%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP686-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 01:28:03 PM UTC 2026
% Result : Unsatisfiable 6.12s 1.57s
% Output : CNFRefutation 6.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 8
% Syntax : Number of clauses : 203 ( 203 unt; 0 nHn; 4 RR)
% Number of literals : 203 ( 202 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 420 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t17,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t4,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t11,plain,
mult(rd(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t19,plain,
X1 = ld(rd(X2,X1),X2),
inference(cp,[status(thm)],[t17,t11]) ).
cnf(t34,plain,
ld(rd(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t19]) ).
cnf(t5,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t13,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t6,axiom,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t21,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(orient,[status(thm)],[t6]) ).
cnf(t26,plain,
mult(X1,mult(X2,X2)) = rd(mult(X1,mult(X2,mult(X2,X3))),X3),
inference(cp,[status(thm)],[t13,t21]) ).
cnf(t128,plain,
rd(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t26]) ).
cnf(t3,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t7,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t135,plain,
mult(X1,mult(X2,X2)) = rd(mult(X1,mult(X2,X3)),ld(X2,X3)),
inference(cp,[status(thm)],[t128,t7]) ).
cnf(t158,plain,
rd(mult(X1,mult(X2,X3)),ld(X2,X3)) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t135]) ).
cnf(t163,plain,
mult(rd(X1,mult(X2,X3)),mult(X2,X2)) = rd(X1,ld(X2,X3)),
inference(cp,[status(thm)],[t158,t11]) ).
cnf(t637,plain,
mult(rd(X1,mult(X2,X3)),mult(X2,X2)) = rd(X1,ld(X2,X3)),
inference(orient,[status(thm)],[t163]) ).
cnf(t647,plain,
rd(X1,ld(X2,ld(X2,X3))) = mult(rd(X1,X3),mult(X2,X2)),
inference(cp,[status(thm)],[t637,t7]) ).
cnf(t672,plain,
mult(rd(X1,X2),mult(X3,X3)) = rd(X1,ld(X3,ld(X3,X2))),
inference(orient,[status(thm)],[t647]) ).
cnf(t14,plain,
X1 = rd(X2,ld(X1,X2)),
inference(cp,[status(thm)],[t13,t7]) ).
cnf(t33,plain,
rd(X1,ld(X2,X1)) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t677,plain,
rd(X1,ld(X2,ld(X2,ld(X3,X1)))) = mult(X3,mult(X2,X2)),
inference(cp,[status(thm)],[t672,t33]) ).
cnf(t804,plain,
rd(X1,ld(X2,ld(X2,ld(X3,X1)))) = mult(X3,mult(X2,X2)),
inference(orient,[status(thm)],[t677]) ).
cnf(t835,plain,
ld(X1,ld(X1,ld(X2,X3))) = ld(mult(X2,mult(X1,X1)),X3),
inference(cp,[status(thm)],[t34,t804]) ).
cnf(t867,plain,
ld(mult(X1,mult(X2,X2)),X3) = ld(X2,ld(X2,ld(X1,X3))),
inference(orient,[status(thm)],[t835]) ).
cnf(t0,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t8,plain,
mult(X1,unit) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t165,plain,
mult(X1,mult(X2,X2)) = rd(mult(X1,X2),ld(X2,unit)),
inference(cp,[status(thm)],[t158,t8]) ).
cnf(t178,plain,
rd(mult(X1,X2),ld(X2,unit)) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t165]) ).
cnf(t184,plain,
mult(rd(X1,X2),mult(X2,X2)) = rd(X1,ld(X2,unit)),
inference(cp,[status(thm)],[t178,t11]) ).
cnf(t194,plain,
mult(rd(X1,X2),mult(X2,X2)) = rd(X1,ld(X2,unit)),
inference(orient,[status(thm)],[t184]) ).
cnf(t212,plain,
mult(rd(X1,X2),mult(X2,mult(X2,X3))) = mult(rd(X1,ld(X2,unit)),X3),
inference(cp,[status(thm)],[t21,t194]) ).
cnf(t1,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t9,plain,
mult(unit,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t24,plain,
mult(unit,mult(X1,mult(X1,X2))) = mult(mult(X1,X1),X2),
inference(cp,[status(thm)],[t21,t9]) ).
cnf(t6168,plain,
mult(X1,mult(X1,X2)) = mult(mult(X1,X1),X2),
inference(step,[status(thm)],[t24,t9]) ).
