%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP668-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:27:59 PM UTC 2026
% Result : Unsatisfiable 12.61s 2.21s
% Output : CNFRefutation 12.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 9
% Syntax : Number of clauses : 173 ( 173 unt; 0 nHn; 6 RR)
% Number of literals : 173 ( 172 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 366 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t6,axiom,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t22,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
inference(orient,[status(thm)],[t6]) ).
cnf(t5,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t14,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t7,axiom,
mult(mult(mult(X1,X2),X2),X3) = mult(X1,mult(X2,mult(X2,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t28,plain,
mult(mult(mult(X1,X2),X2),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(orient,[status(thm)],[t7]) ).
cnf(t0,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
mult(X1,unit) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t31,plain,
mult(X1,mult(X2,mult(X2,unit))) = mult(mult(X1,X2),X2),
inference(cp,[status(thm)],[t28,t9]) ).
cnf(t55666,plain,
mult(X1,mult(X2,X2)) = mult(mult(X1,X2),X2),
inference(step,[status(thm)],[t31,t9]) ).
cnf(t48,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t55666]) ).
cnf(t55667,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(step,[status(thm)],[t28,t48]) ).
cnf(t56,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[t55667]) ).
cnf(t411,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(orient,[status(thm)],[t56]) ).
cnf(t440,plain,
mult(X1,mult(X2,X2)) = rd(mult(X1,mult(X2,mult(X2,X3))),X3),
inference(cp,[status(thm)],[t14,t411]) ).
cnf(t6740,plain,
rd(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t440]) ).
cnf(t4,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t12,plain,
mult(rd(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t51,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(cp,[status(thm)],[t48,t12]) ).
cnf(t101,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(orient,[status(thm)],[t51]) ).
cnf(t422,plain,
mult(rd(X1,X2),mult(X2,mult(X2,X3))) = mult(mult(X1,X2),X3),
inference(cp,[status(thm)],[t411,t101]) ).
cnf(t1600,plain,
mult(rd(X1,X2),mult(X2,mult(X2,X3))) = mult(mult(X1,X2),X3),
inference(orient,[status(thm)],[t422]) ).
cnf(t3,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t1631,plain,
mult(mult(X1,X2),ld(X2,X3)) = mult(rd(X1,X2),mult(X2,X3)),
inference(cp,[status(thm)],[t1600,t8]) ).
cnf(t1673,plain,
mult(mult(X1,X2),ld(X2,X3)) = mult(rd(X1,X2),mult(X2,X3)),
inference(orient,[status(thm)],[t1631]) ).
cnf(t2,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t18,plain,
ld(X1,mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t23,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1),
inference(cp,[status(thm)],[t22,t8]) ).
cnf(t57,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1),
inference(orient,[status(thm)],[t23]) ).
cnf(t61,plain,
mult(ld(X1,X2),X1) = ld(X1,mult(X2,X1)),
inference(cp,[status(thm)],[t18,t57]) ).
cnf(t63,plain,
ld(X1,mult(X2,X1)) = mult(ld(X1,X2),X1),
inference(orient,[status(thm)],[t61]) ).
cnf(t1,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t10,plain,
mult(unit,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t68,plain,
mult(ld(X1,unit),X1) = ld(X1,X1),
inference(cp,[status(thm)],[t63,t10]) ).
cnf(t19,plain,
unit = ld(X1,X1),
inference(cp,[status(thm)],[t18,t9]) ).
cnf(t45,plain,
ld(X1,X1) = unit,
inference(orient,[status(thm)],[t19]) ).
cnf(t55668,plain,
mult(ld(X1,unit),X1) = unit,
inference(step,[status(thm)],[t68,t45]) ).
cnf(t71,plain,
mult(ld(X1,unit),X1) = unit,
inference(orient,[status(thm)],[t55668]) ).
cnf(t76,plain,
ld(X1,unit) = rd(unit,X1),
inference(cp,[status(thm)],[t14,t71]) ).
