%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 01:28:01 PM UTC 2026
% Result : Unsatisfiable 5.78s 6.25s
% Output : CNFRefutation 5.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 84
% Number of leaves : 8
% Syntax : Number of clauses : 184 ( 184 unt; 0 nHn; 5 RR)
% Number of literals : 184 ( 183 equ; 4 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 : 440 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t14,plain,
ld(X1,mult(X1,X2)) = mult(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t2]) ).
cnf(t3,axiom,
rd(mult(X1,X2),X2) = mult(rd(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t16,plain,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
inference(orient,[status(thm)],[t3]) ).
cnf(t5,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t1960,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
inference(step,[status(thm)],[t5,t14]) ).
cnf(t1961,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(step,[status(thm)],[t1960,t14]) ).
cnf(t21,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(orient,[status(thm)],[t1961]) ).
cnf(t22,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(mult(X1,ld(X1,X4)),ld(ld(X1,mult(X1,X4)),mult(X2,X3))),
inference(cp,[status(thm)],[t21,t14]) ).
cnf(t2004,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(mult(X1,ld(X1,X4)),ld(mult(X1,ld(X1,X4)),mult(X2,X3))),
inference(step,[status(thm)],[t22,t14]) ).
cnf(t713,plain,
mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(orient,[status(thm)],[t2004]) ).
cnf(t0,axiom,
ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,plain,
ld(X1,mult(X1,X1)) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t1959,plain,
mult(X1,ld(X1,X1)) = X1,
inference(step,[status(thm)],[t8,t14]) ).
cnf(t15,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[t1959]) ).
cnf(t33,plain,
mult(X1,ld(X1,X1)) = X1,
inference(orient,[status(thm)],[t15]) ).
cnf(t35,plain,
mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
inference(cp,[status(thm)],[t14,t33]) ).
cnf(t4,axiom,
rd(mult(rd(X1,X1),X2),X2) = ld(X1,mult(X1,ld(X2,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t1962,plain,
rd(mult(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(step,[status(thm)],[t4,t14]) ).
cnf(t29,plain,
mult(X1,ld(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(orient,[status(thm)],[t1962]) ).
cnf(t1963,plain,
rd(mult(rd(X1,X1),X1),X1) = ld(X1,X1),
inference(step,[status(thm)],[t35,t29]) ).
cnf(t1964,plain,
rd(rd(mult(X1,X1),X1),X1) = ld(X1,X1),
inference(step,[status(thm)],[t1963,t16]) ).
cnf(t1,axiom,
rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,plain,
rd(mult(X1,X1),X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t1965,plain,
rd(X1,X1) = ld(X1,X1),
inference(step,[status(thm)],[t1964,t7]) ).
cnf(t38,plain,
ld(X1,X1) = rd(X1,X1),
inference(orient,[status(thm)],[t1965]) ).
cnf(t717,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(mult(X1,rd(X1,X1)),ld(mult(X1,ld(X1,X1)),mult(X2,X3))),
inference(cp,[status(thm)],[t713,t38]) ).
cnf(t1966,plain,
mult(X1,rd(X1,X1)) = X1,
inference(step,[status(thm)],[t33,t38]) ).
cnf(t41,plain,
mult(X1,rd(X1,X1)) = X1,
inference(rw,[status(thm)],[t1966]) ).
cnf(t43,plain,
mult(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t41]) ).
cnf(t2005,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(mult(X1,ld(X1,X1)),mult(X2,X3))),
inference(step,[status(thm)],[t717,t43]) ).
cnf(t2006,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(mult(X1,rd(X1,X1)),mult(X2,X3))),
inference(step,[status(thm)],[t2005,t38]) ).
cnf(t2007,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(step,[status(thm)],[t2006,t43]) ).
cnf(t769,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(orient,[status(thm)],[t2007]) ).
cnf(t782,plain,
mult(X1,ld(X1,mult(X1,X2))) = mult(mult(X1,rd(X1,X1)),X2),
inference(cp,[status(thm)],[t769,t38]) ).
cnf(t2014,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(mult(X1,rd(X1,X1)),X2),
inference(step,[status(thm)],[t782,t14]) ).
cnf(t2015,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(step,[status(thm)],[t2014,t43]) ).