cnf(t35,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(orient,[status(thm)],[t6168]) ).
cnf(t40,plain,
mult(X1,X1) = rd(mult(X1,mult(X1,X2)),X2),
inference(cp,[status(thm)],[t13,t35]) ).
cnf(t43,plain,
rd(mult(X1,mult(X1,X2)),X2) = mult(X1,X1),
inference(orient,[status(thm)],[t40]) ).
cnf(t46,plain,
mult(X1,X1) = rd(mult(X1,X2),ld(X1,X2)),
inference(cp,[status(thm)],[t43,t7]) ).
cnf(t51,plain,
rd(mult(X1,X2),ld(X1,X2)) = mult(X1,X1),
inference(orient,[status(thm)],[t46]) ).
cnf(t56,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(X1,ld(rd(X1,X2),X2)),
inference(cp,[status(thm)],[t51,t11]) ).
cnf(t49,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(mult(rd(X1,X2),X1),X2),
inference(cp,[status(thm)],[t43,t11]) ).
cnf(t86,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(mult(rd(X1,X2),X1),X2),
inference(orient,[status(thm)],[t49]) ).
cnf(t6169,plain,
rd(mult(rd(X1,X2),X1),X2) = rd(X1,ld(rd(X1,X2),X2)),
inference(step,[status(thm)],[t56,t86]) ).
cnf(t101,plain,
rd(mult(rd(X1,X2),X1),X2) = rd(X1,ld(rd(X1,X2),X2)),
inference(orient,[status(thm)],[t6169]) ).
cnf(t104,plain,
rd(unit,ld(rd(unit,X1),X1)) = rd(rd(unit,X1),X1),
inference(cp,[status(thm)],[t101,t8]) ).
cnf(t114,plain,
rd(unit,ld(rd(unit,X1),X1)) = rd(rd(unit,X1),X1),
inference(orient,[status(thm)],[t104]) ).
cnf(t210,plain,
mult(X1,X1) = ld(rd(X2,X1),rd(X2,ld(X1,unit))),
inference(cp,[status(thm)],[t17,t194]) ).
cnf(t254,plain,
ld(rd(X1,X2),rd(X1,ld(X2,unit))) = mult(X2,X2),
inference(orient,[status(thm)],[t210]) ).
cnf(t265,plain,
mult(X1,X1) = ld(rd(unit,X1),X1),
inference(cp,[status(thm)],[t254,t33]) ).
cnf(t278,plain,
ld(rd(unit,X1),X1) = mult(X1,X1),
inference(orient,[status(thm)],[t265]) ).
cnf(t6175,plain,
rd(unit,mult(X1,X1)) = rd(rd(unit,X1),X1),
inference(step,[status(thm)],[t114,t278]) ).
cnf(t287,plain,
rd(unit,mult(X1,X1)) = rd(rd(unit,X1),X1),
inference(rw,[status(thm)],[t6175]) ).
cnf(t299,plain,
rd(rd(unit,X1),X1) = rd(unit,mult(X1,X1)),
inference(orient,[status(thm)],[t287]) ).
cnf(t302,plain,
rd(rd(unit,X1),ld(X1,unit)) = mult(rd(unit,mult(X1,X1)),mult(X1,X1)),
inference(cp,[status(thm)],[t194,t299]) ).
cnf(t6177,plain,
rd(rd(unit,X1),ld(X1,unit)) = unit,
inference(step,[status(thm)],[t302,t11]) ).
cnf(t312,plain,
rd(rd(unit,X1),ld(X1,unit)) = unit,
inference(orient,[status(thm)],[t6177]) ).
cnf(t318,plain,
ld(X1,unit) = ld(unit,rd(unit,X1)),
inference(cp,[status(thm)],[t34,t312]) ).
cnf(t10,plain,
ld(unit,X1) = X1,
inference(cp,[status(thm)],[t9,t7]) ).
cnf(t29,plain,
ld(unit,X1) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t6178,plain,
ld(X1,unit) = rd(unit,X1),
inference(step,[status(thm)],[t318,t29]) ).
cnf(t322,plain,
ld(X1,unit) = rd(unit,X1),
inference(orient,[status(thm)],[t6178]) ).
cnf(t6250,plain,
mult(rd(X1,X2),mult(X2,mult(X2,X3))) = mult(rd(X1,rd(unit,X2)),X3),
inference(step,[status(thm)],[t212,t322]) ).
