%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG020-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:37:29 PM UTC 2026
% Result : Unsatisfiable 5.24s 1.09s
% Output : CNFRefutation 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 30
% Syntax : Number of clauses : 236 ( 236 unt; 0 nHn; 171 RR)
% Number of literals : 236 ( 235 equ; 30 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 : 29 ( 29 usr; 25 con; 0-3 aty)
% Number of variables : 88 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t47,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t8]) ).
cnf(t13,axiom,
sF0 = multiply(x,u),
introduced(definition) ).
cnf(t38,plain,
multiply(x,u) = sF0,
inference(orient,[status(thm)],[t13]) ).
cnf(t14,axiom,
sF1 = multiply(multiply(x,u),y),
introduced(definition) ).
cnf(t3438,plain,
sF1 = multiply(sF0,y),
inference(step,[status(thm)],[t14,t38]) ).
cnf(t61,plain,
multiply(sF0,y) = sF1,
inference(orient,[status(thm)],[t3438]) ).
cnf(t15,axiom,
sF2 = multiply(u,y),
introduced(definition) ).
cnf(t39,plain,
multiply(u,y) = sF2,
inference(orient,[status(thm)],[t15]) ).
cnf(t16,axiom,
sF3 = multiply(x,multiply(u,y)),
introduced(definition) ).
cnf(t3439,plain,
sF3 = multiply(x,sF2),
inference(step,[status(thm)],[t16,t39]) ).
cnf(t63,plain,
multiply(x,sF2) = sF3,
inference(orient,[status(thm)],[t3439]) ).
cnf(t17,axiom,
sF4 = additive_inverse(multiply(x,multiply(u,y))),
introduced(definition) ).
cnf(t3460,plain,
sF4 = additive_inverse(multiply(x,sF2)),
inference(step,[status(thm)],[t17,t39]) ).
cnf(t3461,plain,
sF4 = additive_inverse(sF3),
inference(step,[status(thm)],[t3460,t63]) ).
cnf(t283,plain,
additive_inverse(sF3) = sF4,
inference(orient,[status(thm)],[t3461]) ).
cnf(t18,axiom,
sF5 = add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))),
introduced(definition) ).
cnf(t3468,plain,
sF5 = add(multiply(sF0,y),additive_inverse(multiply(x,multiply(u,y)))),
inference(step,[status(thm)],[t18,t38]) ).
cnf(t3469,plain,
sF5 = add(sF1,additive_inverse(multiply(x,multiply(u,y)))),
inference(step,[status(thm)],[t3468,t61]) ).
cnf(t3470,plain,
sF5 = add(sF1,additive_inverse(multiply(x,sF2))),
inference(step,[status(thm)],[t3469,t39]) ).
cnf(t3471,plain,
sF5 = add(sF1,additive_inverse(sF3)),
inference(step,[status(thm)],[t3470,t63]) ).
cnf(t3472,plain,
sF5 = add(sF1,sF4),
inference(step,[status(thm)],[t3471,t283]) ).
cnf(t355,plain,
add(sF1,sF4) = sF5,
inference(orient,[status(thm)],[t3472]) ).
cnf(t357,plain,
add(sF1,add(sF4,X1)) = add(sF5,X1),
inference(cp,[status(thm)],[t47,t355]) ).
cnf(t804,plain,
add(sF1,add(sF4,X1)) = add(sF5,X1),
inference(orient,[status(thm)],[t357]) ).
cnf(t19,axiom,
sF6 = multiply(x,v),
introduced(definition) ).
cnf(t40,plain,
multiply(x,v) = sF6,
inference(orient,[status(thm)],[t19]) ).
cnf(t20,axiom,
sF7 = multiply(multiply(x,v),y),
introduced(definition) ).
cnf(t3440,plain,
sF7 = multiply(sF6,y),
inference(step,[status(thm)],[t20,t40]) ).
cnf(t65,plain,
multiply(sF6,y) = sF7,
inference(orient,[status(thm)],[t3440]) ).
cnf(t7,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t71,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t808,plain,
add(sF5,X1) = add(sF1,add(X1,sF4)),
inference(cp,[status(thm)],[t804,t71]) ).
cnf(t1927,plain,
add(sF1,add(X1,sF4)) = add(sF5,X1),
inference(orient,[status(thm)],[t808]) ).
cnf(t12,axiom,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t173,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t12]) ).
