%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP683-11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 7.05s 6.68s
% Output : CNFRefutation 7.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 8
% Syntax : Number of clauses : 172 ( 172 unt; 0 nHn; 4 RR)
% Number of literals : 172 ( 171 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 : 404 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(t1792,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(t1793,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(step,[status(thm)],[t1792,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)],[t1793]) ).
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(t1836,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)],[t1836]) ).
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(t1791,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)],[t1791]) ).
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(t1794,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)],[t1794]) ).
cnf(t1795,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/sandbox/benchmark/theBenchmark.p') ).
cnf(t16,plain,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
inference(orient,[status(thm)],[t3]) ).
cnf(t1796,plain,
rd(rd(mult(X1,X1),X1),X1) = ld(X1,X1),
inference(step,[status(thm)],[t1795,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(t1797,plain,
rd(X1,X1) = ld(X1,X1),
inference(step,[status(thm)],[t1796,t7]) ).
cnf(t38,plain,
ld(X1,X1) = rd(X1,X1),
inference(orient,[status(thm)],[t1797]) ).
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(t1798,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)],[t1798]) ).
cnf(t43,plain,
mult(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t41]) ).
cnf(t1837,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(t1838,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(mult(X1,rd(X1,X1)),mult(X2,X3))),
inference(step,[status(thm)],[t1837,t38]) ).
cnf(t1839,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(step,[status(thm)],[t1838,t43]) ).
cnf(t769,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(orient,[status(thm)],[t1839]) ).
cnf(t782,plain,
mult(X1,ld(X1,mult(X1,X2))) = mult(mult(X1,rd(X1,X1)),X2),
inference(cp,[status(thm)],[t769,t38]) ).
cnf(t1846,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(mult(X1,rd(X1,X1)),X2),
inference(step,[status(thm)],[t782,t14]) ).
cnf(t1847,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(step,[status(thm)],[t1846,t43]) ).
cnf(t822,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(orient,[status(thm)],[t1847]) ).
cnf(t1799,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)],[t1799]) ).
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(t1801,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)],[t1801]) ).
cnf(t1802,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)],[t1802]) ).
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(t1806,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)],[t1806]) ).
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(t1807,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = mult(rd(X1,X1),X1),
inference(step,[status(thm)],[t111,t75]) ).
cnf(t1808,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = rd(mult(X1,X1),X1),
inference(step,[status(thm)],[t1807,t16]) ).
cnf(t1809,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = X1,
inference(step,[status(thm)],[t1808,t7]) ).
cnf(t115,plain,
mult(rd(rd(X1,X1),rd(X1,X1)),X1) = X1,
inference(orient,[status(thm)],[t1809]) ).
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(t1812,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)],[t1812]) ).
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(t1820,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)],[t1820]) ).
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(t1810,plain,
rd(X1,X2) = rd(mult(rd(X1,X2),X2),X2),
inference(step,[status(thm)],[t121,t115]) ).
cnf(t1811,plain,
rd(X1,X2) = rd(rd(mult(X1,X2),X2),X2),
inference(step,[status(thm)],[t1810,t16]) ).
cnf(t122,plain,
rd(rd(mult(X1,X2),X2),X2) = rd(X1,X2),
inference(orient,[status(thm)],[t1811]) ).
cnf(t1813,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)],[t1813]) ).
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(t1821,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(t1815,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(t1816,plain,
mult(X1,rd(X2,X3)) = mult(rd(mult(X1,X3),X3),rd(X2,X3)),
inference(step,[status(thm)],[t1815,t93]) ).
cnf(t180,plain,
mult(rd(mult(X1,X2),X2),rd(X3,X2)) = mult(X1,rd(X3,X2)),
inference(orient,[status(thm)],[t1816]) ).
cnf(t1822,plain,
mult(rd(X1,X1),rd(X2,X2)) = mult(rd(X1,X1),ld(rd(X1,X1),rd(X2,X2))),
inference(step,[status(thm)],[t1821,t180]) ).
cnf(t1823,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(rd(X1,X1),rd(X1,X1)),X2),X2),
inference(step,[status(thm)],[t1822,t86]) ).
cnf(t1824,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(X1,X1),X2),X2),
inference(step,[status(thm)],[t1823,t158]) ).
cnf(t375,plain,
mult(rd(X1,X1),rd(X2,X2)) = rd(mult(rd(X1,X1),X2),X2),
inference(orient,[status(thm)],[t1824]) ).
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(t1825,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)],[t1825]) ).
cnf(t1826,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)],[t1826]) ).
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(t1832,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(t1833,plain,
rd(mult(mult(X1,rd(X2,X2)),X3),X3) = mult(X1,rd(rd(X2,X2),rd(X3,X3))),
inference(step,[status(thm)],[t1832,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)],[t1833]) ).
cnf(t1851,plain,
mult(X1,rd(X2,X2)) = rd(mult(mult(X1,rd(X1,X1)),X2),X2),
inference(step,[status(thm)],[t824,t451]) ).
cnf(t1852,plain,
mult(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(step,[status(thm)],[t1851,t43]) ).
cnf(t855,plain,
mult(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(orient,[status(thm)],[t1852]) ).