cnf(t1351,plain,
mult(rd(X1,X2),mult(X2,mult(X2,X3))) = mult(rd(X1,rd(unit,X2)),X3),
inference(orient,[status(thm)],[t6250]) ).
cnf(t1362,plain,
mult(rd(rd(unit,X1),rd(unit,X1)),X2) = mult(rd(unit,mult(X1,X1)),mult(X1,mult(X1,X2))),
inference(cp,[status(thm)],[t1351,t299]) ).
cnf(t16,plain,
unit = rd(X1,X1),
inference(cp,[status(thm)],[t13,t9]) ).
cnf(t31,plain,
rd(X1,X1) = unit,
inference(orient,[status(thm)],[t16]) ).
cnf(t6251,plain,
mult(unit,X2) = mult(rd(unit,mult(X1,X1)),mult(X1,mult(X1,X2))),
inference(step,[status(thm)],[t1362,t31]) ).
cnf(t6252,plain,
X2 = mult(rd(unit,mult(X1,X1)),mult(X1,mult(X1,X2))),
inference(step,[status(thm)],[t6251,t9]) ).
cnf(t1406,plain,
mult(rd(unit,mult(X1,X1)),mult(X1,mult(X1,X2))) = X2,
inference(orient,[status(thm)],[t6252]) ).
cnf(t1432,plain,
rd(unit,mult(X1,X1)) = rd(X2,mult(X1,mult(X1,X2))),
inference(cp,[status(thm)],[t13,t1406]) ).
cnf(t1464,plain,
rd(X1,mult(X2,mult(X2,X1))) = rd(unit,mult(X2,X2)),
inference(orient,[status(thm)],[t1432]) ).
cnf(t1474,plain,
rd(unit,mult(X1,X1)) = rd(ld(X1,X2),mult(X1,X2)),
inference(cp,[status(thm)],[t1464,t7]) ).
cnf(t1498,plain,
rd(ld(X1,X2),mult(X1,X2)) = rd(unit,mult(X1,X1)),
inference(orient,[status(thm)],[t1474]) ).
cnf(t1518,plain,
rd(unit,mult(X1,X1)) = rd(ld(X1,ld(X1,X2)),X2),
inference(cp,[status(thm)],[t1498,t7]) ).
cnf(t1537,plain,
rd(ld(X1,ld(X1,X2)),X2) = rd(unit,mult(X1,X1)),
inference(orient,[status(thm)],[t1518]) ).
cnf(t1561,plain,
ld(X1,ld(X1,X2)) = mult(rd(unit,mult(X1,X1)),X2),
inference(cp,[status(thm)],[t11,t1537]) ).
cnf(t1576,plain,
mult(rd(unit,mult(X1,X1)),X2) = ld(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t1561]) ).
cnf(t1595,plain,
mult(rd(X1,rd(unit,rd(unit,mult(X2,X2)))),X3) = mult(rd(X1,rd(unit,mult(X2,X2))),ld(X2,ld(X2,mult(rd(unit,mult(X2,X2)),X3)))),
inference(cp,[status(thm)],[t1351,t1576]) ).
cnf(t328,plain,
rd(unit,rd(unit,X1)) = X1,
inference(cp,[status(thm)],[t322,t34]) ).
cnf(t338,plain,
rd(unit,rd(unit,X1)) = X1,
inference(orient,[status(thm)],[t328]) ).
cnf(t6253,plain,
mult(rd(X1,mult(X2,X2)),X3) = mult(rd(X1,rd(unit,mult(X2,X2))),ld(X2,ld(X2,mult(rd(unit,mult(X2,X2)),X3)))),
inference(step,[status(thm)],[t1595,t338]) ).
cnf(t329,plain,
unit = mult(X1,rd(unit,X1)),
inference(cp,[status(thm)],[t7,t322]) ).
cnf(t346,plain,
mult(X1,rd(unit,X1)) = unit,
inference(orient,[status(thm)],[t329]) ).
cnf(t352,plain,
mult(X1,mult(X2,X2)) = rd(mult(X1,unit),ld(X2,rd(unit,X2))),
inference(cp,[status(thm)],[t158,t346]) ).
cnf(t6197,plain,
mult(X1,mult(X2,X2)) = rd(X1,ld(X2,rd(unit,X2))),
inference(step,[status(thm)],[t352,t8]) ).
cnf(t52,plain,
mult(X1,X1) = rd(X2,ld(X1,ld(X1,X2))),
inference(cp,[status(thm)],[t51,t7]) ).