cnf(t186,plain,
multiply(add(sF0,X1),y) = add(sF1,multiply(X1,y)),
inference(cp,[status(thm)],[t173,t61]) ).
cnf(t502,plain,
add(sF1,multiply(X1,y)) = multiply(add(sF0,X1),y),
inference(orient,[status(thm)],[t186]) ).
cnf(t508,plain,
multiply(add(sF0,sF6),y) = add(sF1,sF7),
inference(cp,[status(thm)],[t502,t65]) ).
cnf(t11,axiom,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t92,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t97,plain,
multiply(x,add(v,X1)) = add(sF6,multiply(x,X1)),
inference(cp,[status(thm)],[t92,t40]) ).
cnf(t235,plain,
add(sF6,multiply(x,X1)) = multiply(x,add(v,X1)),
inference(orient,[status(thm)],[t97]) ).
cnf(t236,plain,
multiply(x,add(v,u)) = add(sF6,sF0),
inference(cp,[status(thm)],[t235,t38]) ).
cnf(t26,axiom,
sF13 = add(u,v),
introduced(definition) ).
cnf(t42,plain,
add(u,v) = sF13,
inference(orient,[status(thm)],[t26]) ).
cnf(t3443,plain,
add(v,u) = sF13,
inference(step,[status(thm)],[t42,t71]) ).
cnf(t72,plain,
add(v,u) = sF13,
inference(rw,[status(thm)],[t3443]) ).
cnf(t77,plain,
add(v,u) = sF13,
inference(orient,[status(thm)],[t72]) ).
cnf(t3451,plain,
multiply(x,sF13) = add(sF6,sF0),
inference(step,[status(thm)],[t236,t77]) ).
cnf(t27,axiom,
sF14 = multiply(x,add(u,v)),
introduced(definition) ).
cnf(t3442,plain,
sF14 = multiply(x,sF13),
inference(step,[status(thm)],[t27,t42]) ).
cnf(t69,plain,
multiply(x,sF13) = sF14,
inference(orient,[status(thm)],[t3442]) ).
cnf(t3452,plain,
sF14 = add(sF6,sF0),
inference(step,[status(thm)],[t3451,t69]) ).
cnf(t3453,plain,
sF14 = add(sF0,sF6),
inference(step,[status(thm)],[t3452,t71]) ).
cnf(t249,plain,
add(sF0,sF6) = sF14,
inference(orient,[status(thm)],[t3453]) ).
cnf(t3499,plain,
multiply(sF14,y) = add(sF1,sF7),
inference(step,[status(thm)],[t508,t249]) ).
cnf(t512,plain,
add(sF1,sF7) = multiply(sF14,y),
inference(orient,[status(thm)],[t3499]) ).
cnf(t514,plain,
add(sF1,add(sF7,X1)) = add(multiply(sF14,y),X1),
inference(cp,[status(thm)],[t47,t512]) ).
cnf(t28,axiom,
sF15 = multiply(multiply(x,add(u,v)),y),
introduced(definition) ).
cnf(t94,plain,
multiply(x,add(X1,u)) = add(multiply(x,X1),sF0),
inference(cp,[status(thm)],[t92,t38]) ).
cnf(t3447,plain,
multiply(x,add(X1,u)) = add(sF0,multiply(x,X1)),
inference(step,[status(thm)],[t94,t71]) ).
cnf(t93,plain,
multiply(x,add(u,X1)) = add(sF0,multiply(x,X1)),
inference(cp,[status(thm)],[t92,t38]) ).
cnf(t154,plain,
add(sF0,multiply(x,X1)) = multiply(x,add(u,X1)),
inference(orient,[status(thm)],[t93]) ).
cnf(t3448,plain,
multiply(x,add(X1,u)) = multiply(x,add(u,X1)),
inference(step,[status(thm)],[t3447,t154]) ).
cnf(t167,plain,
multiply(x,add(X1,u)) = multiply(x,add(u,X1)),
inference(orient,[status(thm)],[t3448]) ).
cnf(t3522,plain,
sF15 = multiply(multiply(x,add(v,u)),y),
inference(step,[status(thm)],[t28,t167]) ).
cnf(t3523,plain,
sF15 = multiply(multiply(x,sF13),y),
inference(step,[status(thm)],[t3522,t77]) ).
cnf(t3524,plain,
sF15 = multiply(sF14,y),
inference(step,[status(thm)],[t3523,t69]) ).
