%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP410-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 01:26:06 PM UTC 2026
% Result : Unsatisfiable 23.58s 3.55s
% Output : CNFRefutation 23.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 5
% Syntax : Number of clauses : 161 ( 161 unt; 0 nHn; 54 RR)
% Number of literals : 161 ( 160 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 213 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(multiply(inverse(X3),X3))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,plain,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(multiply(inverse(X3),X3))) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t1,axiom,
sFlat0 = inverse(b2),
introduced(definition) ).
cnf(t14,plain,
inverse(b2) = sFlat0,
inference(orient,[status(thm)],[t1]) ).
cnf(t15,plain,
X1 = multiply(multiply(inverse(multiply(X2,inverse(multiply(X1,b2)))),multiply(X2,sFlat0)),inverse(multiply(inverse(b2),b2))),
inference(cp,[status(thm)],[t4,t14]) ).
cnf(t2987,plain,
X1 = multiply(multiply(inverse(multiply(X2,inverse(multiply(X1,b2)))),multiply(X2,sFlat0)),inverse(multiply(sFlat0,b2))),
inference(step,[status(thm)],[t15,t14]) ).
cnf(t2,axiom,
sFlat1 = multiply(inverse(b2),b2),
introduced(definition) ).
cnf(t10,plain,
multiply(inverse(b2),b2) = sFlat1,
inference(orient,[status(thm)],[t2]) ).
cnf(t2983,plain,
multiply(sFlat0,b2) = sFlat1,
inference(step,[status(thm)],[t10,t14]) ).
cnf(t17,plain,
multiply(sFlat0,b2) = sFlat1,
inference(rw,[status(thm)],[t2983]) ).
cnf(t20,plain,
multiply(sFlat0,b2) = sFlat1,
inference(orient,[status(thm)],[t17]) ).
cnf(t2988,plain,
X1 = multiply(multiply(inverse(multiply(X2,inverse(multiply(X1,b2)))),multiply(X2,sFlat0)),inverse(sFlat1)),
inference(step,[status(thm)],[t2987,t20]) ).
cnf(t26,plain,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,b2)))),multiply(X1,sFlat0)),inverse(sFlat1)) = X2,
inference(orient,[status(thm)],[t2988]) ).
cnf(t29,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,b2)))),multiply(X1,sFlat0)) = multiply(multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,inverse(inverse(sFlat1)))),inverse(multiply(inverse(inverse(sFlat1)),inverse(sFlat1)))),
inference(cp,[status(thm)],[t4,t26]) ).
cnf(t332,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,b2)))),multiply(X1,sFlat0)) = multiply(multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,inverse(inverse(sFlat1)))),inverse(multiply(inverse(inverse(sFlat1)),inverse(sFlat1)))),
inference(orient,[status(thm)],[t29]) ).
cnf(t344,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(X2,inverse(sFlat1)),b2)))),multiply(X1,sFlat0)) = X2,
inference(cp,[status(thm)],[t332,t4]) ).
cnf(t368,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(X2,inverse(sFlat1)),b2)))),multiply(X1,sFlat0)) = X2,
inference(orient,[status(thm)],[t344]) ).
cnf(t371,plain,
inverse(multiply(X1,inverse(multiply(multiply(X2,inverse(sFlat1)),b2)))) = multiply(multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,inverse(multiply(X1,sFlat0)))),inverse(multiply(inverse(multiply(X1,sFlat0)),multiply(X1,sFlat0)))),
inference(cp,[status(thm)],[t4,t368]) ).
cnf(t385,plain,
multiply(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(multiply(X3,sFlat0)))),inverse(multiply(inverse(multiply(X3,sFlat0)),multiply(X3,sFlat0)))) = inverse(multiply(X3,inverse(multiply(multiply(X2,inverse(sFlat1)),b2)))),
inference(orient,[status(thm)],[t371]) ).
