%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP669-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 01:27:59 PM UTC 2026
% Result : Unsatisfiable 14.18s 7.33s
% Output : CNFRefutation 14.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 18
% Syntax : Number of clauses : 137 ( 137 unt; 0 nHn; 85 RR)
% Number of literals : 137 ( 136 equ; 9 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 : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t9,axiom,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(X2,mult(X3,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t31,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(X2,mult(X3,X2))),
inference(orient,[status(thm)],[t9]) ).
cnf(t1,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
mult(unit,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t36,plain,
mult(unit,mult(X1,mult(X2,X1))) = mult(mult(X1,X2),X1),
inference(cp,[status(thm)],[t31,t19]) ).
cnf(t8991,plain,
mult(X1,mult(X2,X1)) = mult(mult(X1,X2),X1),
inference(step,[status(thm)],[t36,t19]) ).
cnf(t281,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
inference(orient,[status(thm)],[t8991]) ).
cnf(t6,axiom,
mult(mult(X1,X2),mult(X3,X1)) = mult(X1,mult(mult(X2,X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t54,plain,
mult(mult(X1,X2),mult(X3,X1)) = mult(X1,mult(mult(X2,X3),X1)),
inference(orient,[status(thm)],[t6]) ).
cnf(t14,axiom,
sFlat4 = mult(a,b),
introduced(definition) ).
cnf(t129,plain,
mult(a,b) = sFlat4,
inference(orient,[status(thm)],[t14]) ).
cnf(t130,plain,
mult(a,mult(mult(b,X1),a)) = mult(sFlat4,mult(X1,a)),
inference(cp,[status(thm)],[t54,t129]) ).
cnf(t2364,plain,
mult(a,mult(mult(b,X1),a)) = mult(sFlat4,mult(X1,a)),
inference(orient,[status(thm)],[t130]) ).
cnf(t10,axiom,
sFlat0 = mult(b,c),
introduced(definition) ).
cnf(t138,plain,
mult(b,c) = sFlat0,
inference(orient,[status(thm)],[t10]) ).
cnf(t2369,plain,
mult(sFlat4,mult(c,a)) = mult(a,mult(sFlat0,a)),
inference(cp,[status(thm)],[t2364,t138]) ).
cnf(t12,axiom,
sFlat2 = mult(mult(a,mult(b,c)),a),
introduced(definition) ).
cnf(t7,axiom,
mult(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),mult(X3,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8980,plain,
mult(mult(X1,mult(X2,X3)),X1) = mult(X1,mult(mult(X2,X3),X1)),
inference(step,[status(thm)],[t7,t54]) ).
cnf(t72,plain,
mult(mult(X1,mult(X2,X3)),X1) = mult(X1,mult(mult(X2,X3),X1)),
inference(orient,[status(thm)],[t8980]) ).
cnf(t8983,plain,
sFlat2 = mult(a,mult(mult(b,c),a)),
inference(step,[status(thm)],[t12,t72]) ).
cnf(t101,plain,
mult(a,mult(mult(b,c),a)) = sFlat2,
inference(orient,[status(thm)],[t8983]) ).
cnf(t8987,plain,
mult(a,mult(sFlat0,a)) = sFlat2,
inference(step,[status(thm)],[t101,t138]) ).
cnf(t147,plain,
mult(a,mult(sFlat0,a)) = sFlat2,
inference(rw,[status(thm)],[t8987]) ).
cnf(t189,plain,
mult(a,mult(sFlat0,a)) = sFlat2,
inference(orient,[status(thm)],[t147]) ).
cnf(t9029,plain,
mult(sFlat4,mult(c,a)) = sFlat2,
inference(step,[status(thm)],[t2369,t189]) ).
cnf(t2396,plain,
mult(sFlat4,mult(c,a)) = sFlat2,
inference(orient,[status(thm)],[t9029]) ).
cnf(t5,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t23,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t11,axiom,
sFlat1 = mult(a,mult(b,c)),
introduced(definition) ).
cnf(t120,plain,
mult(a,mult(b,c)) = sFlat1,
inference(orient,[status(thm)],[t11]) ).