cnf(t578,plain,
multiply(sF14,y) = sF15,
inference(orient,[status(thm)],[t3524]) ).
cnf(t3590,plain,
add(sF1,add(sF7,X1)) = add(sF15,X1),
inference(step,[status(thm)],[t514,t578]) ).
cnf(t1196,plain,
add(sF1,add(sF7,X1)) = add(sF15,X1),
inference(orient,[status(thm)],[t3590]) ).
cnf(t1931,plain,
add(sF5,sF7) = add(sF15,sF4),
inference(cp,[status(thm)],[t1927,t1196]) ).
cnf(t3625,plain,
add(sF5,sF7) = add(sF4,sF15),
inference(step,[status(thm)],[t1931,t71]) ).
cnf(t1935,plain,
add(sF5,sF7) = add(sF4,sF15),
inference(orient,[status(thm)],[t3625]) ).
cnf(t1937,plain,
add(sF5,add(sF7,X1)) = add(add(sF4,sF15),X1),
inference(cp,[status(thm)],[t47,t1935]) ).
cnf(t3707,plain,
add(sF5,add(sF7,X1)) = add(sF4,add(sF15,X1)),
inference(step,[status(thm)],[t1937,t47]) ).
cnf(t3300,plain,
add(sF5,add(sF7,X1)) = add(sF4,add(sF15,X1)),
inference(orient,[status(thm)],[t3707]) ).
cnf(t21,axiom,
sF8 = multiply(v,y),
introduced(definition) ).
cnf(t41,plain,
multiply(v,y) = sF8,
inference(orient,[status(thm)],[t21]) ).
cnf(t22,axiom,
sF9 = multiply(x,multiply(v,y)),
introduced(definition) ).
cnf(t3441,plain,
sF9 = multiply(x,sF8),
inference(step,[status(thm)],[t22,t41]) ).
cnf(t67,plain,
multiply(x,sF8) = sF9,
inference(orient,[status(thm)],[t3441]) ).
cnf(t23,axiom,
sF10 = additive_inverse(multiply(x,multiply(v,y))),
introduced(definition) ).
cnf(t3479,plain,
sF10 = additive_inverse(multiply(x,sF8)),
inference(step,[status(thm)],[t23,t41]) ).
cnf(t3480,plain,
sF10 = additive_inverse(sF9),
inference(step,[status(thm)],[t3479,t67]) ).
cnf(t408,plain,
additive_inverse(sF9) = sF10,
inference(orient,[status(thm)],[t3480]) ).
cnf(t24,axiom,
sF11 = add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))),
introduced(definition) ).
cnf(t3485,plain,
sF11 = add(multiply(sF6,y),additive_inverse(multiply(x,multiply(v,y)))),
inference(step,[status(thm)],[t24,t40]) ).
cnf(t3486,plain,
sF11 = add(sF7,additive_inverse(multiply(x,multiply(v,y)))),
inference(step,[status(thm)],[t3485,t65]) ).
cnf(t3487,plain,
sF11 = add(sF7,additive_inverse(multiply(x,sF8))),
inference(step,[status(thm)],[t3486,t41]) ).
cnf(t3488,plain,
sF11 = add(sF7,additive_inverse(sF9)),
inference(step,[status(thm)],[t3487,t67]) ).
cnf(t3489,plain,
sF11 = add(sF7,sF10),
inference(step,[status(thm)],[t3488,t408]) ).
cnf(t459,plain,
add(sF7,sF10) = sF11,
inference(orient,[status(thm)],[t3489]) ).
cnf(t1201,plain,
add(sF15,sF10) = add(sF1,sF11),
inference(cp,[status(thm)],[t1196,t459]) ).
cnf(t3591,plain,
add(sF10,sF15) = add(sF1,sF11),
inference(step,[status(thm)],[t1201,t71]) ).
cnf(t1207,plain,
add(sF10,sF15) = add(sF1,sF11),
inference(orient,[status(thm)],[t3591]) ).
cnf(t75,plain,
add(X1,add(X2,X3)) = add(X2,add(X3,X1)),
inference(cp,[status(thm)],[t71,t47]) ).
cnf(t1112,plain,
add(X1,add(X2,X3)) = add(X2,add(X3,X1)),
inference(orient,[status(thm)],[t75]) ).
cnf(t25,axiom,
sF12 = add(add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y))))),
introduced(definition) ).