cnf(t66,plain,
rd(X1,ld(X2,ld(X2,X1))) = mult(X2,X2),
inference(orient,[status(thm)],[t52]) ).
cnf(t69,plain,
ld(X1,ld(X1,X2)) = ld(mult(X1,X1),X2),
inference(cp,[status(thm)],[t34,t66]) ).
cnf(t70,plain,
ld(mult(X1,X1),X2) = ld(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t69]) ).
cnf(t327,plain,
rd(unit,mult(X1,X1)) = ld(X1,ld(X1,unit)),
inference(cp,[status(thm)],[t322,t70]) ).
cnf(t6187,plain,
rd(unit,mult(X1,X1)) = ld(X1,rd(unit,X1)),
inference(step,[status(thm)],[t327,t322]) ).
cnf(t362,plain,
ld(X1,rd(unit,X1)) = rd(unit,mult(X1,X1)),
inference(orient,[status(thm)],[t6187]) ).
cnf(t6198,plain,
mult(X1,mult(X2,X2)) = rd(X1,rd(unit,mult(X2,X2))),
inference(step,[status(thm)],[t6197,t362]) ).
cnf(t431,plain,
rd(X1,rd(unit,mult(X2,X2))) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t6198]) ).
cnf(t6254,plain,
mult(rd(X1,mult(X2,X2)),X3) = mult(mult(X1,mult(X2,X2)),ld(X2,ld(X2,mult(rd(unit,mult(X2,X2)),X3)))),
inference(step,[status(thm)],[t6253,t431]) ).
cnf(t6255,plain,
mult(rd(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,ld(X2,ld(X2,mult(rd(unit,mult(X2,X2)),X3)))))),
inference(step,[status(thm)],[t6254,t21]) ).
cnf(t6256,plain,
mult(rd(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,ld(X2,mult(rd(unit,mult(X2,X2)),X3)))),
inference(step,[status(thm)],[t6255,t7]) ).
cnf(t6257,plain,
mult(rd(X1,mult(X2,X2)),X3) = mult(X1,mult(rd(unit,mult(X2,X2)),X3)),
inference(step,[status(thm)],[t6256,t7]) ).
cnf(t6258,plain,
mult(rd(X1,mult(X2,X2)),X3) = mult(X1,ld(X2,ld(X2,X3))),
inference(step,[status(thm)],[t6257,t1576]) ).
cnf(t1618,plain,
mult(rd(X1,mult(X2,X2)),X3) = mult(X1,ld(X2,ld(X2,X3))),
inference(orient,[status(thm)],[t6258]) ).
cnf(t283,plain,
rd(unit,X1) = rd(X1,mult(X1,X1)),
inference(cp,[status(thm)],[t33,t278]) ).
cnf(t288,plain,
rd(X1,mult(X1,X1)) = rd(unit,X1),
inference(orient,[status(thm)],[t283]) ).
cnf(t1627,plain,
mult(X1,ld(X1,ld(X1,X2))) = mult(rd(unit,X1),X2),
inference(cp,[status(thm)],[t1618,t288]) ).
cnf(t6259,plain,
ld(X1,X2) = mult(rd(unit,X1),X2),
inference(step,[status(thm)],[t1627,t7]) ).
cnf(t1696,plain,
mult(rd(unit,X1),X2) = ld(X1,X2),
inference(orient,[status(thm)],[t6259]) ).
cnf(t1715,plain,
mult(rd(unit,X1),mult(X2,mult(X2,X3))) = mult(ld(X1,mult(X2,X2)),X3),
inference(cp,[status(thm)],[t21,t1696]) ).
cnf(t6280,plain,
ld(X1,mult(X2,mult(X2,X3))) = mult(ld(X1,mult(X2,X2)),X3),
inference(step,[status(thm)],[t1715,t1696]) ).
cnf(t2276,plain,
ld(X1,mult(X2,mult(X2,X3))) = mult(ld(X1,mult(X2,X2)),X3),
inference(orient,[status(thm)],[t6280]) ).
cnf(t2292,plain,
mult(ld(X1,mult(X2,X2)),ld(X2,X3)) = ld(X1,mult(X2,X3)),
inference(cp,[status(thm)],[t2276,t7]) ).
cnf(t4046,plain,
mult(ld(X1,mult(X2,X2)),ld(X2,X3)) = ld(X1,mult(X2,X3)),
inference(orient,[status(thm)],[t2292]) ).
