%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP670-1 : 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 01:27:59 PM UTC 2026
% Result : Unsatisfiable 24.86s 11.21s
% Output : CNFRefutation 24.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 10
% Syntax : Number of clauses : 150 ( 150 unt; 0 nHn; 5 RR)
% Number of literals : 150 ( 149 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 365 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
mult(mult(mult(X1,mult(X2,X3)),X1),X2) = mult(mult(X1,X2),mult(X3,mult(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t41,plain,
mult(mult(mult(X1,mult(X2,X3)),X1),X2) = mult(mult(X1,X2),mult(X3,mult(X1,X2))),
inference(orient,[status(thm)],[t8]) ).
cnf(t0,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t10,plain,
mult(X1,unit) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t43,plain,
mult(mult(X1,unit),mult(X2,mult(X1,unit))) = mult(mult(X1,mult(unit,X2)),X1),
inference(cp,[status(thm)],[t41,t10]) ).
cnf(t331160,plain,
mult(X1,mult(X2,mult(X1,unit))) = mult(mult(X1,mult(unit,X2)),X1),
inference(step,[status(thm)],[t43,t10]) ).
cnf(t331161,plain,
mult(X1,mult(X2,X1)) = mult(mult(X1,mult(unit,X2)),X1),
inference(step,[status(thm)],[t331160,t10]) ).
cnf(t1,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t15,plain,
mult(unit,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t331162,plain,
mult(X1,mult(X2,X1)) = mult(mult(X1,X2),X1),
inference(step,[status(thm)],[t331161,t15]) ).
cnf(t166,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
inference(orient,[status(thm)],[t331162]) ).
cnf(t5,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t29,plain,
rd(mult(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t6,axiom,
mult(i(X1),mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t18,plain,
mult(i(X1),mult(X1,X2)) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t3,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t9,plain,
mult(X1,ld(X1,X2)) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t19,plain,
ld(X1,X2) = mult(i(X1),X2),
inference(cp,[status(thm)],[t18,t9]) ).
cnf(t91,plain,
mult(i(X1),X2) = ld(X1,X2),
inference(orient,[status(thm)],[t19]) ).
cnf(t95,plain,
i(X1) = rd(ld(X1,X2),X2),
inference(cp,[status(thm)],[t29,t91]) ).
cnf(t118,plain,
rd(ld(X1,X2),X2) = i(X1),
inference(orient,[status(thm)],[t95]) ).
cnf(t2,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t35,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(t25,plain,
mult(rd(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t37,plain,
X1 = ld(rd(X2,X1),X2),
inference(cp,[status(thm)],[t35,t25]) ).
cnf(t112,plain,
ld(rd(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t37]) ).
cnf(t120,plain,
i(rd(X1,X2)) = rd(X2,X1),
inference(cp,[status(thm)],[t118,t112]) ).
cnf(t121,plain,
i(rd(X1,X2)) = rd(X2,X1),
inference(orient,[status(thm)],[t120]) ).
cnf(t7,axiom,
mult(mult(X1,X2),i(X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t11,plain,
mult(mult(X1,X2),i(X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t28,plain,
rd(X1,X2) = mult(X1,i(X2)),
inference(cp,[status(thm)],[t11,t25]) ).
cnf(t99,plain,
mult(X1,i(X2)) = rd(X1,X2),
inference(orient,[status(thm)],[t28]) ).
cnf(t17,plain,
unit = mult(X1,i(X1)),
inference(cp,[status(thm)],[t11,t15]) ).
cnf(t76,plain,
mult(X1,i(X1)) = unit,
inference(orient,[status(thm)],[t17]) ).
cnf(t79,plain,
X1 = mult(unit,i(i(X1))),
inference(cp,[status(thm)],[t11,t76]) ).
cnf(t331157,plain,
X1 = i(i(X1)),
inference(step,[status(thm)],[t79,t15]) ).
cnf(t81,plain,
i(i(X1)) = X1,
inference(orient,[status(thm)],[t331157]) ).
cnf(t103,plain,
rd(X1,i(X2)) = mult(X1,X2),
inference(cp,[status(thm)],[t99,t81]) ).
cnf(t109,plain,
rd(X1,i(X2)) = mult(X1,X2),
inference(orient,[status(thm)],[t103]) ).
cnf(t122,plain,
rd(i(X1),X2) = i(mult(X2,X1)),
inference(cp,[status(thm)],[t121,t109]) ).
