2,sFlat5),X1)) = mult(sFlat5,mult(sFlat2,X1)),
inference(orient,[status(thm)],[t278]) ).
cnf(t198,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)],[t57,t184]) ).
cnf(t2600,plain,
sFlat2 = mult(mult(sFlat2,mult(mult(a,b),mult(c,d))),mult(mult(a,b),mult(c,d))),
inference(step,[status(thm)],[t198,t184]) ).
cnf(t2601,plain,
sFlat2 = mult(mult(sFlat2,sFlat5),mult(mult(a,b),mult(c,d))),
inference(step,[status(thm)],[t2600,t159]) ).
cnf(t2602,plain,
sFlat2 = mult(mult(sFlat2,sFlat5),sFlat5),
inference(step,[status(thm)],[t2601,t159]) ).
cnf(t311,plain,
mult(mult(sFlat2,sFlat5),sFlat5) = sFlat2,
inference(orient,[status(thm)],[t2602]) ).
cnf(t2504,plain,
mult(sFlat5,mult(sFlat2,sFlat5)) = mult(sFlat2,sFlat2),
inference(cp,[status(thm)],[t2500,t311]) ).
cnf(t2544,plain,
mult(sFlat5,mult(sFlat2,sFlat5)) = mult(sFlat2,sFlat2),
inference(orient,[status(thm)],[t2504]) ).
cnf(t2547,plain,
mult(sFlat5,mult(mult(sFlat2,sFlat5),sFlat5)) = mult(mult(sFlat2,sFlat2),sFlat5),
inference(cp,[status(thm)],[t2256,t2544]) ).
cnf(t2649,plain,
mult(sFlat5,sFlat2) = mult(mult(sFlat2,sFlat2),sFlat5),
inference(step,[status(thm)],[t2547,t311]) ).
cnf(t2650,plain,
mult(sFlat5,sFlat2) = mult(sFlat2,mult(sFlat5,sFlat5)),
inference(step,[status(thm)],[t2649,t379]) ).
cnf(t380,plain,
mult(mult(X1,X2),mult(X3,X3)) = mult(mult(X1,mult(X2,X2)),X3),
inference(cp,[status(thm)],[t379,t12]) ).
cnf(t1647,plain,
mult(mult(X1,X2),mult(X3,X3)) = mult(mult(X1,mult(X2,X2)),X3),
inference(orient,[status(thm)],[t380]) ).
cnf(t1666,plain,
mult(mult(mult(sFlat2,sFlat5),mult(sFlat5,sFlat5)),X1) = mult(sFlat2,mult(X1,X1)),
inference(cp,[status(thm)],[t1647,t311]) ).
cnf(t2628,plain,
mult(mult(mult(sFlat2,sFlat5),sFlat5),X1) = mult(sFlat2,mult(X1,X1)),
inference(step,[status(thm)],[t1666,t15]) ).
cnf(t2629,plain,
mult(sFlat2,X1) = mult(sFlat2,mult(X1,X1)),
inference(step,[status(thm)],[t2628,t311]) ).
cnf(t1794,plain,
mult(sFlat2,mult(X1,X1)) = mult(sFlat2,X1),
inference(orient,[status(thm)],[t2629]) ).
cnf(t2651,plain,
mult(sFlat5,sFlat2) = mult(sFlat2,sFlat5),
inference(step,[status(thm)],[t2650,t1794]) ).
cnf(t2567,plain,
mult(sFlat5,sFlat2) = mult(sFlat2,sFlat5),
inference(orient,[status(thm)],[t2651]) ).
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,t225]) ).
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,t243]) ).
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,t362]) ).
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,t207]) ).
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,t260]) ).
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,t345]) ).
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,t207]) ).
cnf(g0_7,plain,
mult(sFlat2,sFlat5) != mult(mult(sFlat3,sFlat4),mult(mult(a,c),mult(b,d))),
inference(rw,[status(thm)],[g0_6,t260]) ).
cnf(g0_8,plain,
mult(sFlat2,sFlat5) != mult(sFlat5,mult(mult(a,c),mult(b,d))),
inference(rw,[status(thm)],[g0_7,t345]) ).
cnf(g0_9,plain,
mult(sFlat2,sFlat5) != mult(sFlat5,mult(sFlat0,mult(b,d))),
inference(rw,[status(thm)],[g0_8,t225]) ).
cnf(g0_10,plain,
mult(sFlat2,sFlat5) != mult(sFlat5,mult(sFlat0,sFlat1)),
inference(rw,[status(thm)],[g0_9,t243]) ).
cnf(g0_11,plain,
mult(sFlat2,sFlat5) != mult(sFlat5,sFlat2),
inference(rw,[status(thm)],[g0_10,t362]) ).
cnf(g0_12,plain,
mult(sFlat2,sFlat5) != mult(sFlat2,sFlat5),
inference(rw,[status(thm)],[g0_11,t2567]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG240-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.65 % Computer : n017.cluster.edu
% 0.19/0.65 % Model : x86_64 x86_64
% 0.19/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.65 % Memory : 8046.5625MB
% 0.19/0.65 % OS : Linux 6.8.0-71-generic
% 0.19/0.65 % CPULimit : 300
% 0.19/0.65 % WCLimit : 300
% 0.19/0.65 % DateTime : Fri Sep 25 05:10:32 UTC 2026
% 0.19/0.65 % CPUTime :
% 0.19/0.65 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 20.97/3.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.97/3.33 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------