cnf(t386,plain,
inverse(multiply(X1,inverse(multiply(multiply(multiply(X2,multiply(X1,sFlat0)),inverse(sFlat1)),b2)))) = X2,
inference(cp,[status(thm)],[t385,t4]) ).
cnf(t413,plain,
inverse(multiply(X1,inverse(multiply(multiply(multiply(X2,multiply(X1,sFlat0)),inverse(sFlat1)),b2)))) = X2,
inference(orient,[status(thm)],[t386]) ).
cnf(t433,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(multiply(multiply(X2,multiply(X3,sFlat0)),inverse(sFlat1)),b2),b2)))),multiply(X1,sFlat0)) = multiply(multiply(X2,multiply(X3,inverse(inverse(sFlat1)))),inverse(multiply(inverse(inverse(sFlat1)),inverse(sFlat1)))),
inference(cp,[status(thm)],[t332,t413]) ).
cnf(t450,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(multiply(multiply(X2,multiply(X3,sFlat0)),inverse(sFlat1)),b2),b2)))),multiply(X1,sFlat0)) = multiply(multiply(X2,multiply(X3,inverse(inverse(sFlat1)))),inverse(multiply(inverse(inverse(sFlat1)),inverse(sFlat1)))),
inference(orient,[status(thm)],[t433]) ).
cnf(t465,plain,
multiply(multiply(multiply(X1,multiply(X2,sFlat0)),inverse(sFlat1)),b2) = multiply(multiply(multiply(X1,multiply(X2,inverse(inverse(sFlat1)))),inverse(multiply(inverse(inverse(sFlat1)),inverse(sFlat1)))),inverse(sFlat1)),
inference(cp,[status(thm)],[t26,t450]) ).
cnf(t471,plain,
multiply(multiply(multiply(X1,multiply(X2,inverse(inverse(sFlat1)))),inverse(multiply(inverse(inverse(sFlat1)),inverse(sFlat1)))),inverse(sFlat1)) = multiply(multiply(multiply(X1,multiply(X2,sFlat0)),inverse(sFlat1)),b2),
inference(orient,[status(thm)],[t465]) ).
cnf(t475,plain,
multiply(multiply(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,sFlat0)),inverse(sFlat1)),b2) = multiply(multiply(inverse(multiply(X3,inverse(multiply(X2,b2)))),multiply(X3,sFlat0)),inverse(sFlat1)),
inference(cp,[status(thm)],[t471,t332]) ).
cnf(t2991,plain,
multiply(multiply(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,sFlat0)),inverse(sFlat1)),b2) = X2,
inference(step,[status(thm)],[t475,t26]) ).
cnf(t492,plain,
multiply(multiply(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,sFlat0)),inverse(sFlat1)),b2) = X2,
inference(orient,[status(thm)],[t2991]) ).
cnf(t512,plain,
b2 = multiply(multiply(multiply(inverse(multiply(X1,sFlat0)),multiply(X1,sFlat0)),inverse(sFlat1)),b2),
inference(cp,[status(thm)],[t492,t14]) ).
cnf(t523,plain,
multiply(multiply(multiply(inverse(multiply(X1,sFlat0)),multiply(X1,sFlat0)),inverse(sFlat1)),b2) = b2,
inference(orient,[status(thm)],[t512]) ).
cnf(t6,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))) = multiply(multiply(inverse(multiply(Y3,inverse(X2))),multiply(Y3,inverse(inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))),
inference(cp,[status(thm)],[t4,t4]) ).
cnf(t840,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))) = multiply(multiply(inverse(multiply(Y3,inverse(X2))),multiply(Y3,inverse(inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))),
inference(orient,[status(thm)],[t6]) ).
cnf(t926,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(X2,inverse(multiply(inverse(X3),X3))),X3)))),multiply(X1,inverse(X3))) = X2,
inference(cp,[status(thm)],[t840,t4]) ).
cnf(t984,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(X2,inverse(multiply(inverse(X3),X3))),X3)))),multiply(X1,inverse(X3))) = X2,
inference(orient,[status(thm)],[t926]) ).