cnf(t129,plain,
i(mult(X1,X2)) = rd(i(X2),X1),
inference(orient,[status(thm)],[t122]) ).
cnf(t131,plain,
rd(i(X1),i(X2)) = i(ld(X2,X1)),
inference(cp,[status(thm)],[t129,t91]) ).
cnf(t331158,plain,
mult(i(X1),X2) = i(ld(X2,X1)),
inference(step,[status(thm)],[t131,t109]) ).
cnf(t331159,plain,
ld(X1,X2) = i(ld(X2,X1)),
inference(step,[status(thm)],[t331158,t91]) ).
cnf(t139,plain,
i(ld(X1,X2)) = ld(X2,X1),
inference(orient,[status(thm)],[t331159]) ).
cnf(t331163,plain,
mult(mult(X1,mult(mult(X2,X3),X1)),X2) = mult(mult(X1,X2),mult(X3,mult(X1,X2))),
inference(step,[status(thm)],[t41,t166]) ).
cnf(t179,plain,
mult(mult(X1,mult(mult(X2,X3),X1)),X2) = mult(mult(X1,X2),mult(X3,mult(X1,X2))),
inference(rw,[status(thm)],[t331163]) ).
cnf(t1970,plain,
mult(mult(X1,mult(mult(X2,X3),X1)),X2) = mult(mult(X1,X2),mult(X3,mult(X1,X2))),
inference(orient,[status(thm)],[t179]) ).
cnf(t1976,plain,
mult(mult(X1,i(X2)),mult(X3,mult(X1,i(X2)))) = rd(mult(X1,mult(mult(i(X2),X3),X1)),X2),
inference(cp,[status(thm)],[t1970,t99]) ).
cnf(t331486,plain,
mult(rd(X1,X2),mult(X3,mult(X1,i(X2)))) = rd(mult(X1,mult(mult(i(X2),X3),X1)),X2),
inference(step,[status(thm)],[t1976,t99]) ).
cnf(t331487,plain,
mult(rd(X1,X2),mult(X3,rd(X1,X2))) = rd(mult(X1,mult(mult(i(X2),X3),X1)),X2),
inference(step,[status(thm)],[t331486,t99]) ).
cnf(t125,plain,
mult(X1,rd(X2,X3)) = rd(X1,rd(X3,X2)),
inference(cp,[status(thm)],[t109,t121]) ).
cnf(t180,plain,
mult(X1,rd(X2,X3)) = rd(X1,rd(X3,X2)),
inference(orient,[status(thm)],[t125]) ).
cnf(t331488,plain,
mult(rd(X1,X2),rd(X3,rd(X2,X1))) = rd(mult(X1,mult(mult(i(X2),X3),X1)),X2),
inference(step,[status(thm)],[t331487,t180]) ).
cnf(t331489,plain,
rd(rd(X1,X2),rd(rd(X2,X1),X3)) = rd(mult(X1,mult(mult(i(X2),X3),X1)),X2),
inference(step,[status(thm)],[t331488,t180]) ).
cnf(t331490,plain,
rd(rd(X1,X2),rd(rd(X2,X1),X3)) = rd(mult(X1,mult(ld(X2,X3),X1)),X2),
inference(step,[status(thm)],[t331489,t91]) ).
cnf(t143,plain,
mult(X1,ld(X2,X3)) = rd(X1,ld(X3,X2)),
inference(cp,[status(thm)],[t109,t139]) ).
cnf(t194,plain,
mult(X1,ld(X2,X3)) = rd(X1,ld(X3,X2)),
inference(orient,[status(thm)],[t143]) ).
cnf(t93,plain,
ld(i(X1),X2) = mult(X1,X2),
inference(cp,[status(thm)],[t91,t81]) ).
cnf(t108,plain,
ld(i(X1),X2) = mult(X1,X2),
inference(orient,[status(thm)],[t93]) ).
cnf(t144,plain,
mult(ld(X1,X2),X3) = ld(ld(X2,X1),X3),
inference(cp,[status(thm)],[t108,t139]) ).
cnf(t203,plain,
ld(ld(X1,X2),X3) = mult(ld(X2,X1),X3),
inference(orient,[status(thm)],[t144]) ).
cnf(t209,plain,
rd(X1,ld(X2,ld(X3,Y3))) = mult(X1,mult(ld(Y3,X3),X2)),
inference(cp,[status(thm)],[t194,t203]) ).
cnf(t772,plain,
mult(X1,mult(ld(X2,X3),Y3)) = rd(X1,ld(Y3,ld(X3,X2))),
inference(orient,[status(thm)],[t209]) ).
