%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP683-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:28:02 PM UTC 2026
% Result : Unsatisfiable 5.27s 1.23s
% Output : CNFRefutation 5.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 83
% Number of leaves : 8
% Syntax : Number of clauses : 181 ( 181 unt; 0 nHn; 4 RR)
% Number of literals : 181 ( 180 equ; 3 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 : 431 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t14,plain,
ld(X1,mult(X1,X2)) = mult(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t2]) ).
cnf(t5,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t1851,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(t1852,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(step,[status(thm)],[t1851,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)],[t1852]) ).
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(t1895,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)],[t1895]) ).
cnf(t0,axiom,
ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t8,plain,
ld(X1,mult(X1,X1)) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t1850,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)],[t1850]) ).
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/sandbox2/benchmark/theBenchmark.p') ).
cnf(t1853,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)],[t1853]) ).
cnf(t1854,plain,
rd(mult(rd(X1,X1),X1),X1) = ld(X1,X1),
inference(step,[status(thm)],[t35,t29]) ).
cnf(t3,axiom,
rd(mult(X1,X2),X2) = mult(rd(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t16,plain,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
inference(orient,[status(thm)],[t3]) ).
cnf(t1855,plain,
rd(rd(mult(X1,X1),X1),X1) = ld(X1,X1),
inference(step,[status(thm)],[t1854,t16]) ).
cnf(t1,axiom,
rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t7,plain,
rd(mult(X1,X1),X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t1856,plain,
rd(X1,X1) = ld(X1,X1),
inference(step,[status(thm)],[t1855,t7]) ).
cnf(t38,plain,
ld(X1,X1) = rd(X1,X1),
inference(orient,[status(thm)],[t1856]) ).
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(t1857,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)],[t1857]) ).
cnf(t43,plain,
mult(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t41]) ).
cnf(t1896,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(t1897,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(mult(X1,rd(X1,X1)),mult(X2,X3))),
inference(step,[status(thm)],[t1896,t38]) ).
cnf(t1898,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(step,[status(thm)],[t1897,t43]) ).
cnf(t769,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(orient,[status(thm)],[t1898]) ).
cnf(t782,plain,
mult(X1,ld(X1,mult(X1,X2))) = mult(mult(X1,rd(X1,X1)),X2),
inference(cp,[status(thm)],[t769,t38]) ).
cnf(t1905,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(mult(X1,rd(X1,X1)),X2),
inference(step,[status(thm)],[t782,t14]) ).
cnf(t1906,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(step,[status(thm)],[t1905,t43]) ).
cnf(t822,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(orient,[status(thm)],[t1906]) ).
cnf(t1858,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)],[t1858]) ).
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/sandbox2/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(t1860,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)],[t1860]) ).
cnf(t1861,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)],[t1861]) ).
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(t1865,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)],[t1865]) ).
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(t1866,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = mult(rd(X1,X1),X1),
inference(step,[status(thm)],[t111,t75]) ).
cnf(t1867,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = rd(mult(X1,X1),X1),
inference(step,[status(thm)],[t1866,t16]) ).
cnf(t1868,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = X1,
inference(step,[status(thm)],[t1867,t7]) ).
cnf(t115,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = X1,
inference(orient,[status(thm)],[t1868]) ).
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(t1871,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)],[t1871]) ).
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(t1879,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)],[t1879]) ).
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(t1869,plain,
rd(X1,X2) = rd(mult(rd(X1,X2),X2),X2),
inference(step,[status(thm)],[t121,t115]) ).
cnf(t1870,plain,
rd(X1,X2) = rd(rd(mult(X1,X2),X2),X2),
inference(step,[status(thm)],[t1869,t16]) ).
cnf(t122,plain,
rd(rd(mult(X1,X2),X2),X2) = rd(X1,X2),
inference(orient,[status(thm)],[t1870]) ).
cnf(t1872,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)],[t1872]) ).
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(t1880,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(t1874,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(t1875,plain,
mult(X1,rd(X2,X3)) = mult(rd(mult(X1,X3),X3),rd(X2,X3)),
inference(step,[status(thm)],[t1874,t93]) ).
cnf(t180,plain,
mult(rd(mult(X1,X2),X2),rd(X3,X2)) = mult(X1,rd(X3,X2)),
inference(orient,[status(thm)],[t1875]) ).
cnf(t1881,plain,
mult(rd(X1,X1),rd(X2,X2)) = mult(rd(X1,X1),ld(rd(X1,X1),rd(X2,X2))),
inference(step,[status(thm)],[t1880,t180]) ).
cnf(t1882,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(rd(X1,X1),rd(X1,X1)),X2),X2),
inference(step,[status(thm)],[t1881,t86]) ).
cnf(t1883,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(X1,X1),X2),X2),
inference(step,[status(thm)],[t1882,t158]) ).
cnf(t375,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(X1,X1),X2),X2),
inference(orient,[status(thm)],[t1883]) ).
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(t1884,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)],[t1884]) ).
cnf(t1885,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)],[t1885]) ).
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(t1891,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(t1892,plain,
rd(mult(mult(X1,rd(X2,X2)),X3),X3) = mult(X1,rd(rd(X2,X2),rd(X3,X3))),
inference(step,[status(thm)],[t1891,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)],[t1892]) ).
cnf(t1910,plain,
mult(X1,rd(X2,X2)) = rd(mult(mult(X1,rd(X1,X1)),X2),X2),
inference(step,[status(thm)],[t824,t451]) ).
cnf(t1911,plain,
mult(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(step,[status(thm)],[t1910,t43]) ).
cnf(t855,plain,
mult(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(orient,[status(thm)],[t1911]) ).