cnf(t3500,plain,
sF12 = add(multiply(multiply(x,u),y),add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))),
inference(step,[status(thm)],[t25,t47]) ).
cnf(t3501,plain,
sF12 = add(multiply(sF0,y),add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))),
inference(step,[status(thm)],[t3500,t38]) ).
cnf(t3502,plain,
sF12 = add(sF1,add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))),
inference(step,[status(thm)],[t3501,t61]) ).
cnf(t3503,plain,
sF12 = add(sF1,add(additive_inverse(multiply(x,sF2)),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))),
inference(step,[status(thm)],[t3502,t39]) ).
cnf(t3504,plain,
sF12 = add(sF1,add(additive_inverse(sF3),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))),
inference(step,[status(thm)],[t3503,t63]) ).
cnf(t3505,plain,
sF12 = add(sF1,add(sF4,add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))),
inference(step,[status(thm)],[t3504,t283]) ).
cnf(t3506,plain,
sF12 = add(sF1,add(sF4,add(multiply(sF6,y),additive_inverse(multiply(x,multiply(v,y)))))),
inference(step,[status(thm)],[t3505,t40]) ).
cnf(t3507,plain,
sF12 = add(sF1,add(sF4,add(sF7,additive_inverse(multiply(x,multiply(v,y)))))),
inference(step,[status(thm)],[t3506,t65]) ).
cnf(t3508,plain,
sF12 = add(sF1,add(sF4,add(sF7,additive_inverse(multiply(x,sF8))))),
inference(step,[status(thm)],[t3507,t41]) ).
cnf(t3509,plain,
sF12 = add(sF1,add(sF4,add(sF7,additive_inverse(sF9)))),
inference(step,[status(thm)],[t3508,t67]) ).
cnf(t3510,plain,
sF12 = add(sF1,add(sF4,add(sF7,sF10))),
inference(step,[status(thm)],[t3509,t408]) ).
cnf(t3511,plain,
sF12 = add(sF1,add(sF4,sF11)),
inference(step,[status(thm)],[t3510,t459]) ).
cnf(t515,plain,
add(sF1,add(sF4,sF11)) = sF12,
inference(orient,[status(thm)],[t3511]) ).
cnf(t3553,plain,
add(sF5,sF11) = sF12,
inference(step,[status(thm)],[t515,t804]) ).
cnf(t805,plain,
add(sF5,sF11) = sF12,
inference(rw,[status(thm)],[t3553]) ).
cnf(t810,plain,
add(sF5,sF11) = sF12,
inference(orient,[status(thm)],[t805]) ).
cnf(t177,plain,
multiply(add(X1,u),y) = add(multiply(X1,y),sF2),
inference(cp,[status(thm)],[t173,t39]) ).
cnf(t3490,plain,
multiply(add(X1,u),y) = add(sF2,multiply(X1,y)),
inference(step,[status(thm)],[t177,t71]) ).
cnf(t176,plain,
multiply(add(u,X1),y) = add(sF2,multiply(X1,y)),
inference(cp,[status(thm)],[t173,t39]) ).
cnf(t449,plain,
add(sF2,multiply(X1,y)) = multiply(add(u,X1),y),
inference(orient,[status(thm)],[t176]) ).
cnf(t3491,plain,
multiply(add(X1,u),y) = multiply(add(u,X1),y),
inference(step,[status(thm)],[t3490,t449]) ).
cnf(t462,plain,
multiply(add(X1,u),y) = multiply(add(u,X1),y),
inference(orient,[status(thm)],[t3491]) ).
cnf(t29,axiom,
sF16 = multiply(add(u,v),y),
introduced(definition) ).
cnf(t3444,plain,
sF16 = multiply(add(v,u),y),
inference(step,[status(thm)],[t29,t71]) ).
cnf(t3445,plain,
sF16 = multiply(sF13,y),
inference(step,[status(thm)],[t3444,t77]) ).
cnf(t80,plain,
multiply(sF13,y) = sF16,
inference(orient,[status(thm)],[t3445]) ).
cnf(t30,axiom,
sF17 = multiply(x,multiply(add(u,v),y)),
introduced(definition) ).
cnf(t3533,plain,
sF17 = multiply(x,multiply(add(v,u),y)),
inference(step,[status(thm)],[t30,t462]) ).
cnf(t3534,plain,
sF17 = multiply(x,multiply(sF13,y)),
inference(step,[status(thm)],[t3533,t77]) ).