cnf(t331491,plain,
rd(rd(X1,X2),rd(rd(X2,X1),X3)) = rd(rd(X1,ld(X1,ld(X3,X2))),X2),
inference(step,[status(thm)],[t331490,t772]) ).
cnf(t17654,plain,
rd(rd(X1,ld(X1,ld(X2,X3))),X3) = rd(rd(X1,X3),rd(rd(X3,X1),X2)),
inference(orient,[status(thm)],[t331491]) ).
cnf(t113,plain,
i(X1) = ld(mult(X2,X1),X2),
inference(cp,[status(thm)],[t112,t109]) ).
cnf(t154,plain,
ld(mult(X1,X2),X1) = i(X2),
inference(orient,[status(thm)],[t113]) ).
cnf(t17709,plain,
rd(rd(X1,X2),rd(rd(X2,X1),mult(X2,X3))) = rd(rd(X1,ld(X1,i(X3))),X2),
inference(cp,[status(thm)],[t17654,t154]) ).
cnf(t17720,plain,
rd(rd(X1,X2),rd(rd(X2,X1),i(X3))) = rd(rd(X1,ld(X1,mult(X3,X2))),X2),
inference(cp,[status(thm)],[t17654,t108]) ).
cnf(t331884,plain,
rd(rd(X1,X2),mult(rd(X2,X1),X3)) = rd(rd(X1,ld(X1,mult(X3,X2))),X2),
inference(step,[status(thm)],[t17720,t109]) ).
cnf(t53137,plain,
rd(rd(X1,ld(X1,mult(X2,X3))),X3) = rd(rd(X1,X3),mult(rd(X3,X1),X2)),
inference(orient,[status(thm)],[t331884]) ).
cnf(t53281,plain,
rd(X1,rd(X2,ld(X2,mult(X3,X1)))) = i(rd(rd(X2,X1),mult(rd(X1,X2),X3))),
inference(cp,[status(thm)],[t121,t53137]) ).
cnf(t332184,plain,
rd(X1,rd(X2,ld(X2,mult(X3,X1)))) = rd(mult(rd(X1,X2),X3),rd(X2,X1)),
inference(step,[status(thm)],[t53281,t121]) ).
cnf(t181,plain,
rd(mult(rd(X1,X2),X3),rd(X2,X1)) = mult(rd(X1,X2),mult(X3,rd(X1,X2))),
inference(cp,[status(thm)],[t180,t166]) ).
cnf(t331310,plain,
rd(mult(rd(X1,X2),X3),rd(X2,X1)) = mult(rd(X1,X2),rd(X3,rd(X2,X1))),
inference(step,[status(thm)],[t181,t180]) ).
cnf(t331311,plain,
rd(mult(rd(X1,X2),X3),rd(X2,X1)) = rd(rd(X1,X2),rd(rd(X2,X1),X3)),
inference(step,[status(thm)],[t331310,t180]) ).
cnf(t4934,plain,
rd(mult(rd(X1,X2),X3),rd(X2,X1)) = rd(rd(X1,X2),rd(rd(X2,X1),X3)),
inference(orient,[status(thm)],[t331311]) ).
cnf(t332185,plain,
rd(X1,rd(X2,ld(X2,mult(X3,X1)))) = rd(rd(X1,X2),rd(rd(X2,X1),X3)),
inference(step,[status(thm)],[t332184,t4934]) ).
cnf(t80273,plain,
rd(rd(X1,X2),rd(rd(X2,X1),X3)) = rd(X1,rd(X2,ld(X2,mult(X3,X1)))),
inference(orient,[status(thm)],[t332185]) ).
cnf(t333963,plain,
rd(X1,rd(X2,ld(X2,mult(mult(X2,X3),X1)))) = rd(rd(X1,ld(X1,i(X3))),X2),
inference(step,[status(thm)],[t17709,t80273]) ).
cnf(t100,plain,
rd(i(X1),X2) = ld(X1,i(X2)),
inference(cp,[status(thm)],[t99,t91]) ).
cnf(t114,plain,
ld(X1,i(X2)) = rd(i(X1),X2),
inference(orient,[status(thm)],[t100]) ).
cnf(t333964,plain,
rd(X1,rd(X2,ld(X2,mult(mult(X2,X3),X1)))) = rd(rd(X1,rd(i(X1),X3)),X2),
inference(step,[status(thm)],[t333963,t114]) ).