cnf(t77,plain,
ld(X1,unit) = rd(unit,X1),
inference(orient,[status(thm)],[t76]) ).
cnf(t1702,plain,
mult(rd(X1,X2),mult(X2,unit)) = mult(mult(X1,X2),rd(unit,X2)),
inference(cp,[status(thm)],[t1673,t77]) ).
cnf(t55724,plain,
mult(rd(X1,X2),X2) = mult(mult(X1,X2),rd(unit,X2)),
inference(step,[status(thm)],[t1702,t9]) ).
cnf(t55725,plain,
X1 = mult(mult(X1,X2),rd(unit,X2)),
inference(step,[status(thm)],[t55724,t12]) ).
cnf(t2128,plain,
mult(mult(X1,X2),rd(unit,X2)) = X1,
inference(orient,[status(thm)],[t55725]) ).
cnf(t2147,plain,
rd(X1,X2) = mult(X1,rd(unit,X2)),
inference(cp,[status(thm)],[t2128,t12]) ).
cnf(t2179,plain,
mult(X1,rd(unit,X2)) = rd(X1,X2),
inference(orient,[status(thm)],[t2147]) ).
cnf(t15,plain,
X1 = rd(X2,ld(X1,X2)),
inference(cp,[status(thm)],[t14,t8]) ).
cnf(t46,plain,
rd(X1,ld(X2,X1)) = X2,
inference(orient,[status(thm)],[t15]) ).
cnf(t2189,plain,
rd(X1,ld(X2,unit)) = mult(X1,X2),
inference(cp,[status(thm)],[t2179,t46]) ).
cnf(t55726,plain,
rd(X1,rd(unit,X2)) = mult(X1,X2),
inference(step,[status(thm)],[t2189,t77]) ).
cnf(t2233,plain,
rd(X1,rd(unit,X2)) = mult(X1,X2),
inference(orient,[status(thm)],[t55726]) ).
cnf(t6742,plain,
mult(X1,mult(X2,X2)) = mult(mult(X1,mult(X2,mult(X2,rd(unit,X3)))),X3),
inference(cp,[status(thm)],[t6740,t2233]) ).
cnf(t55971,plain,
mult(X1,mult(X2,X2)) = mult(mult(X1,mult(X2,rd(X2,X3))),X3),
inference(step,[status(thm)],[t6742,t2179]) ).
cnf(t1698,plain,
mult(rd(unit,X1),mult(X1,X2)) = mult(X1,ld(X1,X2)),
inference(cp,[status(thm)],[t1673,t10]) ).
cnf(t55713,plain,
mult(rd(unit,X1),mult(X1,X2)) = X2,
inference(step,[status(thm)],[t1698,t8]) ).
cnf(t1744,plain,
mult(rd(unit,X1),mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t55713]) ).
cnf(t1754,plain,
ld(X1,X2) = mult(rd(unit,X1),X2),
inference(cp,[status(thm)],[t1744,t8]) ).
cnf(t1797,plain,
mult(rd(unit,X1),X2) = ld(X1,X2),
inference(orient,[status(thm)],[t1754]) ).
cnf(t1824,plain,
rd(unit,X1) = rd(ld(X1,X2),X2),
inference(cp,[status(thm)],[t14,t1797]) ).
cnf(t1900,plain,
rd(ld(X1,X2),X2) = rd(unit,X1),
inference(orient,[status(thm)],[t1824]) ).
cnf(t20,plain,
X1 = ld(rd(X2,X1),X2),
inference(cp,[status(thm)],[t18,t12]) ).
cnf(t47,plain,
ld(rd(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(t1915,plain,
rd(unit,rd(X1,X2)) = rd(X2,X1),
inference(cp,[status(thm)],[t1900,t47]) ).
cnf(t1973,plain,
rd(unit,rd(X1,X2)) = rd(X2,X1),
inference(orient,[status(thm)],[t1915]) ).
cnf(t2187,plain,
rd(X1,rd(X2,X3)) = mult(X1,rd(X3,X2)),
inference(cp,[status(thm)],[t2179,t1973]) ).