cnf(t21,plain,
sFlat0 = multiply(multiply(inverse(multiply(X1,inverse(sFlat1))),multiply(X1,inverse(b2))),inverse(multiply(inverse(b2),b2))),
inference(cp,[status(thm)],[t4,t20]) ).
cnf(t2984,plain,
sFlat0 = multiply(multiply(inverse(multiply(X1,inverse(sFlat1))),multiply(X1,sFlat0)),inverse(multiply(inverse(b2),b2))),
inference(step,[status(thm)],[t21,t14]) ).
cnf(t2985,plain,
sFlat0 = multiply(multiply(inverse(multiply(X1,inverse(sFlat1))),multiply(X1,sFlat0)),inverse(multiply(sFlat0,b2))),
inference(step,[status(thm)],[t2984,t14]) ).
cnf(t2986,plain,
sFlat0 = multiply(multiply(inverse(multiply(X1,inverse(sFlat1))),multiply(X1,sFlat0)),inverse(sFlat1)),
inference(step,[status(thm)],[t2985,t20]) ).
cnf(t22,plain,
multiply(multiply(inverse(multiply(X1,inverse(sFlat1))),multiply(X1,sFlat0)),inverse(sFlat1)) = sFlat0,
inference(orient,[status(thm)],[t2986]) ).
cnf(t1026,plain,
X1 = multiply(inverse(multiply(multiply(inverse(multiply(X2,inverse(sFlat1))),multiply(X2,sFlat0)),inverse(multiply(multiply(X1,inverse(multiply(inverse(sFlat1),sFlat1))),sFlat1)))),sFlat0),
inference(cp,[status(thm)],[t984,t22]) ).
cnf(t2008,plain,
multiply(inverse(multiply(multiply(inverse(multiply(X1,inverse(sFlat1))),multiply(X1,sFlat0)),inverse(multiply(multiply(X2,inverse(multiply(inverse(sFlat1),sFlat1))),sFlat1)))),sFlat0) = X2,
inference(orient,[status(thm)],[t1026]) ).
cnf(t2025,plain,
b2 = multiply(multiply(multiply(inverse(X1),multiply(inverse(multiply(multiply(inverse(multiply(X2,inverse(sFlat1))),multiply(X2,sFlat0)),inverse(multiply(multiply(X1,inverse(multiply(inverse(sFlat1),sFlat1))),sFlat1)))),sFlat0)),inverse(sFlat1)),b2),
inference(cp,[status(thm)],[t523,t2008]) ).
cnf(t3010,plain,
b2 = multiply(multiply(multiply(inverse(X1),X1),inverse(sFlat1)),b2),
inference(step,[status(thm)],[t2025,t2008]) ).
cnf(t2073,plain,
multiply(multiply(multiply(inverse(X1),X1),inverse(sFlat1)),b2) = b2,
inference(orient,[status(thm)],[t3010]) ).
cnf(t2079,plain,
b2 = multiply(multiply(multiply(sFlat0,b2),inverse(sFlat1)),b2),
inference(cp,[status(thm)],[t2073,t14]) ).
cnf(t3011,plain,
b2 = multiply(multiply(sFlat1,inverse(sFlat1)),b2),
inference(step,[status(thm)],[t2079,t20]) ).
cnf(t2107,plain,
multiply(multiply(sFlat1,inverse(sFlat1)),b2) = b2,
inference(orient,[status(thm)],[t3011]) ).
cnf(t2116,plain,
sFlat1 = multiply(inverse(multiply(X1,inverse(b2))),multiply(X1,sFlat0)),
inference(cp,[status(thm)],[t368,t2107]) ).
cnf(t3012,plain,
sFlat1 = multiply(inverse(multiply(X1,sFlat0)),multiply(X1,sFlat0)),
inference(step,[status(thm)],[t2116,t14]) ).
cnf(t2127,plain,
multiply(inverse(multiply(X1,sFlat0)),multiply(X1,sFlat0)) = sFlat1,
inference(orient,[status(thm)],[t3012]) ).