cnf(t135,plain,
mult(X1,mult(X2,X3)) = rd(X1,rd(i(X3),X2)),
inference(cp,[status(thm)],[t109,t129]) ).
cnf(t246,plain,
rd(X1,rd(i(X2),X3)) = mult(X1,mult(X3,X2)),
inference(orient,[status(thm)],[t135]) ).
cnf(t333965,plain,
rd(X1,rd(X2,ld(X2,mult(mult(X2,X3),X1)))) = rd(mult(X1,mult(X3,X1)),X2),
inference(step,[status(thm)],[t333964,t246]) ).
cnf(t288200,plain,
rd(X1,rd(X2,ld(X2,mult(mult(X2,X3),X1)))) = rd(mult(X1,mult(X3,X1)),X2),
inference(orient,[status(thm)],[t333965]) ).
cnf(t288429,plain,
rd(mult(X1,mult(X2,X1)),rd(X3,X2)) = rd(X1,rd(rd(X3,X2),ld(rd(X3,X2),mult(X3,X1)))),
inference(cp,[status(thm)],[t288200,t25]) ).
cnf(t126,plain,
mult(rd(X1,X2),X3) = ld(rd(X2,X1),X3),
inference(cp,[status(thm)],[t108,t121]) ).
cnf(t188,plain,
ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3),
inference(orient,[status(thm)],[t126]) ).
cnf(t333966,plain,
rd(mult(X1,mult(X2,X1)),rd(X3,X2)) = rd(X1,rd(rd(X3,X2),mult(rd(X2,X3),mult(X3,X1)))),
inference(step,[status(thm)],[t288429,t188]) ).
cnf(t17740,plain,
rd(X1,rd(X2,ld(X2,ld(X3,X1)))) = i(rd(rd(X2,X1),rd(rd(X1,X2),X3))),
inference(cp,[status(thm)],[t121,t17654]) ).
cnf(t331885,plain,
rd(X1,rd(X2,ld(X2,ld(X3,X1)))) = rd(rd(rd(X1,X2),X3),rd(X2,X1)),
inference(step,[status(thm)],[t17740,t121]) ).
cnf(t169,plain,
mult(X1,mult(i(X2),X1)) = mult(rd(X1,X2),X1),
inference(cp,[status(thm)],[t166,t99]) ).
cnf(t331167,plain,
mult(X1,ld(X2,X1)) = mult(rd(X1,X2),X1),
inference(step,[status(thm)],[t169,t91]) ).
cnf(t331168,plain,
rd(X1,ld(X1,X2)) = mult(rd(X1,X2),X1),
inference(step,[status(thm)],[t331167,t194]) ).
cnf(t225,plain,
mult(rd(X1,X2),X1) = rd(X1,ld(X1,X2)),
inference(orient,[status(thm)],[t331168]) ).
cnf(t227,plain,
rd(rd(X1,X2),ld(rd(X1,X2),X3)) = rd(rd(rd(X1,X2),X3),rd(X2,X1)),
inference(cp,[status(thm)],[t225,t180]) ).
cnf(t331457,plain,
rd(rd(X1,X2),mult(rd(X2,X1),X3)) = rd(rd(rd(X1,X2),X3),rd(X2,X1)),
inference(step,[status(thm)],[t227,t188]) ).
cnf(t14461,plain,
rd(rd(rd(X1,X2),X3),rd(X2,X1)) = rd(rd(X1,X2),mult(rd(X2,X1),X3)),
inference(orient,[status(thm)],[t331457]) ).
cnf(t331886,plain,
rd(X1,rd(X2,ld(X2,ld(X3,X1)))) = rd(rd(X1,X2),mult(rd(X2,X1),X3)),
inference(step,[status(thm)],[t331885,t14461]) ).
cnf(t53389,plain,
rd(rd(X1,X2),mult(rd(X2,X1),X3)) = rd(X1,rd(X2,ld(X2,ld(X3,X1)))),
inference(orient,[status(thm)],[t331886]) ).
cnf(t333967,plain,
rd(mult(X1,mult(X2,X1)),rd(X3,X2)) = rd(X1,rd(X3,rd(X2,ld(X2,ld(mult(X3,X1),X3))))),
inference(step,[status(thm)],[t333966,t53389]) ).
cnf(t333968,plain,
rd(mult(X1,mult(X2,X1)),rd(X3,X2)) = rd(X1,rd(X3,rd(X2,ld(X2,i(X1))))),
inference(step,[status(thm)],[t333967,t154]) ).