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(t1914,plain,
rd(X1,rd(X2,X2)) = rd(mult(X1,rd(X2,X2)),rd(X2,X2)),
inference(step,[status(thm)],[t859,t145]) ).
cnf(t1915,plain,
rd(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(step,[status(thm)],[t1914,t128]) ).
cnf(t888,plain,
rd(mult(X1,X2),X2) = rd(X1,rd(X2,X2)),
inference(orient,[status(thm)],[t1915]) ).
cnf(t1916,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)],[t1916]) ).
cnf(t905,plain,
rd(mult(X1,X2),rd(X2,X2)) = mult(rd(X1,rd(X2,X2)),X2),
inference(cp,[status(thm)],[t889,t888]) ).
cnf(t1934,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)],[t1934]) ).
cnf(t932,plain,
rd(mult(X1,X2),rd(X2,X2)) = mult(X1,X2),
inference(orient,[status(thm)],[t914]) ).
cnf(t1953,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)],[t1953]) ).
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(t1873,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)],[t1873]) ).
cnf(t1930,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(mult(X1,X3),X3),
inference(step,[status(thm)],[t163,t888]) ).
cnf(t1931,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t1930,t888]) ).
cnf(t912,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(X1,rd(X3,X3)),
inference(rw,[status(thm)],[t1931]) ).
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(t1983,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)],[t1983]) ).
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(t1955,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(t1956,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(mult(X2,X3),mult(X2,X3))),
inference(step,[status(thm)],[t1955,t822]) ).
cnf(t1957,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t1956,t1012]) ).
cnf(t1152,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t1957]) ).
cnf(t1984,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(t1985,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)],[t1984,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(t1960,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(t1863,plain,
X1 = rd(mult(X1,rd(X1,X1)),rd(X1,X1)),
inference(step,[status(thm)],[t78,t43]) ).
cnf(t1864,plain,
X1 = rd(X1,rd(X1,X1)),
inference(step,[status(thm)],[t1863,t43]) ).
cnf(t85,plain,
rd(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t1864]) ).
cnf(t1961,plain,
mult(X1,ld(X1,X2)) = mult(rd(X1,X1),X2),
inference(step,[status(thm)],[t1960,t85]) ).
cnf(t1404,plain,
mult(rd(X1,X1),X2) = mult(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t1961]) ).
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(t1986,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)],[t1985,t1432]) ).
cnf(t1987,plain,
rd(X1,rd(X4,X4)) = rd(X1,rd(rd(X2,X2),rd(X4,X4))),
inference(step,[status(thm)],[t1986,t1012]) ).
cnf(t1680,plain,
rd(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t1987]) ).
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(t1912,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)],[t1912]) ).
cnf(t1918,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(t1919,plain,
mult(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(rd(X1,rd(X2,X2)),rd(X3,X3)),
inference(step,[status(thm)],[t1918,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)],[t1919]) ).
cnf(t1988,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(t1941,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)],[t1941]) ).
cnf(t1119,plain,
rd(rd(X1,rd(X2,X3)),rd(X3,X3)) = rd(X1,rd(X2,X3)),
inference(orient,[status(thm)],[t919]) ).
cnf(t1989,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)],[t1988,t1119]) ).
cnf(t1932,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(mult(X1,X3),X3),
inference(step,[status(thm)],[t128,t888]) ).
cnf(t1933,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t1932,t888]) ).
cnf(t913,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(X1,rd(X3,X3)),
inference(rw,[status(thm)],[t1933]) ).
cnf(t1058,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t913]) ).
cnf(t1990,plain,
rd(rd(X1,rd(X2,X2)),rd(X3,X3)) = rd(X1,rd(rd(X3,X3),rd(X3,X3))),
inference(step,[status(thm)],[t1989,t1058]) ).
cnf(t1991,plain,
rd(rd(X1,rd(X2,X2)),rd(X3,X3)) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t1990,t1058]) ).
cnf(t1737,plain,
rd(rd(X1,rd(X2,X2)),rd(X3,X3)) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t1991]) ).
cnf(t1765,plain,
mult(rd(X1,rd(X2,X2)),X3) = mult(rd(X1,rd(X3,X3)),X3),
inference(cp,[status(thm)],[t956,t1737]) ).
cnf(t1992,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)],[t1992]) ).
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(t1996,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(t1997,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)],[t1996,t1404]) ).
cnf(t1998,plain,
mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(rd(X1,X1),X3),
inference(step,[status(thm)],[t1997,t1773]) ).
cnf(t1999,plain,
mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(X1,ld(X1,X3)),
inference(step,[status(thm)],[t1998,t1404]) ).
cnf(t1820,plain,
mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(X1,ld(X1,X3)),
inference(orient,[status(thm)],[t1999]) ).
cnf(t1834,plain,
mult(X1,mult(X2,ld(X2,X3))) = mult(X1,mult(X1,ld(X1,X3))),
inference(cp,[status(thm)],[t822,t1820]) ).
cnf(t2000,plain,
mult(X1,mult(X2,ld(X2,X3))) = mult(X1,X3),
inference(step,[status(thm)],[t1834,t822]) ).
cnf(t1842,plain,
mult(X1,mult(X2,ld(X2,X3))) = mult(X1,X3),
inference(orient,[status(thm)],[t2000]) ).
cnf(goal_0,negated_conjecture,
mult(x3,ld(x4,mult(x4,x5))) != mult(x3,x5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
mult(x3,mult(x4,ld(x4,x5))) != mult(x3,x5),
inference(rw,[status(thm)],[goal_0,t14]) ).
cnf(g0_1,plain,
mult(x3,x5) != mult(x3,x5),
inference(rw,[status(thm)],[g0_0,t1842]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP683-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 15:41:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.27/1.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.27/1.23 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------