cnf(t1697,plain,
ld(X1,mult(X2,X2)) = rd(unit,ld(X2,ld(X2,X1))),
inference(cp,[status(thm)],[t1696,t672]) ).
cnf(t1999,plain,
rd(unit,ld(X1,ld(X1,X2))) = ld(X2,mult(X1,X1)),
inference(orient,[status(thm)],[t1697]) ).
cnf(t2006,plain,
ld(mult(X1,X2),mult(X1,X1)) = rd(unit,ld(X1,X2)),
inference(cp,[status(thm)],[t1999,t17]) ).
cnf(t2132,plain,
ld(mult(X1,X2),mult(X1,X1)) = rd(unit,ld(X1,X2)),
inference(orient,[status(thm)],[t2006]) ).
cnf(t4048,plain,
ld(mult(X1,X2),mult(X1,X3)) = mult(rd(unit,ld(X1,X2)),ld(X1,X3)),
inference(cp,[status(thm)],[t4046,t2132]) ).
cnf(t6326,plain,
ld(mult(X1,X2),mult(X1,X3)) = ld(ld(X1,X2),ld(X1,X3)),
inference(step,[status(thm)],[t4048,t1696]) ).
cnf(t4093,plain,
ld(ld(X1,X2),ld(X1,X3)) = ld(mult(X1,X2),mult(X1,X3)),
inference(orient,[status(thm)],[t6326]) ).
cnf(t1698,plain,
ld(X1,mult(X1,mult(X1,X2))) = mult(rd(unit,rd(unit,X1)),X2),
inference(cp,[status(thm)],[t1696,t1351]) ).
cnf(t6260,plain,
mult(X1,X2) = mult(rd(unit,rd(unit,X1)),X2),
inference(step,[status(thm)],[t1698,t17]) ).
cnf(t6261,plain,
mult(X1,X2) = ld(rd(unit,X1),X2),
inference(step,[status(thm)],[t6260,t1696]) ).
cnf(t1739,plain,
ld(rd(unit,X1),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t6261]) ).
cnf(t1714,plain,
rd(unit,X1) = rd(ld(X1,X2),X2),
inference(cp,[status(thm)],[t13,t1696]) ).
cnf(t1751,plain,
rd(ld(X1,X2),X2) = rd(unit,X1),
inference(orient,[status(thm)],[t1714]) ).
cnf(t1762,plain,
rd(unit,rd(X1,X2)) = rd(X2,X1),
inference(cp,[status(thm)],[t1751,t34]) ).
cnf(t1797,plain,
rd(unit,rd(X1,X2)) = rd(X2,X1),
inference(orient,[status(thm)],[t1762]) ).
cnf(t1813,plain,
mult(rd(X1,X2),X3) = ld(rd(X2,X1),X3),
inference(cp,[status(thm)],[t1739,t1797]) ).
cnf(t1841,plain,
ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3),
inference(orient,[status(thm)],[t1813]) ).
cnf(t2012,plain,
mult(rd(ld(X1,ld(X1,X2)),unit),X3) = ld(ld(X2,mult(X1,X1)),X3),
inference(cp,[status(thm)],[t1841,t1999]) ).
cnf(t12,plain,
X1 = rd(X1,unit),
inference(cp,[status(thm)],[t11,t8]) ).
cnf(t30,plain,
rd(X1,unit) = X1,
inference(orient,[status(thm)],[t12]) ).
cnf(t6293,plain,
mult(ld(X1,ld(X1,X2)),X3) = ld(ld(X2,mult(X1,X1)),X3),
inference(step,[status(thm)],[t2012,t30]) ).
cnf(t2705,plain,
ld(ld(X1,mult(X2,X2)),X3) = mult(ld(X2,ld(X2,X1)),X3),
inference(orient,[status(thm)],[t6293]) ).
cnf(t4094,plain,
ld(mult(X1,mult(X2,X2)),mult(X1,X3)) = mult(ld(X2,ld(X2,X1)),ld(X1,X3)),
inference(cp,[status(thm)],[t4093,t2705]) ).
cnf(t6340,plain,
ld(X2,ld(X2,ld(X1,mult(X1,X3)))) = mult(ld(X2,ld(X2,X1)),ld(X1,X3)),
inference(step,[status(thm)],[t4094,t867]) ).