cnf(t2128,plain,
sFlat1 = multiply(inverse(X1),multiply(inverse(multiply(multiply(inverse(multiply(X2,inverse(sFlat1))),multiply(X2,sFlat0)),inverse(multiply(multiply(X1,inverse(multiply(inverse(sFlat1),sFlat1))),sFlat1)))),sFlat0)),
inference(cp,[status(thm)],[t2127,t2008]) ).
cnf(t3015,plain,
sFlat1 = multiply(inverse(X1),X1),
inference(step,[status(thm)],[t2128,t2008]) ).
cnf(t2156,plain,
multiply(inverse(X1),X1) = sFlat1,
inference(orient,[status(thm)],[t3015]) ).
cnf(t3024,plain,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(sFlat1)) = X2,
inference(step,[status(thm)],[t4,t2156]) ).
cnf(t2237,plain,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(sFlat1)) = X2,
inference(rw,[status(thm)],[t3024]) ).
cnf(t2554,plain,
multiply(multiply(inverse(multiply(X1,inverse(multiply(X2,X3)))),multiply(X1,inverse(X3))),inverse(sFlat1)) = X2,
inference(orient,[status(thm)],[t2237]) ).
cnf(t2166,plain,
sFlat1 = multiply(X1,multiply(X2,inverse(multiply(multiply(multiply(X1,multiply(X2,sFlat0)),inverse(sFlat1)),b2)))),
inference(cp,[status(thm)],[t2156,t413]) ).
cnf(t2553,plain,
multiply(X1,multiply(X2,inverse(multiply(multiply(multiply(X1,multiply(X2,sFlat0)),inverse(sFlat1)),b2)))) = sFlat1,
inference(orient,[status(thm)],[t2166]) ).
cnf(t2565,plain,
X1 = multiply(multiply(inverse(multiply(X2,inverse(sFlat1))),multiply(X2,inverse(multiply(X3,inverse(multiply(multiply(multiply(X1,multiply(X3,sFlat0)),inverse(sFlat1)),b2)))))),inverse(sFlat1)),
inference(cp,[status(thm)],[t2554,t2553]) ).
cnf(t3069,plain,
X1 = multiply(multiply(inverse(multiply(X2,inverse(sFlat1))),multiply(X2,X1)),inverse(sFlat1)),
inference(step,[status(thm)],[t2565,t413]) ).
cnf(t2617,plain,
multiply(multiply(inverse(multiply(X1,inverse(sFlat1))),multiply(X1,X2)),inverse(sFlat1)) = X2,
inference(orient,[status(thm)],[t3069]) ).
cnf(t2619,plain,
inverse(sFlat1) = multiply(sFlat1,inverse(sFlat1)),
inference(cp,[status(thm)],[t2617,t2156]) ).
cnf(t2670,plain,
multiply(sFlat1,inverse(sFlat1)) = inverse(sFlat1),
inference(orient,[status(thm)],[t2619]) ).
cnf(t2675,plain,
sFlat1 = multiply(multiply(inverse(multiply(X1,inverse(inverse(sFlat1)))),multiply(X1,inverse(inverse(sFlat1)))),inverse(sFlat1)),
inference(cp,[status(thm)],[t2554,t2670]) ).
cnf(t1002,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(inverse(sFlat1)))) = multiply(inverse(multiply(X3,inverse(multiply(multiply(inverse(multiply(Y3,inverse(multiply(X2,b2)))),multiply(Y3,sFlat0)),inverse(sFlat1))))),multiply(X3,inverse(inverse(sFlat1)))),
inference(cp,[status(thm)],[t984,t332]) ).
cnf(t3006,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(inverse(sFlat1)))) = multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,inverse(inverse(sFlat1)))),
inference(step,[status(thm)],[t1002,t26]) ).
cnf(t1439,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(inverse(sFlat1)))) = multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,inverse(inverse(sFlat1)))),
inference(orient,[status(thm)],[t3006]) ).