cnf(t2492,plain,
mult(X1,rd(X2,X3)) = rd(X1,rd(X3,X2)),
inference(orient,[status(thm)],[t2187]) ).
cnf(t55972,plain,
mult(X1,mult(X2,X2)) = mult(mult(X1,rd(X2,rd(X3,X2))),X3),
inference(step,[status(thm)],[t55971,t2492]) ).
cnf(t55973,plain,
mult(X1,mult(X2,X2)) = mult(rd(X1,rd(rd(X3,X2),X2)),X3),
inference(step,[status(thm)],[t55972,t2492]) ).
cnf(t109,plain,
rd(X1,X2) = rd(mult(X1,X2),mult(X2,X2)),
inference(cp,[status(thm)],[t14,t101]) ).
cnf(t167,plain,
rd(mult(X1,X2),mult(X2,X2)) = rd(X1,X2),
inference(orient,[status(thm)],[t109]) ).
cnf(t173,plain,
rd(rd(X1,X2),X2) = rd(X1,mult(X2,X2)),
inference(cp,[status(thm)],[t167,t12]) ).
cnf(t184,plain,
rd(rd(X1,X2),X2) = rd(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t173]) ).
cnf(t55974,plain,
mult(X1,mult(X2,X2)) = mult(rd(X1,rd(X3,mult(X2,X2))),X3),
inference(step,[status(thm)],[t55973,t184]) ).
cnf(t10184,plain,
mult(rd(X1,rd(X2,mult(X3,X3))),X2) = mult(X1,mult(X3,X3)),
inference(orient,[status(thm)],[t55974]) ).
cnf(t1816,plain,
rd(rd(unit,X1),X2) = rd(ld(X1,X2),mult(X2,X2)),
inference(cp,[status(thm)],[t167,t1797]) ).
cnf(t2240,plain,
rd(rd(unit,X1),X2) = rd(unit,mult(X2,X1)),
inference(cp,[status(thm)],[t1973,t2233]) ).
cnf(t2566,plain,
rd(rd(unit,X1),X2) = rd(unit,mult(X2,X1)),
inference(orient,[status(thm)],[t2240]) ).
cnf(t55775,plain,
rd(unit,mult(X2,X1)) = rd(ld(X1,X2),mult(X2,X2)),
inference(step,[status(thm)],[t1816,t2566]) ).
cnf(t3040,plain,
rd(ld(X1,X2),mult(X2,X2)) = rd(unit,mult(X2,X1)),
inference(orient,[status(thm)],[t55775]) ).
cnf(t10224,plain,
mult(X1,mult(X2,X2)) = mult(rd(X1,rd(unit,mult(X2,X3))),ld(X3,X2)),
inference(cp,[status(thm)],[t10184,t3040]) ).
cnf(t2204,plain,
rd(unit,X1) = ld(X2,rd(X2,X1)),
inference(cp,[status(thm)],[t18,t2179]) ).
cnf(t2249,plain,
ld(X1,rd(X1,X2)) = rd(unit,X2),
inference(orient,[status(thm)],[t2204]) ).
cnf(t2254,plain,
rd(unit,ld(X1,X2)) = ld(X2,X1),
inference(cp,[status(thm)],[t2249,t46]) ).
cnf(t2284,plain,
rd(unit,ld(X1,X2)) = ld(X2,X1),
inference(orient,[status(thm)],[t2254]) ).
cnf(t2297,plain,
mult(X1,ld(X2,X3)) = rd(X1,ld(X3,X2)),
inference(cp,[status(thm)],[t2233,t2284]) ).
cnf(t2702,plain,
mult(X1,ld(X2,X3)) = rd(X1,ld(X3,X2)),
inference(orient,[status(thm)],[t2297]) ).
cnf(t56013,plain,
mult(X1,mult(X2,X2)) = rd(rd(X1,rd(unit,mult(X2,X3))),ld(X2,X3)),
inference(step,[status(thm)],[t10224,t2702]) ).