cnf(t6341,plain,
ld(X2,ld(X2,X3)) = mult(ld(X2,ld(X2,X1)),ld(X1,X3)),
inference(step,[status(thm)],[t6340,t17]) ).
cnf(t5660,plain,
mult(ld(X1,ld(X1,X2)),ld(X2,X3)) = ld(X1,ld(X1,X3)),
inference(orient,[status(thm)],[t6341]) ).
cnf(t5734,plain,
ld(ld(X1,ld(X1,X1)),ld(ld(X1,ld(X1,X1)),ld(X2,X3))) = ld(mult(X2,ld(X1,ld(X1,ld(X1,X1)))),X3),
inference(cp,[status(thm)],[t867,t5660]) ).
cnf(t2014,plain,
ld(ld(X1,ld(X1,X2)),X3) = mult(ld(X2,mult(X1,X1)),X3),
inference(cp,[status(thm)],[t1696,t1999]) ).
cnf(t2746,plain,
ld(ld(X1,ld(X1,X2)),X3) = mult(ld(X2,mult(X1,X1)),X3),
inference(orient,[status(thm)],[t2014]) ).
cnf(t6350,plain,
mult(ld(X1,mult(X1,X1)),ld(ld(X1,ld(X1,X1)),ld(X2,X3))) = ld(mult(X2,ld(X1,ld(X1,ld(X1,X1)))),X3),
inference(step,[status(thm)],[t5734,t2746]) ).
cnf(t6351,plain,
mult(X1,ld(ld(X1,ld(X1,X1)),ld(X2,X3))) = ld(mult(X2,ld(X1,ld(X1,ld(X1,X1)))),X3),
inference(step,[status(thm)],[t6350,t17]) ).
cnf(t6352,plain,
mult(X1,mult(ld(X1,mult(X1,X1)),ld(X2,X3))) = ld(mult(X2,ld(X1,ld(X1,ld(X1,X1)))),X3),
inference(step,[status(thm)],[t6351,t2746]) ).
cnf(t2303,plain,
mult(X1,mult(X1,X2)) = mult(X3,mult(ld(X3,mult(X1,X1)),X2)),
inference(cp,[status(thm)],[t7,t2276]) ).
cnf(t4298,plain,
mult(X1,mult(ld(X1,mult(X2,X2)),X3)) = mult(X2,mult(X2,X3)),
inference(orient,[status(thm)],[t2303]) ).
cnf(t6353,plain,
mult(X1,mult(X1,ld(X2,X3))) = ld(mult(X2,ld(X1,ld(X1,ld(X1,X1)))),X3),
inference(step,[status(thm)],[t6352,t4298]) ).
cnf(t18,plain,
unit = ld(X1,X1),
inference(cp,[status(thm)],[t17,t8]) ).
cnf(t32,plain,
ld(X1,X1) = unit,
inference(orient,[status(thm)],[t18]) ).
cnf(t6354,plain,
mult(X1,mult(X1,ld(X2,X3))) = ld(mult(X2,ld(X1,ld(X1,unit))),X3),
inference(step,[status(thm)],[t6353,t32]) ).
cnf(t6355,plain,
mult(X1,mult(X1,ld(X2,X3))) = ld(mult(X2,ld(X1,rd(unit,X1))),X3),
inference(step,[status(thm)],[t6354,t322]) ).
cnf(t6356,plain,
mult(X1,mult(X1,ld(X2,X3))) = ld(mult(X2,rd(unit,mult(X1,X1))),X3),
inference(step,[status(thm)],[t6355,t362]) ).
cnf(t284,plain,
mult(X1,mult(rd(unit,X2),rd(unit,X2))) = rd(mult(X1,mult(rd(unit,X2),X2)),mult(X2,X2)),
inference(cp,[status(thm)],[t158,t278]) ).
cnf(t53,plain,
mult(X1,X1) = rd(X1,ld(X1,unit)),
inference(cp,[status(thm)],[t51,t8]) ).
cnf(t59,plain,
rd(X1,ld(X1,unit)) = mult(X1,X1),
inference(orient,[status(thm)],[t53]) ).
cnf(t60,plain,
mult(rd(unit,X1),rd(unit,X1)) = rd(rd(unit,X1),X1),
inference(cp,[status(thm)],[t59,t34]) ).
cnf(t77,plain,
mult(rd(unit,X1),rd(unit,X1)) = rd(rd(unit,X1),X1),
inference(orient,[status(thm)],[t60]) ).