cnf(t333969,plain,
rd(mult(X1,mult(X2,X1)),rd(X3,X2)) = rd(X1,rd(X3,rd(X2,rd(i(X2),X1)))),
inference(step,[status(thm)],[t333968,t114]) ).
cnf(t333970,plain,
rd(mult(X1,mult(X2,X1)),rd(X3,X2)) = rd(X1,rd(X3,mult(X2,mult(X1,X2)))),
inference(step,[status(thm)],[t333969,t246]) ).
cnf(t288734,plain,
rd(mult(X1,mult(X2,X1)),rd(X3,X2)) = rd(X1,rd(X3,mult(X2,mult(X1,X2)))),
inference(orient,[status(thm)],[t333970]) ).
cnf(t288758,plain,
rd(i(X1),rd(X2,mult(X3,mult(i(X1),X3)))) = rd(ld(X1,mult(X3,i(X1))),rd(X2,X3)),
inference(cp,[status(thm)],[t288734,t91]) ).
cnf(t124,plain,
rd(i(X1),rd(X2,X3)) = ld(X1,rd(X3,X2)),
inference(cp,[status(thm)],[t114,t121]) ).
cnf(t241,plain,
rd(i(X1),rd(X2,X3)) = ld(X1,rd(X3,X2)),
inference(orient,[status(thm)],[t124]) ).
cnf(t333972,plain,
ld(X1,rd(mult(X3,mult(i(X1),X3)),X2)) = rd(ld(X1,mult(X3,i(X1))),rd(X2,X3)),
inference(step,[status(thm)],[t288758,t241]) ).
cnf(t333973,plain,
ld(X1,rd(mult(X3,ld(X1,X3)),X2)) = rd(ld(X1,mult(X3,i(X1))),rd(X2,X3)),
inference(step,[status(thm)],[t333972,t91]) ).
cnf(t333974,plain,
ld(X1,rd(rd(X3,ld(X3,X1)),X2)) = rd(ld(X1,mult(X3,i(X1))),rd(X2,X3)),
inference(step,[status(thm)],[t333973,t194]) ).
cnf(t333975,plain,
ld(X1,rd(rd(X3,ld(X3,X1)),X2)) = rd(ld(X1,rd(X3,X1)),rd(X2,X3)),
inference(step,[status(thm)],[t333974,t99]) ).
cnf(t167,plain,
mult(i(X1),mult(X2,i(X1))) = rd(mult(i(X1),X2),X1),
inference(cp,[status(thm)],[t166,t99]) ).
cnf(t331164,plain,
ld(X1,mult(X2,i(X1))) = rd(mult(i(X1),X2),X1),
inference(step,[status(thm)],[t167,t91]) ).
cnf(t331165,plain,
ld(X1,rd(X2,X1)) = rd(mult(i(X1),X2),X1),
inference(step,[status(thm)],[t331164,t99]) ).
cnf(t331166,plain,
ld(X1,rd(X2,X1)) = rd(ld(X1,X2),X1),
inference(step,[status(thm)],[t331165,t91]) ).
cnf(t211,plain,
ld(X1,rd(X2,X1)) = rd(ld(X1,X2),X1),
inference(orient,[status(thm)],[t331166]) ).
cnf(t333976,plain,
ld(X1,rd(rd(X3,ld(X3,X1)),X2)) = rd(rd(ld(X1,X3),X1),rd(X2,X3)),
inference(step,[status(thm)],[t333975,t211]) ).
cnf(t290887,plain,
ld(X1,rd(rd(X2,ld(X2,X1)),X3)) = rd(rd(ld(X1,X2),X1),rd(X3,X2)),
inference(orient,[status(thm)],[t333976]) ).
cnf(t291235,plain,
ld(rd(rd(X1,ld(X1,X2)),X3),X2) = i(rd(rd(ld(X2,X1),X2),rd(X3,X1))),
inference(cp,[status(thm)],[t139,t290887]) ).
cnf(t334034,plain,
mult(rd(X3,rd(X1,ld(X1,X2))),X2) = i(rd(rd(ld(X2,X1),X2),rd(X3,X1))),
inference(step,[status(thm)],[t291235,t188]) ).
cnf(t334035,plain,
mult(rd(X3,rd(X1,ld(X1,X2))),X2) = rd(rd(X3,X1),rd(ld(X2,X1),X2)),
inference(step,[status(thm)],[t334034,t121]) ).