cnf(t8986,plain,
mult(a,sFlat0) = sFlat1,
inference(step,[status(thm)],[t120,t138]) ).
cnf(t146,plain,
mult(a,sFlat0) = sFlat1,
inference(rw,[status(thm)],[t8986]) ).
cnf(t164,plain,
mult(a,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t146]) ).
cnf(t289,plain,
mult(a,mult(sFlat0,a)) = mult(sFlat1,a),
inference(cp,[status(thm)],[t281,t164]) ).
cnf(t8993,plain,
sFlat2 = mult(sFlat1,a),
inference(step,[status(thm)],[t289,t189]) ).
cnf(t307,plain,
mult(sFlat1,a) = sFlat2,
inference(orient,[status(thm)],[t8993]) ).
cnf(t314,plain,
mult(sFlat1,mult(a,mult(X1,a))) = mult(mult(sFlat2,X1),a),
inference(cp,[status(thm)],[t31,t307]) ).
cnf(t7233,plain,
mult(sFlat1,mult(a,mult(X1,a))) = mult(mult(sFlat2,X1),a),
inference(orient,[status(thm)],[t314]) ).
cnf(t290,plain,
mult(a,mult(b,a)) = mult(sFlat4,a),
inference(cp,[status(thm)],[t281,t129]) ).
cnf(t350,plain,
mult(a,mult(b,a)) = mult(sFlat4,a),
inference(orient,[status(thm)],[t290]) ).
cnf(t7237,plain,
mult(mult(sFlat2,b),a) = mult(sFlat1,mult(sFlat4,a)),
inference(cp,[status(thm)],[t7233,t350]) ).
cnf(t3,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t17,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t282,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1),
inference(cp,[status(thm)],[t281,t17]) ).
cnf(t440,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1),
inference(orient,[status(thm)],[t282]) ).
cnf(t2,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t27,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t13,axiom,
sFlat3 = mult(mult(mult(a,mult(b,c)),a),b),
introduced(definition) ).
cnf(t8,axiom,
mult(mult(mult(X1,X2),X1),X3) = mult(X1,mult(X2,mult(X1,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t41,plain,
mult(mult(mult(X1,X2),X1),X3) = mult(X1,mult(X2,mult(X1,X3))),
inference(orient,[status(thm)],[t8]) ).
cnf(t8981,plain,
sFlat3 = mult(a,mult(mult(b,c),mult(a,b))),
inference(step,[status(thm)],[t13,t41]) ).
cnf(t8982,plain,
sFlat3 = mult(a,mult(b,mult(mult(c,a),b))),
inference(step,[status(thm)],[t8981,t54]) ).
cnf(t92,plain,
mult(a,mult(b,mult(mult(c,a),b))) = sFlat3,
inference(orient,[status(thm)],[t8982]) ).
cnf(t95,plain,
mult(b,mult(mult(c,a),b)) = ld(a,sFlat3),
inference(cp,[status(thm)],[t27,t92]) ).
cnf(t315,plain,
mult(b,mult(mult(c,a),b)) = ld(a,sFlat3),
inference(orient,[status(thm)],[t95]) ).
cnf(t131,plain,
mult(b,mult(mult(X1,a),b)) = mult(mult(b,X1),sFlat4),
inference(cp,[status(thm)],[t54,t129]) ).
cnf(t2458,plain,
mult(b,mult(mult(X1,a),b)) = mult(mult(b,X1),sFlat4),
inference(orient,[status(thm)],[t131]) ).
cnf(t9033,plain,
mult(mult(b,c),sFlat4) = ld(a,sFlat3),
inference(step,[status(thm)],[t315,t2458]) ).
cnf(t4,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t21,plain,
mult(rd(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t35,plain,
mult(rd(X1,X2),mult(X2,mult(X3,X2))) = mult(mult(X1,X3),X2),
inference(cp,[status(thm)],[t31,t21]) ).
cnf(t1090,plain,
mult(rd(X1,X2),mult(X2,mult(X3,X2))) = mult(mult(X1,X3),X2),
inference(orient,[status(thm)],[t35]) ).