cnf(t6192,plain,
mult(X1,rd(rd(unit,X2),X2)) = rd(mult(X1,mult(rd(unit,X2),X2)),mult(X2,X2)),
inference(step,[status(thm)],[t284,t77]) ).
cnf(t6193,plain,
mult(X1,rd(unit,mult(X2,X2))) = rd(mult(X1,mult(rd(unit,X2),X2)),mult(X2,X2)),
inference(step,[status(thm)],[t6192,t299]) ).
cnf(t6194,plain,
mult(X1,rd(unit,mult(X2,X2))) = rd(mult(X1,unit),mult(X2,X2)),
inference(step,[status(thm)],[t6193,t11]) ).
cnf(t6195,plain,
mult(X1,rd(unit,mult(X2,X2))) = rd(X1,mult(X2,X2)),
inference(step,[status(thm)],[t6194,t8]) ).
cnf(t392,plain,
mult(X1,rd(unit,mult(X2,X2))) = rd(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t6195]) ).
cnf(t6357,plain,
mult(X1,mult(X1,ld(X2,X3))) = ld(rd(X2,mult(X1,X1)),X3),
inference(step,[status(thm)],[t6356,t392]) ).
cnf(t6358,plain,
mult(X1,mult(X1,ld(X2,X3))) = mult(rd(mult(X1,X1),X2),X3),
inference(step,[status(thm)],[t6357,t1841]) ).
cnf(t5834,plain,
mult(rd(mult(X1,X1),X2),X3) = mult(X1,mult(X1,ld(X2,X3))),
inference(orient,[status(thm)],[t6358]) ).
cnf(t830,plain,
ld(X1,ld(X1,ld(X2,unit))) = rd(unit,mult(X2,mult(X1,X1))),
inference(cp,[status(thm)],[t338,t804]) ).
cnf(t6208,plain,
ld(X1,ld(X1,rd(unit,X2))) = rd(unit,mult(X2,mult(X1,X1))),
inference(step,[status(thm)],[t830,t322]) ).
cnf(t848,plain,
ld(X1,ld(X1,rd(unit,X2))) = rd(unit,mult(X2,mult(X1,X1))),
inference(orient,[status(thm)],[t6208]) ).
cnf(t856,plain,
ld(X1,rd(unit,X2)) = mult(X1,rd(unit,mult(X2,mult(X1,X1)))),
inference(cp,[status(thm)],[t7,t848]) ).
cnf(t905,plain,
mult(X1,rd(unit,mult(X2,mult(X1,X1)))) = ld(X1,rd(unit,X2)),
inference(orient,[status(thm)],[t856]) ).
cnf(t914,plain,
ld(X1,rd(unit,rd(X2,mult(X1,X1)))) = mult(X1,rd(unit,X2)),
inference(cp,[status(thm)],[t905,t11]) ).
cnf(t927,plain,
ld(X1,rd(unit,rd(X2,mult(X1,X1)))) = mult(X1,rd(unit,X2)),
inference(orient,[status(thm)],[t914]) ).
cnf(t928,plain,
mult(mult(X1,X1),rd(unit,X2)) = ld(X1,ld(X1,rd(unit,rd(X2,mult(mult(X1,X1),mult(X1,X1)))))),
inference(cp,[status(thm)],[t927,t70]) ).
cnf(t6209,plain,
mult(X1,mult(X1,rd(unit,X2))) = ld(X1,ld(X1,rd(unit,rd(X2,mult(mult(X1,X1),mult(X1,X1)))))),
inference(step,[status(thm)],[t928,t35]) ).
cnf(t6210,plain,
mult(X1,mult(X1,rd(unit,X2))) = rd(unit,mult(rd(X2,mult(mult(X1,X1),mult(X1,X1))),mult(X1,X1))),
inference(step,[status(thm)],[t6209,t848]) ).
cnf(t332,plain,
mult(X1,mult(X2,X2)) = rd(mult(X1,mult(X2,unit)),rd(unit,X2)),
inference(cp,[status(thm)],[t158,t322]) ).
cnf(t6196,plain,
mult(X1,mult(X2,X2)) = rd(mult(X1,X2),rd(unit,X2)),
inference(step,[status(thm)],[t332,t8]) ).
cnf(t415,plain,
rd(mult(X1,X2),rd(unit,X2)) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t6196]) ).
cnf(t424,plain,
mult(X1,mult(rd(unit,X2),rd(unit,X2))) = rd(mult(X1,rd(unit,X2)),X2),
inference(cp,[status(thm)],[t415,t338]) ).