cnf(t302571,plain,
mult(rd(X1,rd(X2,ld(X2,X3))),X3) = rd(rd(X1,X2),rd(ld(X3,X2),X3)),
inference(orient,[status(thm)],[t334035]) ).
cnf(t302592,plain,
rd(rd(X1,i(X2)),rd(ld(X3,i(X2)),X3)) = mult(mult(X1,mult(ld(i(X2),X3),X2)),X3),
inference(cp,[status(thm)],[t302571,t246]) ).
cnf(t334177,plain,
rd(mult(X1,X2),rd(ld(X3,i(X2)),X3)) = mult(mult(X1,mult(ld(i(X2),X3),X2)),X3),
inference(step,[status(thm)],[t302592,t109]) ).
cnf(t334178,plain,
rd(mult(X1,X2),rd(rd(i(X3),X2),X3)) = mult(mult(X1,mult(ld(i(X2),X3),X2)),X3),
inference(step,[status(thm)],[t334177,t114]) ).
cnf(t176,plain,
rd(i(X1),mult(X1,X2)) = i(mult(X1,mult(X2,X1))),
inference(cp,[status(thm)],[t129,t166]) ).
cnf(t331177,plain,
rd(i(X1),mult(X1,X2)) = rd(i(mult(X2,X1)),X1),
inference(step,[status(thm)],[t176,t129]) ).
cnf(t331178,plain,
rd(i(X1),mult(X1,X2)) = rd(rd(i(X1),X2),X1),
inference(step,[status(thm)],[t331177,t129]) ).
cnf(t356,plain,
rd(rd(i(X1),X2),X1) = rd(i(X1),mult(X1,X2)),
inference(orient,[status(thm)],[t331178]) ).
cnf(t334179,plain,
rd(mult(X1,X2),rd(i(X3),mult(X3,X2))) = mult(mult(X1,mult(ld(i(X2),X3),X2)),X3),
inference(step,[status(thm)],[t334178,t356]) ).
cnf(t334180,plain,
mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(ld(i(X2),X3),X2)),X3),
inference(step,[status(thm)],[t334179,t246]) ).
cnf(t334181,plain,
mult(mult(X1,X2),mult(X3,mult(X2,X3))) = mult(mult(X1,mult(ld(i(X2),X3),X2)),X3),
inference(step,[status(thm)],[t334180,t166]) ).
cnf(t334182,plain,
mult(mult(X1,X2),mult(X3,mult(X2,X3))) = mult(rd(X1,ld(X2,ld(X3,i(X2)))),X3),
inference(step,[status(thm)],[t334181,t772]) ).
cnf(t334183,plain,
mult(mult(X1,X2),mult(X3,mult(X2,X3))) = mult(rd(X1,ld(X2,rd(i(X3),X2))),X3),
inference(step,[status(thm)],[t334182,t114]) ).
cnf(t134,plain,
rd(i(X1),mult(X2,X3)) = ld(X1,rd(i(X3),X2)),
inference(cp,[status(thm)],[t114,t129]) ).
cnf(t321,plain,
ld(X1,rd(i(X2),X3)) = rd(i(X1),mult(X3,X2)),
inference(orient,[status(thm)],[t134]) ).
cnf(t334184,plain,
mult(mult(X1,X2),mult(X3,mult(X2,X3))) = mult(rd(X1,rd(i(X2),mult(X2,X3))),X3),
inference(step,[status(thm)],[t334183,t321]) ).
cnf(t334185,plain,
mult(mult(X1,X2),mult(X3,mult(X2,X3))) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
inference(step,[status(thm)],[t334184,t246]) ).
cnf(t334186,plain,
mult(mult(X1,X2),mult(X3,mult(X2,X3))) = mult(mult(X1,mult(X2,mult(X3,X2))),X3),
inference(step,[status(thm)],[t334185,t166]) ).
cnf(t330373,plain,
mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(mult(X1,X2),mult(X3,mult(X2,X3))),
inference(orient,[status(thm)],[t334186]) ).
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/sandbox2/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,t166]) ).
cnf(g0_1,plain,
mult(mult(a,b),mult(c,mult(b,c))) != mult(mult(a,b),mult(mult(c,b),c)),
inference(rw,[status(thm)],[g0_0,t330373]) ).
cnf(g0_2,plain,
mult(mult(a,b),mult(c,mult(b,c))) != mult(mult(a,b),mult(c,mult(b,c))),
inference(rw,[status(thm)],[g0_1,t166]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP670-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 15:37:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.86/11.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.86/11.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------