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(t1855,plain,
rd(X1,rd(X2,X2)) = rd(mult(X1,rd(X2,X2)),rd(X2,X2)),
inference(step,[status(thm)],[t859,t145]) ).
cnf(t1856,plain,
rd(X1,rd(X2,X2)) = rd(mult(X1,X2),X2),
inference(step,[status(thm)],[t1855,t128]) ).
cnf(t888,plain,
rd(mult(X1,X2),X2) = rd(X1,rd(X2,X2)),
inference(orient,[status(thm)],[t1856]) ).
cnf(t1857,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)],[t1857]) ).
cnf(t905,plain,
rd(mult(X1,X2),rd(X2,X2)) = mult(rd(X1,rd(X2,X2)),X2),
inference(cp,[status(thm)],[t889,t888]) ).
cnf(t1875,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)],[t1875]) ).
cnf(t932,plain,
rd(mult(X1,X2),rd(X2,X2)) = mult(X1,X2),
inference(orient,[status(thm)],[t914]) ).
cnf(t1894,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)],[t1894]) ).
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(t1814,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)],[t1814]) ).
cnf(t1871,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(mult(X1,X3),X3),
inference(step,[status(thm)],[t163,t888]) ).
cnf(t1872,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t1871,t888]) ).
cnf(t912,plain,
rd(X1,rd(mult(X2,X3),mult(X2,X3))) = rd(X1,rd(X3,X3)),
inference(rw,[status(thm)],[t1872]) ).
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(t1924,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)],[t1924]) ).
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(t1896,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(t1897,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(mult(X2,X3),mult(X2,X3))),
inference(step,[status(thm)],[t1896,t822]) ).
cnf(t1898,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t1897,t1012]) ).
cnf(t1152,plain,
rd(X1,rd(ld(X2,X3),ld(X2,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t1898]) ).
cnf(t1925,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(t1926,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)],[t1925,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(t1901,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(t1804,plain,
X1 = rd(mult(X1,rd(X1,X1)),rd(X1,X1)),
inference(step,[status(thm)],[t78,t43]) ).
cnf(t1805,plain,
X1 = rd(X1,rd(X1,X1)),
inference(step,[status(thm)],[t1804,t43]) ).
cnf(t85,plain,
rd(X1,rd(X1,X1)) = X1,
inference(orient,[status(thm)],[t1805]) ).
cnf(t1902,plain,
mult(X1,ld(X1,X2)) = mult(rd(X1,X1),X2),
inference(step,[status(thm)],[t1901,t85]) ).
cnf(t1404,plain,
mult(rd(X1,X1),X2) = mult(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t1902]) ).
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(t1927,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)],[t1926,t1432]) ).
cnf(t1928,plain,
rd(X1,rd(X4,X4)) = rd(X1,rd(rd(X2,X2),rd(X4,X4))),
inference(step,[status(thm)],[t1927,t1012]) ).
cnf(t1680,plain,
rd(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t1928]) ).
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(t1853,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)],[t1853]) ).
cnf(t1859,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(t1860,plain,
mult(X1,rd(rd(X2,X2),rd(X3,X3))) = rd(rd(X1,rd(X2,X2)),rd(X3,X3)),
inference(step,[status(thm)],[t1859,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)],[t1860]) ).
cnf(t1929,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(t1882,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)],[t1882]) ).
cnf(t1119,plain,
rd(rd(X1,rd(X2,X3)),rd(X3,X3)) = rd(X1,rd(X2,X3)),
inference(orient,[status(thm)],[t919]) ).
cnf(t1930,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)],[t1929,t1119]) ).
cnf(t1873,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(mult(X1,X3),X3),
inference(step,[status(thm)],[t128,t888]) ).
cnf(t1874,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t1873,t888]) ).
cnf(t913,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(X1,rd(X3,X3)),
inference(rw,[status(thm)],[t1874]) ).
cnf(t1058,plain,
rd(X1,rd(rd(X2,X3),rd(X2,X3))) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t913]) ).
cnf(t1931,plain,
rd(rd(X1,rd(X2,X2)),rd(X3,X3)) = rd(X1,rd(rd(X3,X3),rd(X3,X3))),
inference(step,[status(thm)],[t1930,t1058]) ).
cnf(t1932,plain,
rd(rd(X1,rd(X2,X2)),rd(X3,X3)) = rd(X1,rd(X3,X3)),
inference(step,[status(thm)],[t1931,t1058]) ).
cnf(t1737,plain,
rd(rd(X1,rd(X2,X2)),rd(X3,X3)) = rd(X1,rd(X3,X3)),
inference(orient,[status(thm)],[t1932]) ).
cnf(t1765,plain,
mult(rd(X1,rd(X2,X2)),X3) = mult(rd(X1,rd(X3,X3)),X3),
inference(cp,[status(thm)],[t956,t1737]) ).
cnf(t1933,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)],[t1933]) ).
cnf(goal_0,negated_conjecture,
mult(rd(mult(x3,x4),x4),x5) != mult(x3,x5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
mult(rd(x3,rd(x4,x4)),x5) != mult(x3,x5),
inference(rw,[status(thm)],[goal_0,t888]) ).
cnf(g0_1,plain,
mult(x3,x5) != mult(x3,x5),
inference(rw,[status(thm)],[g0_0,t1773]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP683-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/5.39 % Computer : n001.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.39 % CPULimit : 300
% 0.13/5.39 % WCLimit : 300
% 0.13/5.39 % DateTime : Wed Sep 23 15:47:10 UTC 2026
% 0.13/5.39 % CPUTime :
% 0.13/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.05/6.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.05/6.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------