cnf(t6199,plain,
mult(X1,rd(rd(unit,X2),X2)) = rd(mult(X1,rd(unit,X2)),X2),
inference(step,[status(thm)],[t424,t77]) ).
cnf(t6200,plain,
mult(X1,rd(unit,mult(X2,X2))) = rd(mult(X1,rd(unit,X2)),X2),
inference(step,[status(thm)],[t6199,t299]) ).
cnf(t6201,plain,
rd(X1,mult(X2,X2)) = rd(mult(X1,rd(unit,X2)),X2),
inference(step,[status(thm)],[t6200,t392]) ).
cnf(t460,plain,
rd(mult(X1,rd(unit,X2)),X2) = rd(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t6201]) ).
cnf(t474,plain,
mult(X1,rd(unit,X2)) = mult(rd(X1,mult(X2,X2)),X2),
inference(cp,[status(thm)],[t11,t460]) ).
cnf(t490,plain,
mult(rd(X1,mult(X2,X2)),X2) = mult(X1,rd(unit,X2)),
inference(orient,[status(thm)],[t474]) ).
cnf(t6211,plain,
mult(X1,mult(X1,rd(unit,X2))) = rd(unit,mult(X2,rd(unit,mult(X1,X1)))),
inference(step,[status(thm)],[t6210,t490]) ).
cnf(t6212,plain,
mult(X1,mult(X1,rd(unit,X2))) = rd(unit,rd(X2,mult(X1,X1))),
inference(step,[status(thm)],[t6211,t392]) ).
cnf(t947,plain,
mult(X1,mult(X1,rd(unit,X2))) = rd(unit,rd(X2,mult(X1,X1))),
inference(orient,[status(thm)],[t6212]) ).
cnf(t958,plain,
rd(unit,rd(rd(unit,X1),mult(X2,X2))) = mult(X2,mult(X2,X1)),
inference(cp,[status(thm)],[t947,t338]) ).
cnf(t1070,plain,
rd(unit,rd(rd(unit,X1),mult(X2,X2))) = mult(X2,mult(X2,X1)),
inference(orient,[status(thm)],[t958]) ).
cnf(t1083,plain,
rd(rd(unit,X1),mult(X2,X2)) = rd(unit,mult(X2,mult(X2,X1))),
inference(cp,[status(thm)],[t338,t1070]) ).
cnf(t1105,plain,
rd(rd(unit,X1),mult(X2,X2)) = rd(unit,mult(X2,mult(X2,X1))),
inference(orient,[status(thm)],[t1083]) ).
cnf(t1805,plain,
rd(mult(X1,X1),rd(unit,X2)) = rd(unit,rd(unit,mult(X1,mult(X1,X2)))),
inference(cp,[status(thm)],[t1797,t1105]) ).
cnf(t6277,plain,
rd(mult(X1,X1),rd(unit,X2)) = mult(X1,mult(X1,X2)),
inference(step,[status(thm)],[t1805,t338]) ).
cnf(t2084,plain,
rd(mult(X1,X1),rd(unit,X2)) = mult(X1,mult(X1,X2)),
inference(orient,[status(thm)],[t6277]) ).
cnf(t5847,plain,
mult(X1,mult(X1,ld(rd(unit,X2),X3))) = mult(mult(X1,mult(X1,X2)),X3),
inference(cp,[status(thm)],[t5834,t2084]) ).
cnf(t6360,plain,
mult(X1,mult(X1,mult(X2,X3))) = mult(mult(X1,mult(X1,X2)),X3),
inference(step,[status(thm)],[t5847,t1739]) ).
cnf(t6042,plain,
mult(mult(X1,mult(X1,X2)),X3) = mult(X1,mult(X1,mult(X2,X3))),
inference(orient,[status(thm)],[t6360]) ).
cnf(goal_0,negated_conjecture,
mult(mult(a,mult(a,b)),c) != mult(mult(a,a),mult(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
mult(a,mult(a,mult(b,c))) != mult(mult(a,a),mult(b,c)),
inference(rw,[status(thm)],[goal_0,t6042]) ).
cnf(g0_1,plain,
mult(a,mult(a,mult(b,c))) != mult(a,mult(a,mult(b,c))),
inference(rw,[status(thm)],[g0_0,t35]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP686-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 15:42:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.12/1.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.12/1.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------