cnf(t1462,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(multiply(multiply(X3,multiply(X2,sFlat0)),inverse(sFlat1)),b2)))))),multiply(X1,inverse(inverse(sFlat1)))) = multiply(inverse(multiply(Y3,X3)),multiply(Y3,inverse(inverse(sFlat1)))),
inference(cp,[status(thm)],[t1439,t413]) ).
cnf(t3009,plain,
multiply(inverse(multiply(X1,X3)),multiply(X1,inverse(inverse(sFlat1)))) = multiply(inverse(multiply(Y3,X3)),multiply(Y3,inverse(inverse(sFlat1)))),
inference(step,[status(thm)],[t1462,t413]) ).
cnf(t1542,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(sFlat1)))) = multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(inverse(sFlat1)))),
inference(orient,[status(thm)],[t3009]) ).
cnf(t2220,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(sFlat1)))) = multiply(inverse(sFlat1),multiply(inverse(X2),inverse(inverse(sFlat1)))),
inference(cp,[status(thm)],[t1542,t2156]) ).
cnf(t2459,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(inverse(sFlat1)))) = multiply(inverse(sFlat1),multiply(inverse(X2),inverse(inverse(sFlat1)))),
inference(orient,[status(thm)],[t2220]) ).
cnf(t3073,plain,
sFlat1 = multiply(multiply(inverse(sFlat1),multiply(inverse(inverse(inverse(sFlat1))),inverse(inverse(sFlat1)))),inverse(sFlat1)),
inference(step,[status(thm)],[t2675,t2459]) ).
cnf(t3074,plain,
sFlat1 = multiply(multiply(inverse(sFlat1),sFlat1),inverse(sFlat1)),
inference(step,[status(thm)],[t3073,t2156]) ).
cnf(t3075,plain,
sFlat1 = multiply(sFlat1,inverse(sFlat1)),
inference(step,[status(thm)],[t3074,t2156]) ).
cnf(t3076,plain,
sFlat1 = inverse(sFlat1),
inference(step,[status(thm)],[t3075,t2670]) ).
cnf(t2682,plain,
inverse(sFlat1) = sFlat1,
inference(orient,[status(thm)],[t3076]) ).
cnf(t3118,plain,
multiply(multiply(inverse(multiply(X1,sFlat1)),multiply(X1,X2)),inverse(sFlat1)) = X2,
inference(step,[status(thm)],[t2617,t2682]) ).
cnf(t3119,plain,
multiply(multiply(inverse(multiply(X1,sFlat1)),multiply(X1,X2)),sFlat1) = X2,
inference(step,[status(thm)],[t3118,t2682]) ).
cnf(t2703,plain,
multiply(multiply(inverse(multiply(X1,sFlat1)),multiply(X1,X2)),sFlat1) = X2,
inference(rw,[status(thm)],[t3119]) ).
cnf(t2761,plain,
multiply(multiply(inverse(multiply(X1,sFlat1)),multiply(X1,X2)),sFlat1) = X2,
inference(orient,[status(thm)],[t2703]) ).
cnf(t2773,plain,
X1 = multiply(multiply(inverse(multiply(inverse(X1),sFlat1)),sFlat1),sFlat1),
inference(cp,[status(thm)],[t2761,t2156]) ).
cnf(t2817,plain,
multiply(multiply(inverse(multiply(inverse(X1),sFlat1)),sFlat1),sFlat1) = X1,
inference(orient,[status(thm)],[t2773]) ).
cnf(t2766,plain,
X1 = multiply(multiply(inverse(sFlat1),multiply(inverse(sFlat1),X1)),sFlat1),
inference(cp,[status(thm)],[t2761,t2156]) ).
cnf(t3210,plain,
X1 = multiply(multiply(sFlat1,multiply(inverse(sFlat1),X1)),sFlat1),
inference(step,[status(thm)],[t2766,t2682]) ).
cnf(t3211,plain,
X1 = multiply(multiply(sFlat1,multiply(sFlat1,X1)),sFlat1),
inference(step,[status(thm)],[t3210,t2682]) ).