cnf(t56014,plain,
mult(X1,mult(X2,X2)) = rd(mult(X1,mult(X2,X3)),ld(X2,X3)),
inference(step,[status(thm)],[t56013,t2233]) ).
cnf(t11985,plain,
rd(mult(X1,mult(X2,X3)),ld(X2,X3)) = mult(X1,mult(X2,X2)),
inference(orient,[status(thm)],[t56014]) ).
cnf(t12033,plain,
mult(X1,mult(mult(X2,X3),mult(X2,X3))) = rd(mult(X1,mult(X2,mult(X3,X2))),ld(mult(X2,X3),X2)),
inference(cp,[status(thm)],[t11985,t22]) ).
cnf(t424,plain,
mult(unit,mult(X1,mult(X1,X2))) = mult(mult(X1,X1),X2),
inference(cp,[status(thm)],[t411,t10]) ).
cnf(t55681,plain,
mult(X1,mult(X1,X2)) = mult(mult(X1,X1),X2),
inference(step,[status(thm)],[t424,t10]) ).
cnf(t460,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(orient,[status(thm)],[t55681]) ).
cnf(t480,plain,
mult(X1,X1) = rd(mult(X1,mult(X1,X2)),X2),
inference(cp,[status(thm)],[t14,t460]) ).
cnf(t499,plain,
rd(mult(X1,mult(X1,X2)),X2) = mult(X1,X1),
inference(orient,[status(thm)],[t480]) ).
cnf(t504,plain,
mult(X1,X1) = rd(mult(X1,X2),ld(X1,X2)),
inference(cp,[status(thm)],[t499,t8]) ).
cnf(t525,plain,
rd(mult(X1,X2),ld(X1,X2)) = mult(X1,X1),
inference(orient,[status(thm)],[t504]) ).
cnf(t536,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(X1,ld(rd(X1,X2),X2)),
inference(cp,[status(thm)],[t525,t12]) ).
cnf(t512,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(mult(rd(X1,X2),X1),X2),
inference(cp,[status(thm)],[t499,t12]) ).
cnf(t892,plain,
mult(rd(X1,X2),rd(X1,X2)) = rd(mult(rd(X1,X2),X1),X2),
inference(orient,[status(thm)],[t512]) ).
cnf(t55693,plain,
rd(mult(rd(X1,X2),X1),X2) = rd(X1,ld(rd(X1,X2),X2)),
inference(step,[status(thm)],[t536,t892]) ).
cnf(t952,plain,
rd(mult(rd(X1,X2),X1),X2) = rd(X1,ld(rd(X1,X2),X2)),
inference(orient,[status(thm)],[t55693]) ).
cnf(t1981,plain,
rd(X1,mult(rd(X2,X1),X2)) = rd(unit,rd(X2,ld(rd(X2,X1),X1))),
inference(cp,[status(thm)],[t1973,t952]) ).
cnf(t67,plain,
mult(ld(X1,rd(X2,X1)),X1) = ld(X1,X2),
inference(cp,[status(thm)],[t63,t12]) ).
cnf(t118,plain,
mult(ld(X1,rd(X2,X1)),X1) = ld(X1,X2),
inference(orient,[status(thm)],[t67]) ).
cnf(t126,plain,
ld(X1,rd(X2,X1)) = rd(ld(X1,X2),X1),
inference(cp,[status(thm)],[t14,t118]) ).
cnf(t128,plain,
ld(X1,rd(X2,X1)) = rd(ld(X1,X2),X1),
inference(orient,[status(thm)],[t126]) ).
cnf(t132,plain,
X1 = rd(rd(X2,X1),rd(ld(X1,X2),X1)),
inference(cp,[status(thm)],[t46,t128]) ).
cnf(t291,plain,
rd(rd(X1,X2),rd(ld(X2,X1),X2)) = X2,
inference(orient,[status(thm)],[t132]) ).