cnf(t15,axiom,
sFlat5 = mult(c,mult(a,b)),
introduced(definition) ).
cnf(t8988,plain,
sFlat5 = mult(c,sFlat4),
inference(step,[status(thm)],[t15,t129]) ).
cnf(t148,plain,
mult(c,sFlat4) = sFlat5,
inference(orient,[status(thm)],[t8988]) ).
cnf(t1162,plain,
mult(mult(X1,c),sFlat4) = mult(rd(X1,sFlat4),mult(sFlat4,sFlat5)),
inference(cp,[status(thm)],[t1090,t148]) ).
cnf(t16,axiom,
sFlat6 = mult(mult(a,b),mult(c,mult(a,b))),
introduced(definition) ).
cnf(t110,plain,
mult(mult(a,b),mult(c,mult(a,b))) = sFlat6,
inference(orient,[status(thm)],[t16]) ).
cnf(t8984,plain,
mult(sFlat4,mult(c,mult(a,b))) = sFlat6,
inference(step,[status(thm)],[t110,t129]) ).
cnf(t8985,plain,
mult(sFlat4,mult(c,sFlat4)) = sFlat6,
inference(step,[status(thm)],[t8984,t129]) ).
cnf(t137,plain,
mult(sFlat4,mult(c,sFlat4)) = sFlat6,
inference(rw,[status(thm)],[t8985]) ).
cnf(t8989,plain,
mult(sFlat4,sFlat5) = sFlat6,
inference(step,[status(thm)],[t137,t148]) ).
cnf(t178,plain,
mult(sFlat4,sFlat5) = sFlat6,
inference(orient,[status(thm)],[t8989]) ).
cnf(t9007,plain,
mult(mult(X1,c),sFlat4) = mult(rd(X1,sFlat4),sFlat6),
inference(step,[status(thm)],[t1162,t178]) ).
cnf(t1238,plain,
mult(mult(X1,c),sFlat4) = mult(rd(X1,sFlat4),sFlat6),
inference(orient,[status(thm)],[t9007]) ).
cnf(t9034,plain,
mult(rd(b,sFlat4),sFlat6) = ld(a,sFlat3),
inference(step,[status(thm)],[t9033,t1238]) ).
cnf(t1242,plain,
mult(rd(b,sFlat4),sFlat6) = mult(sFlat0,sFlat4),
inference(cp,[status(thm)],[t1238,t138]) ).
cnf(t1320,plain,
mult(rd(b,sFlat4),sFlat6) = mult(sFlat0,sFlat4),
inference(orient,[status(thm)],[t1242]) ).
cnf(t9035,plain,
mult(sFlat0,sFlat4) = ld(a,sFlat3),
inference(step,[status(thm)],[t9034,t1320]) ).
cnf(t2490,plain,
mult(sFlat0,sFlat4) = ld(a,sFlat3),
inference(rw,[status(thm)],[t9035]) ).
cnf(t2491,plain,
ld(a,sFlat3) = mult(sFlat0,sFlat4),
inference(orient,[status(thm)],[t2490]) ).
cnf(t2496,plain,
mult(sFlat3,a) = mult(a,mult(mult(sFlat0,sFlat4),a)),
inference(cp,[status(thm)],[t440,t2491]) ).
cnf(t2671,plain,
mult(a,mult(mult(sFlat0,sFlat4),a)) = mult(sFlat3,a),
inference(orient,[status(thm)],[t2496]) ).
cnf(t165,plain,
mult(a,mult(mult(sFlat0,X1),a)) = mult(sFlat1,mult(X1,a)),
inference(cp,[status(thm)],[t54,t164]) ).
cnf(t3765,plain,
mult(a,mult(mult(sFlat0,X1),a)) = mult(sFlat1,mult(X1,a)),
inference(orient,[status(thm)],[t165]) ).
cnf(t9071,plain,
mult(sFlat1,mult(sFlat4,a)) = mult(sFlat3,a),
inference(step,[status(thm)],[t2671,t3765]) ).