cnf(t822,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(orient,[status(thm)],[t2015]) ).
cnf(t1967,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(step,[status(thm)],[t29,t38]) ).
cnf(t42,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(rw,[status(thm)],[t1967]) ).
cnf(t86,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(orient,[status(thm)],[t42]) ).
cnf(t6,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
inference(orient,[status(thm)],[t6]) ).
cnf(t10,plain,
mult(X1,rd(mult(X2,X3),X3)) = rd(mult(mult(X1,X2),X3),rd(mult(X3,X3),X3)),
inference(cp,[status(thm)],[t9,t7]) ).
cnf(t1969,plain,
mult(X1,rd(mult(X2,X3),X3)) = rd(mult(mult(X1,X2),X3),X3),
inference(step,[status(thm)],[t10,t7]) ).
cnf(t57,plain,
mult(X1,rd(mult(X2,X3),X3)) = rd(mult(mult(X1,X2),X3),X3),
inference(orient,[status(thm)],[t1969]) ).
cnf(t1970,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = rd(mult(mult(X1,X2),X4),X4),
inference(step,[status(thm)],[t9,t57]) ).
cnf(t58,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = rd(mult(mult(X1,X2),X4),X4),
inference(orient,[status(thm)],[t1970]) ).
cnf(t87,plain,
rd(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1) = mult(rd(X1,X1),rd(rd(X1,X1),rd(X1,X1))),
inference(cp,[status(thm)],[t86,t38]) ).
cnf(t1974,plain,
rd(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1) = rd(X1,X1),
inference(step,[status(thm)],[t87,t43]) ).
cnf(t109,plain,
rd(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1) = rd(X1,X1),
inference(orient,[status(thm)],[t1974]) ).
cnf(t111,plain,
rd(mult(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X1),X1) = mult(rd(X1,X1),X1),
inference(cp,[status(thm)],[t16,t109]) ).
cnf(t61,plain,
rd(mult(mult(X1,X2),X2),X2) = mult(X1,X2),
inference(cp,[status(thm)],[t57,t7]) ).
cnf(t75,plain,
rd(mult(mult(X1,X2),X2),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t61]) ).
cnf(t1975,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = mult(rd(X1,X1),X1),
inference(step,[status(thm)],[t111,t75]) ).
cnf(t1976,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = rd(mult(X1,X1),X1),
inference(step,[status(thm)],[t1975,t16]) ).
cnf(t1977,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = X1,
inference(step,[status(thm)],[t1976,t7]) ).
cnf(t115,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = X1,
inference(orient,[status(thm)],[t1977]) ).
cnf(t118,plain,
rd(mult(mult(rd(rd(X1,X1),rd(X1,X1)),X1),X2),X2) = rd(mult(X1,rd(X3,X2)),rd(X3,X2)),
inference(cp,[status(thm)],[t58,t115]) ).
cnf(t1980,plain,
rd(mult(X1,X2),X2) = rd(mult(X1,rd(X3,X2)),rd(X3,X2)),
inference(step,[status(thm)],[t118,t115]) ).
cnf(t128,plain,
rd(mult(X1,rd(X2,X3)),rd(X2,X3)) = rd(mult(X1,X3),X3),
inference(orient,[status(thm)],[t1980]) ).
cnf(t39,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(rd(X1,X1),ld(ld(X1,X1),mult(X2,X3))),
inference(cp,[status(thm)],[t21,t38]) ).
cnf(t1988,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(rd(X1,X1),ld(rd(X1,X1),mult(X2,X3))),
inference(step,[status(thm)],[t39,t38]) ).
cnf(t339,plain,
mult(rd(X1,X1),ld(rd(X1,X1),mult(X2,X3))) = mult(mult(X1,ld(X1,X2)),X3),
inference(orient,[status(thm)],[t1988]) ).
cnf(t132,plain,
rd(mult(rd(X1,rd(X2,X3)),X3),X3) = rd(rd(mult(X1,rd(X2,X3)),rd(X2,X3)),rd(X2,X3)),
inference(cp,[status(thm)],[t128,t16]) ).