cnf(t2265,plain,
rd(unit,rd(ld(X1,X2),X1)) = ld(rd(X2,X1),X1),
inference(cp,[status(thm)],[t2249,t291]) ).
cnf(t55738,plain,
rd(X1,ld(X1,X2)) = ld(rd(X2,X1),X1),
inference(step,[status(thm)],[t2265,t1973]) ).
cnf(t78,plain,
rd(unit,rd(unit,X1)) = X1,
inference(cp,[status(thm)],[t77,t47]) ).
cnf(t81,plain,
rd(unit,rd(unit,X1)) = X1,
inference(orient,[status(thm)],[t78]) ).
cnf(t1804,plain,
ld(rd(unit,X1),X2) = mult(X1,X2),
inference(cp,[status(thm)],[t1797,t81]) ).
cnf(t1872,plain,
ld(rd(unit,X1),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t1804]) ).
cnf(t1995,plain,
mult(rd(X1,X2),X3) = ld(rd(X2,X1),X3),
inference(cp,[status(thm)],[t1872,t1973]) ).
cnf(t2079,plain,
ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3),
inference(orient,[status(thm)],[t1995]) ).
cnf(t55739,plain,
rd(X1,ld(X1,X2)) = mult(rd(X1,X2),X1),
inference(step,[status(thm)],[t55738,t2079]) ).
cnf(t2574,plain,
mult(rd(X1,X2),X1) = rd(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t55739]) ).
cnf(t55799,plain,
rd(X1,rd(X2,ld(X2,X1))) = rd(unit,rd(X2,ld(rd(X2,X1),X1))),
inference(step,[status(thm)],[t1981,t2574]) ).
cnf(t55800,plain,
rd(X1,rd(X2,ld(X2,X1))) = rd(ld(rd(X2,X1),X1),X2),
inference(step,[status(thm)],[t55799,t1973]) ).
cnf(t55801,plain,
rd(X1,rd(X2,ld(X2,X1))) = rd(mult(rd(X1,X2),X1),X2),
inference(step,[status(thm)],[t55800,t2079]) ).
cnf(t55802,plain,
rd(X1,rd(X2,ld(X2,X1))) = rd(rd(X1,ld(X1,X2)),X2),
inference(step,[status(thm)],[t55801,t2574]) ).
cnf(t3783,plain,
rd(rd(X1,ld(X1,X2)),X2) = rd(X1,rd(X2,ld(X2,X1))),
inference(orient,[status(thm)],[t55802]) ).
cnf(t3784,plain,
rd(X1,rd(rd(unit,X2),ld(rd(unit,X2),X1))) = mult(rd(X1,ld(X1,rd(unit,X2))),X2),
inference(cp,[status(thm)],[t3783,t2233]) ).
cnf(t55867,plain,
rd(X1,rd(unit,mult(ld(rd(unit,X2),X1),X2))) = mult(rd(X1,ld(X1,rd(unit,X2))),X2),
inference(step,[status(thm)],[t3784,t2566]) ).
cnf(t2180,plain,
rd(rd(unit,X1),X2) = ld(X1,rd(unit,X2)),
inference(cp,[status(thm)],[t2179,t1797]) ).
cnf(t2416,plain,
ld(X1,rd(unit,X2)) = rd(rd(unit,X1),X2),
inference(orient,[status(thm)],[t2180]) ).
cnf(t2419,plain,
rd(rd(unit,X1),ld(X2,X3)) = ld(X1,ld(X3,X2)),
inference(cp,[status(thm)],[t2416,t2284]) ).
cnf(t55789,plain,
rd(unit,mult(ld(X2,X3),X1)) = ld(X1,ld(X3,X2)),
inference(step,[status(thm)],[t2419,t2566]) ).
cnf(t3400,plain,
rd(unit,mult(ld(X1,X2),X3)) = ld(X3,ld(X2,X1)),
inference(orient,[status(thm)],[t55789]) ).
cnf(t55868,plain,
rd(X1,ld(X2,ld(X1,rd(unit,X2)))) = mult(rd(X1,ld(X1,rd(unit,X2))),X2),
inference(step,[status(thm)],[t55867,t3400]) ).