cnf(t3535,plain,
sF17 = multiply(x,sF16),
inference(step,[status(thm)],[t3534,t80]) ).
cnf(t662,plain,
multiply(x,sF16) = sF17,
inference(orient,[status(thm)],[t3535]) ).
cnf(t31,axiom,
sF18 = additive_inverse(multiply(x,multiply(add(u,v),y))),
introduced(definition) ).
cnf(t3538,plain,
sF18 = additive_inverse(multiply(x,multiply(add(v,u),y))),
inference(step,[status(thm)],[t31,t462]) ).
cnf(t3539,plain,
sF18 = additive_inverse(multiply(x,multiply(sF13,y))),
inference(step,[status(thm)],[t3538,t77]) ).
cnf(t3540,plain,
sF18 = additive_inverse(multiply(x,sF16)),
inference(step,[status(thm)],[t3539,t80]) ).
cnf(t3541,plain,
sF18 = additive_inverse(sF17),
inference(step,[status(thm)],[t3540,t662]) ).
cnf(t701,plain,
additive_inverse(sF17) = sF18,
inference(orient,[status(thm)],[t3541]) ).
cnf(t32,axiom,
sF19 = add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
introduced(definition) ).
cnf(t3544,plain,
sF19 = add(multiply(multiply(x,add(v,u)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(step,[status(thm)],[t32,t167]) ).
cnf(t3545,plain,
sF19 = add(multiply(multiply(x,sF13),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(step,[status(thm)],[t3544,t77]) ).
cnf(t3546,plain,
sF19 = add(multiply(sF14,y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(step,[status(thm)],[t3545,t69]) ).
cnf(t3547,plain,
sF19 = add(sF15,additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(step,[status(thm)],[t3546,t578]) ).
cnf(t3548,plain,
sF19 = add(sF15,additive_inverse(multiply(x,multiply(add(v,u),y)))),
inference(step,[status(thm)],[t3547,t462]) ).
cnf(t3549,plain,
sF19 = add(sF15,additive_inverse(multiply(x,multiply(sF13,y)))),
inference(step,[status(thm)],[t3548,t77]) ).
cnf(t3550,plain,
sF19 = add(sF15,additive_inverse(multiply(x,sF16))),
inference(step,[status(thm)],[t3549,t80]) ).
cnf(t3551,plain,
sF19 = add(sF15,additive_inverse(sF17)),
inference(step,[status(thm)],[t3550,t662]) ).
cnf(t3552,plain,
sF19 = add(sF15,sF18),
inference(step,[status(thm)],[t3551,t701]) ).
cnf(t728,plain,
add(sF15,sF18) = sF19,
inference(orient,[status(thm)],[t3552]) ).
cnf(t105,plain,
multiply(x,add(sF2,X1)) = add(sF3,multiply(x,X1)),
inference(cp,[status(thm)],[t92,t63]) ).
cnf(t290,plain,
add(sF3,multiply(x,X1)) = multiply(x,add(sF2,X1)),
inference(orient,[status(thm)],[t105]) ).
cnf(t294,plain,
multiply(x,add(sF2,sF8)) = add(sF3,sF9),
inference(cp,[status(thm)],[t290,t67]) ).
cnf(t180,plain,
multiply(add(v,X1),y) = add(sF8,multiply(X1,y)),
inference(cp,[status(thm)],[t173,t41]) ).
cnf(t481,plain,
add(sF8,multiply(X1,y)) = multiply(add(v,X1),y),
inference(orient,[status(thm)],[t180]) ).
cnf(t482,plain,
multiply(add(v,u),y) = add(sF8,sF2),
inference(cp,[status(thm)],[t481,t39]) ).
cnf(t3494,plain,
multiply(sF13,y) = add(sF8,sF2),
inference(step,[status(thm)],[t482,t77]) ).
cnf(t3495,plain,
sF16 = add(sF8,sF2),
inference(step,[status(thm)],[t3494,t80]) ).
cnf(t3496,plain,
sF16 = add(sF2,sF8),
inference(step,[status(thm)],[t3495,t71]) ).
cnf(t491,plain,
add(sF2,sF8) = sF16,
inference(orient,[status(thm)],[t3496]) ).
cnf(t3542,plain,
multiply(x,sF16) = add(sF3,sF9),
inference(step,[status(thm)],[t294,t491]) ).