cnf(t76,plain,
mult(X1,rd(X2,X3)) = rd(mult(mult(X1,rd(X2,X3)),X3),X3),
inference(cp,[status(thm)],[t75,t58]) ).
cnf(t93,plain,
rd(mult(mult(X1,rd(X2,X3)),X3),X3) = mult(X1,rd(X2,X3)),
inference(orient,[status(thm)],[t76]) ).
cnf(t121,plain,
mult(rd(rd(rd(X1,X2),rd(X1,X2)),rd(rd(X1,X2),rd(X1,X2))),rd(X1,X2)) = rd(mult(rd(X1,X2),X2),X2),
inference(cp,[status(thm)],[t93,t115]) ).
cnf(t1978,plain,
rd(X1,X2) = rd(mult(rd(X1,X2),X2),X2),
inference(step,[status(thm)],[t121,t115]) ).
cnf(t1979,plain,
rd(X1,X2) = rd(rd(mult(X1,X2),X2),X2),
inference(step,[status(thm)],[t1978,t16]) ).
cnf(t122,plain,
rd(rd(mult(X1,X2),X2),X2) = rd(X1,X2),
inference(orient,[status(thm)],[t1979]) ).
cnf(t1981,plain,
rd(mult(rd(X1,rd(X2,X3)),X3),X3) = rd(X1,rd(X2,X3)),
inference(step,[status(thm)],[t132,t122]) ).
cnf(t145,plain,
rd(mult(rd(X1,rd(X2,X3)),X3),X3) = rd(X1,rd(X2,X3)),
inference(orient,[status(thm)],[t1981]) ).
cnf(t147,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(cp,[status(thm)],[t145,t115]) ).
cnf(t158,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(orient,[status(thm)],[t147]) ).
cnf(t159,plain,
rd(X1,X1) = mult(rd(X1,X1),rd(X1,X1)),
inference(cp,[status(thm)],[t43,t158]) ).
cnf(t161,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(orient,[status(thm)],[t159]) ).
cnf(t353,plain,
mult(mult(X1,ld(X1,rd(X2,X2))),rd(X2,X2)) = mult(rd(X1,X1),ld(rd(X1,X1),rd(X2,X2))),
inference(cp,[status(thm)],[t339,t161]) ).
cnf(t1989,plain,
mult(rd(mult(rd(X1,X1),X2),X2),rd(X2,X2)) = mult(rd(X1,X1),ld(rd(X1,X1),rd(X2,X2))),
inference(step,[status(thm)],[t353,t86]) ).
cnf(t140,plain,
rd(mult(mult(X1,rd(X2,X3)),rd(X2,X3)),rd(X2,X3)) = mult(rd(mult(X1,X3),X3),rd(X2,X3)),
inference(cp,[status(thm)],[t16,t128]) ).
cnf(t1983,plain,
rd(mult(mult(X1,rd(X2,X3)),X3),X3) = mult(rd(mult(X1,X3),X3),rd(X2,X3)),
inference(step,[status(thm)],[t140,t58]) ).
cnf(t1984,plain,
mult(X1,rd(X2,X3)) = mult(rd(mult(X1,X3),X3),rd(X2,X3)),
inference(step,[status(thm)],[t1983,t93]) ).
cnf(t180,plain,
mult(rd(mult(X1,X2),X2),rd(X3,X2)) = mult(X1,rd(X3,X2)),
inference(orient,[status(thm)],[t1984]) ).
cnf(t1990,plain,
mult(rd(X1,X1),rd(X2,X2)) = mult(rd(X1,X1),ld(rd(X1,X1),rd(X2,X2))),
inference(step,[status(thm)],[t1989,t180]) ).
cnf(t1991,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(rd(X1,X1),rd(X1,X1)),X2),X2),
inference(step,[status(thm)],[t1990,t86]) ).
cnf(t1992,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(X1,X1),X2),X2),
inference(step,[status(thm)],[t1991,t158]) ).
cnf(t375,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(X1,X1),X2),X2),
inference(orient,[status(thm)],[t1992]) ).
cnf(t389,plain,
rd(mult(rd(X1,X1),X2),X2) = rd(rd(mult(rd(X1,X1),X2),X2),rd(X2,X2)),
inference(cp,[status(thm)],[t128,t375]) ).