cnf(t55736,plain,
ld(X1,rd(unit,X2)) = rd(unit,mult(X2,X1)),
inference(step,[status(thm)],[t2416,t2566]) ).
cnf(t2567,plain,
ld(X1,rd(unit,X2)) = rd(unit,mult(X2,X1)),
inference(orient,[status(thm)],[t55736]) ).
cnf(t55869,plain,
rd(X1,ld(X2,rd(unit,mult(X2,X1)))) = mult(rd(X1,ld(X1,rd(unit,X2))),X2),
inference(step,[status(thm)],[t55868,t2567]) ).
cnf(t55870,plain,
rd(X1,rd(unit,mult(mult(X2,X1),X2))) = mult(rd(X1,ld(X1,rd(unit,X2))),X2),
inference(step,[status(thm)],[t55869,t2567]) ).
cnf(t55871,plain,
mult(X1,mult(mult(X2,X1),X2)) = mult(rd(X1,ld(X1,rd(unit,X2))),X2),
inference(step,[status(thm)],[t55870,t2233]) ).
cnf(t55872,plain,
mult(X1,mult(X2,mult(X1,X2))) = mult(rd(X1,ld(X1,rd(unit,X2))),X2),
inference(step,[status(thm)],[t55871,t22]) ).
cnf(t55873,plain,
mult(X1,mult(X2,mult(X1,X2))) = mult(rd(X1,rd(unit,mult(X2,X1))),X2),
inference(step,[status(thm)],[t55872,t2567]) ).
cnf(t55874,plain,
mult(X1,mult(X2,mult(X1,X2))) = mult(mult(X1,mult(X2,X1)),X2),
inference(step,[status(thm)],[t55873,t2233]) ).
cnf(t2267,plain,
rd(unit,X1) = ld(mult(X2,X1),X2),
inference(cp,[status(thm)],[t2249,t14]) ).
cnf(t2311,plain,
ld(mult(X1,X2),X1) = rd(unit,X2),
inference(orient,[status(thm)],[t2267]) ).
cnf(t2336,plain,
mult(mult(X1,X2),mult(X1,X2)) = rd(mult(mult(X1,X2),X1),rd(unit,X2)),
inference(cp,[status(thm)],[t525,t2311]) ).
cnf(t55823,plain,
mult(mult(X1,X2),mult(X1,X2)) = mult(mult(mult(X1,X2),X1),X2),
inference(step,[status(thm)],[t2336,t2233]) ).
cnf(t55824,plain,
mult(mult(X1,X2),mult(X1,X2)) = mult(mult(X1,mult(X2,X1)),X2),
inference(step,[status(thm)],[t55823,t22]) ).
cnf(t4193,plain,
mult(mult(X1,mult(X2,X1)),X2) = mult(mult(X1,X2),mult(X1,X2)),
inference(orient,[status(thm)],[t55824]) ).
cnf(t55875,plain,
mult(X1,mult(X2,mult(X1,X2))) = mult(mult(X1,X2),mult(X1,X2)),
inference(step,[status(thm)],[t55874,t4193]) ).
cnf(t5802,plain,
mult(mult(X1,X2),mult(X1,X2)) = mult(X1,mult(X2,mult(X1,X2))),
inference(orient,[status(thm)],[t55875]) ).
cnf(t56592,plain,
mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = rd(mult(X1,mult(X2,mult(X3,X2))),ld(mult(X2,X3),X2)),
inference(step,[status(thm)],[t12033,t5802]) ).
cnf(t56593,plain,
mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = rd(mult(X1,mult(X2,mult(X3,X2))),rd(unit,X3)),
inference(step,[status(thm)],[t56592,t2311]) ).
cnf(t56594,plain,
mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = mult(mult(X1,mult(X2,mult(X3,X2))),X3),
inference(step,[status(thm)],[t56593,t2233]) ).