cnf(t3543,plain,
sF17 = add(sF3,sF9),
inference(step,[status(thm)],[t3542,t662]) ).
cnf(t708,plain,
add(sF3,sF9) = sF17,
inference(orient,[status(thm)],[t3543]) ).
cnf(t710,plain,
add(sF3,add(sF9,X1)) = add(sF17,X1),
inference(cp,[status(thm)],[t47,t708]) ).
cnf(t1673,plain,
add(sF3,add(sF9,X1)) = add(sF17,X1),
inference(orient,[status(thm)],[t710]) ).
cnf(t461,plain,
add(sF7,add(sF10,X1)) = add(sF11,X1),
inference(cp,[status(thm)],[t47,t459]) ).
cnf(t1016,plain,
add(sF7,add(sF10,X1)) = add(sF11,X1),
inference(orient,[status(thm)],[t461]) ).
cnf(t5,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t43,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t50,plain,
add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t47,t43]) ).
cnf(t1,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t34,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t3557,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t50,t34]) ).
cnf(t829,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t3557]) ).
cnf(t1021,plain,
add(sF11,add(additive_inverse(sF10),X1)) = add(sF7,X1),
inference(cp,[status(thm)],[t1016,t829]) ).
cnf(t2,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t35,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t409,plain,
sF9 = additive_inverse(sF10),
inference(cp,[status(thm)],[t35,t408]) ).
cnf(t411,plain,
additive_inverse(sF10) = sF9,
inference(orient,[status(thm)],[t409]) ).
cnf(t3651,plain,
add(sF11,add(sF9,X1)) = add(sF7,X1),
inference(step,[status(thm)],[t1021,t411]) ).
cnf(t3652,plain,
add(sF9,add(X1,sF11)) = add(sF7,X1),
inference(step,[status(thm)],[t3651,t1112]) ).
cnf(t2340,plain,
add(sF9,add(X1,sF11)) = add(sF7,X1),
inference(orient,[status(thm)],[t3652]) ).
cnf(t2343,plain,
add(sF7,sF5) = add(sF9,sF12),
inference(cp,[status(thm)],[t2340,t810]) ).
cnf(t3653,plain,
add(sF5,sF7) = add(sF9,sF12),
inference(step,[status(thm)],[t2343,t71]) ).
cnf(t3654,plain,
add(sF4,sF15) = add(sF9,sF12),
inference(step,[status(thm)],[t3653,t1935]) ).
cnf(t2350,plain,
add(sF9,sF12) = add(sF4,sF15),
inference(orient,[status(thm)],[t3654]) ).
cnf(t2356,plain,
add(sF17,sF12) = add(sF3,add(sF4,sF15)),
inference(cp,[status(thm)],[t1673,t2350]) ).
cnf(t3655,plain,
add(sF12,sF17) = add(sF3,add(sF4,sF15)),
inference(step,[status(thm)],[t2356,t71]) ).
cnf(t285,plain,
additive_identity = add(sF3,sF4),
inference(cp,[status(thm)],[t43,t283]) ).
cnf(t288,plain,
add(sF3,sF4) = additive_identity,
inference(orient,[status(thm)],[t285]) ).
cnf(t289,plain,
add(sF3,add(sF4,X1)) = add(additive_identity,X1),
inference(cp,[status(thm)],[t47,t288]) ).
cnf(t3537,plain,
add(sF3,add(sF4,X1)) = X1,
inference(step,[status(thm)],[t289,t34]) ).
cnf(t688,plain,
add(sF3,add(sF4,X1)) = X1,
inference(orient,[status(thm)],[t3537]) ).
cnf(t3656,plain,
add(sF12,sF17) = sF15,
inference(step,[status(thm)],[t3655,t688]) ).
cnf(t2358,plain,
add(sF12,sF17) = sF15,
inference(orient,[status(thm)],[t3656]) ).
cnf(t2360,plain,
add(sF12,add(sF17,X1)) = add(sF15,X1),
inference(cp,[status(thm)],[t47,t2358]) ).
cnf(t3407,plain,
add(sF12,add(sF17,X1)) = add(sF15,X1),
inference(orient,[status(thm)],[t2360]) ).
cnf(t3408,plain,
add(sF15,additive_inverse(sF17)) = add(sF12,additive_identity),
inference(cp,[status(thm)],[t3407,t43]) ).