cnf(t141,plain,
rd(X1,rd(X2,X3)) = rd(rd(mult(X1,X3),X3),rd(X2,X3)),
inference(cp,[status(thm)],[t122,t128]) ).
cnf(t197,plain,
rd(rd(mult(X1,X2),X2),rd(X3,X2)) = rd(X1,rd(X3,X2)),
inference(orient,[status(thm)],[t141]) ).
cnf(t1993,plain,
rd(mult(rd(X1,X1),X2),X2) = rd(rd(X1,X1),rd(X2,X2)),
inference(step,[status(thm)],[t389,t197]) ).
cnf(t396,plain,
rd(mult(rd(X1,X1),X2),X2) = rd(rd(X1,X1),rd(X2,X2)),
inference(orient,[status(thm)],[t1993]) ).
cnf(t1994,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(rd(X1,X1),rd(X2,X2)),
inference(step,[status(thm)],[t86,t396]) ).
cnf(t397,plain,
mult(X1,ld(X1,rd(X2,X2))) = rd(rd(X1,X1),rd(X2,X2)),
inference(orient,[status(thm)],[t1994]) ).
cnf(t824,plain,
mult(X1,rd(X2,X2)) = mult(X1,rd(rd(X1,X1),rd(X2,X2))),
inference(cp,[status(thm)],[t822,t397]) ).
cnf(t390,plain,
rd(mult(mult(X1,rd(X2,X2)),rd(X3,X3)),rd(X3,X3)) = mult(X1,rd(rd(mult(rd(X2,X2),X3),X3),rd(X3,X3))),
inference(cp,[status(thm)],[t57,t375]) ).
cnf(t2000,plain,
rd(mult(mult(X1,rd(X2,X2)),X3),X3) = mult(X1,rd(rd(mult(rd(X2,X2),X3),X3),rd(X3,X3))),
inference(step,[status(thm)],[t390,t58]) ).
cnf(t2001,plain,
rd(mult(mult(X1,rd(X2,X2)),X3),X3) = mult(X1,rd(rd(X2,X2),rd(X3,X3))),
inference(step,[status(thm)],[t2000,t197]) ).
cnf(t451,plain,
mult(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(mult(mult(X1,rd(X2,X2)),X3),X3),
inference(orient,[status(thm)],[t2001]) ).
cnf(t2019,plain,
mult(X1,rd(X2,X2)) = rd(mult(mult(X1,rd(X1,X1)),X2),X2),
inference(step,[status(thm)],[t824,t451]) ).
cnf(t2020,plain,
mult(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(step,[status(thm)],[t2019,t43]) ).
cnf(t855,plain,
mult(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(orient,[status(thm)],[t2020]) ).
cnf(t859,plain,
rd(mult(rd(X1,rd(X2,X2)),X2),X2) = rd(mult(X1,rd(X2,X2)),rd(X2,X2)),
inference(cp,[status(thm)],[t855,t16]) ).
cnf(t2023,plain,
rd(X1,rd(X2,X2)) = rd(mult(X1,rd(X2,X2)),rd(X2,X2)),
inference(step,[status(thm)],[t859,t145]) ).
cnf(t2024,plain,
rd(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(step,[status(thm)],[t2023,t128]) ).
cnf(t888,plain,
rd(mult(X1,X2),X2) = rd(X1,rd(X2,X2)),
inference(orient,[status(thm)],[t2024]) ).
cnf(t2025,plain,
mult(rd(X1,X2),X2) = rd(X1,rd(X2,X2)),
inference(step,[status(thm)],[t16,t888]) ).
cnf(t889,plain,
mult(rd(X1,X2),X2) = rd(X1,rd(X2,X2)),
inference(orient,[status(thm)],[t2025]) ).
cnf(t905,plain,
rd(mult(X1,X2),rd(X2,X2)) = mult(rd(X1,rd(X2,X2)),X2),
inference(cp,[status(thm)],[t889,t888]) ).
cnf(t2043,plain,
rd(mult(X1,X2),rd(X2,X2)) = mult(X1,X2),
inference(step,[status(thm)],[t75,t888]) ).
cnf(t914,plain,
rd(mult(X1,X2),rd(X2,X2)) = mult(X1,X2),
inference(rw,[status(thm)],[t2043]) ).