cnf(t3795,plain,
mult(sFlat1,mult(sFlat4,a)) = mult(sFlat3,a),
inference(rw,[status(thm)],[t9071]) ).
cnf(t3813,plain,
mult(sFlat1,mult(sFlat4,a)) = mult(sFlat3,a),
inference(orient,[status(thm)],[t3795]) ).
cnf(t9158,plain,
mult(mult(sFlat2,b),a) = mult(sFlat3,a),
inference(step,[status(thm)],[t7237,t3813]) ).
cnf(t7277,plain,
mult(mult(sFlat2,b),a) = mult(sFlat3,a),
inference(orient,[status(thm)],[t9158]) ).
cnf(t7289,plain,
mult(sFlat2,b) = rd(mult(sFlat3,a),a),
inference(cp,[status(thm)],[t23,t7277]) ).
cnf(t9159,plain,
mult(sFlat2,b) = sFlat3,
inference(step,[status(thm)],[t7289,t23]) ).
cnf(t7308,plain,
mult(sFlat2,b) = sFlat3,
inference(orient,[status(thm)],[t9159]) ).
cnf(t190,plain,
mult(a,mult(mult(mult(sFlat0,a),X1),a)) = mult(sFlat2,mult(X1,a)),
inference(cp,[status(thm)],[t54,t189]) ).
cnf(t9193,plain,
mult(a,mult(sFlat0,mult(a,mult(X1,a)))) = mult(sFlat2,mult(X1,a)),
inference(step,[status(thm)],[t190,t31]) ).
cnf(t8531,plain,
mult(a,mult(sFlat0,mult(a,mult(X1,a)))) = mult(sFlat2,mult(X1,a)),
inference(orient,[status(thm)],[t9193]) ).
cnf(t8555,plain,
mult(sFlat2,mult(rd(X1,a),a)) = mult(a,mult(sFlat0,mult(a,X1))),
inference(cp,[status(thm)],[t8531,t21]) ).
cnf(t9198,plain,
mult(sFlat2,X1) = mult(a,mult(sFlat0,mult(a,X1))),
inference(step,[status(thm)],[t8555,t21]) ).
cnf(t8723,plain,
mult(a,mult(sFlat0,mult(a,X1))) = mult(sFlat2,X1),
inference(orient,[status(thm)],[t9198]) ).
cnf(t0,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t18,plain,
mult(X1,unit) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t33,plain,
mult(X1,mult(X2,mult(unit,X2))) = mult(mult(X1,X2),X2),
inference(cp,[status(thm)],[t31,t18]) ).
cnf(t8990,plain,
mult(X1,mult(X2,X2)) = mult(mult(X1,X2),X2),
inference(step,[status(thm)],[t33,t19]) ).
cnf(t201,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t8990]) ).
cnf(t209,plain,
mult(a,mult(b,b)) = mult(sFlat4,b),
inference(cp,[status(thm)],[t201,t129]) ).
cnf(t262,plain,
mult(a,mult(b,b)) = mult(sFlat4,b),
inference(orient,[status(thm)],[t209]) ).
cnf(t8735,plain,
mult(sFlat2,mult(b,b)) = mult(a,mult(sFlat0,mult(sFlat4,b))),
inference(cp,[status(thm)],[t8723,t262]) ).
cnf(t7316,plain,
mult(sFlat2,mult(b,b)) = mult(sFlat3,b),
inference(cp,[status(thm)],[t201,t7308]) ).
cnf(t7450,plain,
mult(sFlat2,mult(b,b)) = mult(sFlat3,b),
inference(orient,[status(thm)],[t7316]) ).
cnf(t9199,plain,
mult(sFlat3,b) = mult(a,mult(sFlat0,mult(sFlat4,b))),
inference(step,[status(thm)],[t8735,t7450]) ).
cnf(t134,plain,
mult(a,mult(b,mult(X1,b))) = mult(mult(sFlat4,X1),b),
inference(cp,[status(thm)],[t31,t129]) ).
cnf(t2712,plain,
mult(a,mult(b,mult(X1,b))) = mult(mult(sFlat4,X1),b),
inference(orient,[status(thm)],[t134]) ).