cnf(t3712,plain,
add(sF15,sF18) = add(sF12,additive_identity),
inference(step,[status(thm)],[t3408,t701]) ).
cnf(t3713,plain,
sF19 = add(sF12,additive_identity),
inference(step,[status(thm)],[t3712,t728]) ).
cnf(t0,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t33,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t3714,plain,
sF19 = sF12,
inference(step,[status(thm)],[t3713,t33]) ).
cnf(t3423,plain,
sF19 = sF12,
inference(orient,[status(thm)],[t3714]) ).
cnf(t3715,plain,
add(sF15,sF18) = sF12,
inference(step,[status(thm)],[t728,t3423]) ).
cnf(t3424,plain,
add(sF15,sF18) = sF12,
inference(orient,[status(thm)],[t3715]) ).
cnf(u0,negated_conjecture,
associator(x,add(u,v),y) != add(associator(x,u,y),associator(x,v,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(d0,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(goal_0,negated_conjecture,
add(add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(g0_0,plain,
add(multiply(multiply(x,u),y),add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[goal_0,t47]) ).
cnf(g0_1,plain,
add(multiply(sF0,y),add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_0,t38]) ).
cnf(g0_2,plain,
add(sF1,add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_1,t61]) ).
cnf(g0_3,plain,
add(sF1,add(additive_inverse(multiply(x,sF2)),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_2,t39]) ).
cnf(g0_4,plain,
add(sF1,add(additive_inverse(sF3),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_3,t63]) ).
cnf(g0_5,plain,
add(sF1,add(sF4,add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_4,t283]) ).
cnf(g0_6,plain,
add(sF5,add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_5,t804]) ).
cnf(g0_7,plain,
add(sF5,add(multiply(sF6,y),additive_inverse(multiply(x,multiply(v,y))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_6,t40]) ).
cnf(g0_8,plain,
add(sF5,add(sF7,additive_inverse(multiply(x,multiply(v,y))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_7,t65]) ).
cnf(g0_9,plain,
add(sF4,add(sF15,additive_inverse(multiply(x,multiply(v,y))))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_8,t3300]) ).
cnf(g0_10,plain,
add(sF4,add(sF15,additive_inverse(multiply(x,sF8)))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_9,t41]) ).
cnf(g0_11,plain,
add(sF4,add(sF15,additive_inverse(sF9))) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_10,t67]) ).
cnf(g0_12,plain,
add(sF4,add(sF15,sF10)) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_11,t408]) ).
cnf(g0_13,plain,
add(sF4,add(sF10,sF15)) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_12,t71]) ).
cnf(g0_14,plain,
add(sF4,add(sF1,sF11)) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_13,t1207]) ).
cnf(g0_15,plain,
add(sF1,add(sF11,sF4)) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_14,t1112]) ).
cnf(g0_16,plain,
add(sF5,sF11) != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_15,t1927]) ).
cnf(g0_17,plain,
sF12 != add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_16,t810]) ).
cnf(g0_18,plain,
sF12 != add(multiply(multiply(x,add(v,u)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_17,t167]) ).
cnf(g0_19,plain,
sF12 != add(multiply(multiply(x,sF13),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_18,t77]) ).
cnf(g0_20,plain,
sF12 != add(multiply(sF14,y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_19,t69]) ).
cnf(g0_21,plain,
sF12 != add(sF15,additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(rw,[status(thm)],[g0_20,t578]) ).
cnf(g0_22,plain,
sF12 != add(sF15,additive_inverse(multiply(x,multiply(add(v,u),y)))),
inference(rw,[status(thm)],[g0_21,t462]) ).
cnf(g0_23,plain,
sF12 != add(sF15,additive_inverse(multiply(x,multiply(sF13,y)))),
inference(rw,[status(thm)],[g0_22,t77]) ).
cnf(g0_24,plain,
sF12 != add(sF15,additive_inverse(multiply(x,sF16))),
inference(rw,[status(thm)],[g0_23,t80]) ).
cnf(g0_25,plain,
sF12 != add(sF15,additive_inverse(sF17)),
inference(rw,[status(thm)],[g0_24,t662]) ).
cnf(g0_26,plain,
sF12 != add(sF15,sF18),
inference(rw,[status(thm)],[g0_25,t701]) ).
cnf(g0_27,plain,
sF12 != sF12,
inference(rw,[status(thm)],[g0_26,t3424]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG020-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n026.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 07:49:23 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.24/1.09 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.24/1.09 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------