cnf(t932,plain,
rd(mult(X1,X2),rd(X2,X2)) = mult(X1,X2),
inference(orient,[status(thm)],[t914]) ).
cnf(t2062,plain,
mult(X1,X2) = mult(rd(X1,rd(X2,X2)),X2),
inference(step,[status(thm)],[t905,t932]) ).
cnf(t956,plain,
mult(rd(X1,rd(X2,X2)),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t2062]) ).
cnf(t136,plain,
rd(mult(X1,X2),X2) = rd(mult(X1,mult(X3,X2)),rd(mult(mult(X3,X2),X2),X2)),
inference(cp,[status(thm)],[t128,t75]) ).
cnf(t1982,plain,
rd(mult(X1,X2),X2) = rd(mult(X1,mult(X3,X2)),mult(X3,X2)),
inference(step,[status(thm)],[t136,t75]) ).
cnf(t163,plain,
rd(mult(X1,mult(X2,X3)),mult(X2,X3)) = rd(mult(X1,X3),X3),
inference(orient,[status(thm)],[t1982]) ).
cnf(t2039,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(mult(X1,X3),X3),
inference(step,[status(thm)],[t163,t888]) ).
cnf(t2040,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t2039,t888]) ).
cnf(t912,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(X1,rd(X3,X3)),
inference(rw,[status(thm)],[t2040]) ).
cnf(t1012,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t912]) ).
cnf(t785,plain,
mult(X1,ld(X1,mult(mult(X1,X2),X3))) = mult(mult(X1,mult(X1,ld(X1,X2))),X3),
inference(cp,[status(thm)],[t769,t14]) ).
cnf(t2092,plain,
mult(X1,ld(X1,mult(mult(X1,X2),X3))) = mult(mult(X1,X2),X3),
inference(step,[status(thm)],[t785,t822]) ).
cnf(t1653,plain,
mult(X1,ld(X1,mult(mult(X1,X2),X3))) = mult(mult(X1,X2),X3),
inference(orient,[status(thm)],[t2092]) ).
cnf(t1677,plain,
rd(X1,rd(ld(X2,mult(mult(X2,X3),X4)),ld(X2,mult(mult(X2,X3),X4)))) = rd(X1,rd(mult(X2,ld(X2,mult(mult(X2,X3),X4))),mult(mult(X2,X3),X4))),
inference(cp,[status(thm)],[t1012,t1653]) ).
cnf(t1017,plain,
rd(X1,rd(mult(X2,ld(X2,X3)),mult(X2,ld(X2,X3)))) = rd(X1,rd(mult(X2,X3),mult(X2,mult(X2,ld(X2,X3))))),
inference(cp,[status(thm)],[t1012,t822]) ).
cnf(t2064,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(mult(X2,X3),mult(X2,mult(X2,ld(X2,X3))))),
inference(step,[status(thm)],[t1017,t1012]) ).
cnf(t2065,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(mult(X2,X3),mult(X2,X3))),
inference(step,[status(thm)],[t2064,t822]) ).
cnf(t2066,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t2065,t1012]) ).
cnf(t1152,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t2066]) ).
cnf(t2093,plain,
rd(X1,rd(mult(mult(X2,X3),X4),mult(mult(X2,X3),X4))) = rd(X1,rd(mult(X2,ld(X2,mult(mult(X2,X3),X4))),mult(mult(X2,X3),X4))),
inference(step,[status(thm)],[t1677,t1152]) ).
cnf(t2094,plain,
rd(X1,rd(X4,X4)) = rd(X1,rd(mult(X2,ld(X2,mult(mult(X2,X3),X4))),mult(mult(X2,X3),X4))),
inference(step,[status(thm)],[t2093,t1012]) ).
cnf(t779,plain,
mult(X1,ld(X1,mult(rd(X2,X2),X3))) = mult(rd(rd(X1,X1),rd(X2,X2)),X3),
inference(cp,[status(thm)],[t769,t397]) ).
cnf(t1367,plain,
mult(rd(rd(X1,X1),rd(X2,X2)),X3) = mult(X1,ld(X1,mult(rd(X2,X2),X3))),
inference(orient,[status(thm)],[t779]) ).