cnf(t54798,plain,
mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(X1,mult(X2,mult(X3,mult(X2,X3)))),
inference(orient,[status(thm)],[t56594]) ).
cnf(t10225,plain,
mult(X1,mult(X2,X2)) = mult(rd(X1,rd(unit,X3)),ld(X3,mult(X2,X2))),
inference(cp,[status(thm)],[t10184,t1900]) ).
cnf(t56015,plain,
mult(X1,mult(X2,X2)) = rd(rd(X1,rd(unit,X3)),ld(mult(X2,X2),X3)),
inference(step,[status(thm)],[t10225,t2702]) ).
cnf(t56016,plain,
mult(X1,mult(X2,X2)) = rd(mult(X1,X3),ld(mult(X2,X2),X3)),
inference(step,[status(thm)],[t56015,t2233]) ).
cnf(t529,plain,
mult(X1,X1) = rd(X2,ld(X1,ld(X1,X2))),
inference(cp,[status(thm)],[t525,t8]) ).
cnf(t592,plain,
rd(X1,ld(X2,ld(X2,X1))) = mult(X2,X2),
inference(orient,[status(thm)],[t529]) ).
cnf(t607,plain,
ld(X1,ld(X1,X2)) = ld(mult(X1,X1),X2),
inference(cp,[status(thm)],[t47,t592]) ).
cnf(t613,plain,
ld(mult(X1,X1),X2) = ld(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t607]) ).
cnf(t56017,plain,
mult(X1,mult(X2,X2)) = rd(mult(X1,X3),ld(X2,ld(X2,X3))),
inference(step,[status(thm)],[t56016,t613]) ).
cnf(t12108,plain,
rd(mult(X1,X2),ld(X3,ld(X3,X2))) = mult(X1,mult(X3,X3)),
inference(orient,[status(thm)],[t56017]) ).
cnf(t12167,plain,
mult(X1,mult(mult(X2,X3),mult(X2,X3))) = rd(mult(X1,X2),ld(mult(X2,X3),rd(unit,X3))),
inference(cp,[status(thm)],[t12108,t2311]) ).
cnf(t56601,plain,
mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = rd(mult(X1,X2),ld(mult(X2,X3),rd(unit,X3))),
inference(step,[status(thm)],[t12167,t5802]) ).
cnf(t56602,plain,
mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = rd(mult(X1,X2),rd(unit,mult(X3,mult(X2,X3)))),
inference(step,[status(thm)],[t56601,t2567]) ).
cnf(t56603,plain,
mult(X1,mult(X2,mult(X3,mult(X2,X3)))) = mult(mult(X1,X2),mult(X3,mult(X2,X3))),
inference(step,[status(thm)],[t56602,t2233]) ).
cnf(t55345,plain,
mult(mult(X1,X2),mult(X3,mult(X2,X3))) = mult(X1,mult(X2,mult(X3,mult(X2,X3)))),
inference(orient,[status(thm)],[t56603]) ).
cnf(goal_0,negated_conjecture,
mult(mult(a,mult(mult(b,c),b)),c) != mult(mult(a,b),mult(mult(c,b),c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
mult(mult(a,mult(b,mult(c,b))),c) != mult(mult(a,b),mult(mult(c,b),c)),
inference(rw,[status(thm)],[goal_0,t22]) ).
cnf(g0_1,plain,
mult(a,mult(b,mult(c,mult(b,c)))) != mult(mult(a,b),mult(mult(c,b),c)),
inference(rw,[status(thm)],[g0_0,t54798]) ).
cnf(g0_2,plain,
mult(a,mult(b,mult(c,mult(b,c)))) != mult(mult(a,b),mult(c,mult(b,c))),
inference(rw,[status(thm)],[g0_1,t22]) ).
cnf(g0_3,plain,
mult(a,mult(b,mult(c,mult(b,c)))) != mult(a,mult(b,mult(c,mult(b,c)))),
inference(rw,[status(thm)],[g0_2,t55345]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP668-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 15:37:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.61/2.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.61/2.21 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------