cnf(t139,plain,
mult(b,mult(mult(c,X1),b)) = mult(sFlat0,mult(X1,b)),
inference(cp,[status(thm)],[t54,t138]) ).
cnf(t2834,plain,
mult(b,mult(mult(c,X1),b)) = mult(sFlat0,mult(X1,b)),
inference(orient,[status(thm)],[t139]) ).
cnf(t2838,plain,
mult(sFlat0,mult(sFlat4,b)) = mult(b,mult(sFlat5,b)),
inference(cp,[status(thm)],[t2834,t148]) ).
cnf(t2868,plain,
mult(b,mult(sFlat5,b)) = mult(sFlat0,mult(sFlat4,b)),
inference(orient,[status(thm)],[t2838]) ).
cnf(t2879,plain,
mult(mult(sFlat4,sFlat5),b) = mult(a,mult(sFlat0,mult(sFlat4,b))),
inference(cp,[status(thm)],[t2712,t2868]) ).
cnf(t9042,plain,
mult(sFlat6,b) = mult(a,mult(sFlat0,mult(sFlat4,b))),
inference(step,[status(thm)],[t2879,t178]) ).
cnf(t2894,plain,
mult(a,mult(sFlat0,mult(sFlat4,b))) = mult(sFlat6,b),
inference(orient,[status(thm)],[t9042]) ).
cnf(t9200,plain,
mult(sFlat3,b) = mult(sFlat6,b),
inference(step,[status(thm)],[t9199,t2894]) ).
cnf(t8768,plain,
mult(sFlat6,b) = mult(sFlat3,b),
inference(orient,[status(thm)],[t9200]) ).
cnf(t8780,plain,
sFlat6 = rd(mult(sFlat3,b),b),
inference(cp,[status(thm)],[t23,t8768]) ).
cnf(t9204,plain,
sFlat6 = sFlat3,
inference(step,[status(thm)],[t8780,t23]) ).
cnf(t8796,plain,
sFlat6 = sFlat3,
inference(orient,[status(thm)],[t9204]) ).
cnf(t9205,plain,
mult(sFlat4,sFlat5) = sFlat3,
inference(step,[status(thm)],[t178,t8796]) ).
cnf(t8797,plain,
mult(sFlat4,sFlat5) = sFlat3,
inference(orient,[status(thm)],[t9205]) ).
cnf(goal_0,negated_conjecture,
mult(mult(mult(a,mult(b,c)),a),b) != mult(mult(a,b),mult(c,mult(a,b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
mult(mult(a,mult(mult(b,c),a)),b) != mult(mult(a,b),mult(c,mult(a,b))),
inference(rw,[status(thm)],[goal_0,t281]) ).
cnf(g0_1,plain,
mult(mult(sFlat4,mult(c,a)),b) != mult(mult(a,b),mult(c,mult(a,b))),
inference(rw,[status(thm)],[g0_0,t2364]) ).
cnf(g0_2,plain,
mult(sFlat2,b) != mult(mult(a,b),mult(c,mult(a,b))),
inference(rw,[status(thm)],[g0_1,t2396]) ).
cnf(g0_3,plain,
sFlat3 != mult(mult(a,b),mult(c,mult(a,b))),
inference(rw,[status(thm)],[g0_2,t7308]) ).
cnf(g0_4,plain,
sFlat3 != mult(sFlat4,mult(c,mult(a,b))),
inference(rw,[status(thm)],[g0_3,t129]) ).
cnf(g0_5,plain,
sFlat3 != mult(sFlat4,mult(c,sFlat4)),
inference(rw,[status(thm)],[g0_4,t129]) ).
cnf(g0_6,plain,
sFlat3 != mult(sFlat4,sFlat5),
inference(rw,[status(thm)],[g0_5,t148]) ).
cnf(g0_7,plain,
sFlat3 != sFlat3,
inference(rw,[status(thm)],[g0_6,t8797]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP669-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.37 % Computer : n009.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 15:38:05 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.18/7.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.18/7.33 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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