cnf(t1368,plain,
mult(X1,ld(X1,mult(rd(X2,X2),X2))) = mult(rd(X1,X1),X2),
inference(cp,[status(thm)],[t1367,t956]) ).
cnf(t2069,plain,
mult(X1,ld(X1,rd(X2,rd(X2,X2)))) = mult(rd(X1,X1),X2),
inference(step,[status(thm)],[t1368,t889]) ).
cnf(t78,plain,
mult(X1,rd(X1,X1)) = rd(mult(X1,rd(X1,X1)),rd(X1,X1)),
inference(cp,[status(thm)],[t75,t43]) ).
cnf(t1972,plain,
X1 = rd(mult(X1,rd(X1,X1)),rd(X1,X1)),
inference(step,[status(thm)],[t78,t43]) ).
cnf(t1973,plain,
X1 = rd(X1,rd(X1,X1)),
inference(step,[status(thm)],[t1972,t43]) ).
cnf(t85,plain,
rd(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t1973]) ).
cnf(t2070,plain,
mult(X1,ld(X1,X2)) = mult(rd(X1,X1),X2),
inference(step,[status(thm)],[t2069,t85]) ).
cnf(t1404,plain,
mult(rd(X1,X1),X2) = mult(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t2070]) ).
cnf(t1419,plain,
rd(rd(X1,X1),rd(X2,X2)) = rd(mult(X1,ld(X1,X2)),X2),
inference(cp,[status(thm)],[t888,t1404]) ).
cnf(t1432,plain,
rd(mult(X1,ld(X1,X2)),X2) = rd(rd(X1,X1),rd(X2,X2)),
inference(orient,[status(thm)],[t1419]) ).
cnf(t2095,plain,
rd(X1,rd(X4,X4)) = rd(X1,rd(rd(X2,X2),rd(mult(mult(X2,X3),X4),mult(mult(X2,X3),X4)))),
inference(step,[status(thm)],[t2094,t1432]) ).
cnf(t2096,plain,
rd(X1,rd(X4,X4)) = rd(X1,rd(rd(X2,X2),rd(X4,X4))),
inference(step,[status(thm)],[t2095,t1012]) ).
cnf(t1680,plain,
rd(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t2096]) ).
cnf(t1689,plain,
rd(mult(X1,rd(rd(X2,X2),rd(X3,X3))),rd(X3,X3)) = rd(X1,rd(rd(rd(X2,X2),rd(X3,X3)),rd(rd(X2,X2),rd(X3,X3)))),
inference(cp,[status(thm)],[t1680,t888]) ).
cnf(t2021,plain,
mult(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(mult(rd(mult(X1,X2),X2),X3),X3),
inference(step,[status(thm)],[t451,t855]) ).
cnf(t856,plain,
mult(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(mult(rd(mult(X1,X2),X2),X3),X3),
inference(orient,[status(thm)],[t2021]) ).
cnf(t2027,plain,
mult(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(rd(mult(X1,X2),X2),rd(X3,X3)),
inference(step,[status(thm)],[t856,t888]) ).
cnf(t2028,plain,
mult(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(rd(X1,rd(X2,X2)),rd(X3,X3)),
inference(step,[status(thm)],[t2027,t888]) ).
cnf(t891,plain,
mult(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(rd(X1,rd(X2,X2)),rd(X3,X3)),
inference(orient,[status(thm)],[t2028]) ).
cnf(t2097,plain,
rd(rd(rd(X1,rd(X2,X2)),rd(X3,X3)),rd(X3,X3)) = rd(X1,rd(rd(rd(X2,X2),rd(X3,X3)),rd(rd(X2,X2),rd(X3,X3)))),
inference(step,[status(thm)],[t1689,t891]) ).
cnf(t2050,plain,
rd(rd(X1,rd(X2,X3)),rd(X3,X3)) = rd(X1,rd(X2,X3)),
inference(step,[status(thm)],[t145,t888]) ).
cnf(t919,plain,
rd(rd(X1,rd(X2,X3)),rd(X3,X3)) = rd(X1,rd(X2,X3)),
inference(rw,[status(thm)],[t2050]) ).
cnf(t1119,plain,
rd(rd(X1,rd(X2,X3)),rd(X3,X3)) = rd(X1,rd(X2,X3)),
inference(orient,[status(thm)],[t919]) ).
cnf(t2098,plain,
rd(rd(X1,rd(X2,X2)),rd(X3,X3)) = rd(X1,rd(rd(rd(X2,X2),rd(X3,X3)),rd(rd(X2,X2),rd(X3,X3)))),
inference(step,[status(thm)],[t2097,t1119]) ).
cnf(t2041,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(mult(X1,X3),X3),
inference(step,[status(thm)],[t128,t888]) ).
cnf(t2042,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t2041,t888]) ).
cnf(t913,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(X1,rd(X3,X3)),
inference(rw,[status(thm)],[t2042]) ).
cnf(t1058,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t913]) ).
cnf(t2099,plain,
rd(rd(X1,rd(X2,X2)),rd(X3,X3)) = rd(X1,rd(rd(X3,X3),rd(X3,X3))),
inference(step,[status(thm)],[t2098,t1058]) ).
cnf(t2100,plain,
rd(rd(X1,rd(X2,X2)),rd(X3,X3)) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t2099,t1058]) ).
cnf(t1737,plain,
rd(rd(X1,rd(X2,X2)),rd(X3,X3)) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t2100]) ).
cnf(t1765,plain,
mult(rd(X1,rd(X2,X2)),X3) = mult(rd(X1,rd(X3,X3)),X3),
inference(cp,[status(thm)],[t956,t1737]) ).
cnf(t2101,plain,
mult(rd(X1,rd(X2,X2)),X3) = mult(X1,X3),
inference(step,[status(thm)],[t1765,t956]) ).
cnf(t1773,plain,
mult(rd(X1,rd(X2,X2)),X3) = mult(X1,X3),
inference(orient,[status(thm)],[t2101]) ).
cnf(t1780,plain,
mult(mult(X1,ld(X1,rd(X2,X2))),X3) = mult(rd(rd(X1,X1),rd(rd(X2,X2),rd(X2,X2))),X3),
inference(cp,[status(thm)],[t1773,t1432]) ).
cnf(t2105,plain,
mult(X1,ld(X1,mult(rd(X2,X2),X3))) = mult(rd(rd(X1,X1),rd(rd(X2,X2),rd(X2,X2))),X3),
inference(step,[status(thm)],[t1780,t769]) ).
cnf(t2106,plain,
mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(rd(rd(X1,X1),rd(rd(X2,X2),rd(X2,X2))),X3),
inference(step,[status(thm)],[t2105,t1404]) ).
cnf(t2107,plain,
mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(rd(X1,X1),X3),
inference(step,[status(thm)],[t2106,t1773]) ).
cnf(t2108,plain,
mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(X1,ld(X1,X3)),
inference(step,[status(thm)],[t2107,t1404]) ).
cnf(t1820,plain,
mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(X1,ld(X1,X3)),
inference(orient,[status(thm)],[t2108]) ).
cnf(t2008,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(X1,ld(X1,mult(X3,X4))),
inference(step,[status(thm)],[t21,t769]) ).
cnf(t770,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(X1,ld(X1,mult(X3,X4))),
inference(orient,[status(thm)],[t2008]) ).
cnf(t1824,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,mult(X4,ld(X4,X3)))),
inference(cp,[status(thm)],[t1820,t770]) ).
cnf(t2115,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(step,[status(thm)],[t1824,t1820]) ).
cnf(t1934,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(orient,[status(thm)],[t2115]) ).
cnf(goal_0,negated_conjecture,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
mult(ld(x0,x1),ld(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
inference(rw,[status(thm)],[goal_0,t14]) ).
cnf(g0_1,plain,
mult(x0,ld(x0,x2)) != ld(x0,mult(x0,x2)),
inference(rw,[status(thm)],[g0_0,t1934]) ).
cnf(g0_2,plain,
mult(x0,ld(x0,x2)) != mult(x0,ld(x0,x2)),
inference(rw,[status(thm)],[g0_1,t14]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.36 % Computer : n006.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
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Wed Sep 23 15:40:54 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.78/6.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.78/6.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------