cnf(t2804,plain,
multiply(multiply(sFlat1,multiply(sFlat1,X1)),sFlat1) = X1,
inference(orient,[status(thm)],[t3211]) ).
cnf(t3102,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(sFlat1))) = multiply(inverse(sFlat1),multiply(inverse(X2),inverse(inverse(sFlat1)))),
inference(step,[status(thm)],[t2459,t2682]) ).
cnf(t3103,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,sFlat1)) = multiply(inverse(sFlat1),multiply(inverse(X2),inverse(inverse(sFlat1)))),
inference(step,[status(thm)],[t3102,t2682]) ).
cnf(t3104,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,sFlat1)) = multiply(sFlat1,multiply(inverse(X2),inverse(inverse(sFlat1)))),
inference(step,[status(thm)],[t3103,t2682]) ).
cnf(t3105,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,sFlat1)) = multiply(sFlat1,multiply(inverse(X2),inverse(sFlat1))),
inference(step,[status(thm)],[t3104,t2682]) ).
cnf(t3106,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,sFlat1)) = multiply(sFlat1,multiply(inverse(X2),sFlat1)),
inference(step,[status(thm)],[t3105,t2682]) ).
cnf(t2700,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,sFlat1)) = multiply(sFlat1,multiply(inverse(X2),sFlat1)),
inference(rw,[status(thm)],[t3106]) ).
cnf(t2918,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,sFlat1)) = multiply(sFlat1,multiply(inverse(X2),sFlat1)),
inference(orient,[status(thm)],[t2700]) ).
cnf(t516,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,sFlat0)) = multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,sFlat0)),
inference(cp,[status(thm)],[t368,t492]) ).
cnf(t542,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,sFlat0)) = multiply(inverse(multiply(X3,inverse(X2))),multiply(X3,sFlat0)),
inference(orient,[status(thm)],[t516]) ).
cnf(t564,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(multiply(multiply(X3,multiply(X2,sFlat0)),inverse(sFlat1)),b2)))))),multiply(X1,sFlat0)) = multiply(inverse(multiply(Y3,X3)),multiply(Y3,sFlat0)),
inference(cp,[status(thm)],[t542,t413]) ).
cnf(t2993,plain,
multiply(inverse(multiply(X1,X3)),multiply(X1,sFlat0)) = multiply(inverse(multiply(Y3,X3)),multiply(Y3,sFlat0)),
inference(step,[status(thm)],[t564,t413]) ).
cnf(t571,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,sFlat0)) = multiply(inverse(multiply(X3,X2)),multiply(X3,sFlat0)),
inference(orient,[status(thm)],[t2993]) ).
cnf(t592,plain,
multiply(inverse(multiply(X1,b2)),multiply(X1,sFlat0)) = multiply(inverse(sFlat1),multiply(sFlat0,sFlat0)),
inference(cp,[status(thm)],[t571,t20]) ).
cnf(t619,plain,
multiply(inverse(multiply(X1,b2)),multiply(X1,sFlat0)) = multiply(inverse(sFlat1),multiply(sFlat0,sFlat0)),
inference(orient,[status(thm)],[t592]) ).
cnf(t620,plain,
multiply(inverse(sFlat1),multiply(sFlat0,sFlat0)) = multiply(inverse(X1),multiply(multiply(multiply(inverse(multiply(X2,inverse(X1))),multiply(X2,sFlat0)),inverse(sFlat1)),sFlat0)),
inference(cp,[status(thm)],[t619,t492]) ).
cnf(t1035,plain,
multiply(inverse(X1),multiply(multiply(multiply(inverse(multiply(X2,inverse(X1))),multiply(X2,sFlat0)),inverse(sFlat1)),sFlat0)) = multiply(inverse(sFlat1),multiply(sFlat0,sFlat0)),
inference(orient,[status(thm)],[t620]) ).
cnf(t1036,plain,
multiply(inverse(sFlat1),multiply(sFlat0,sFlat0)) = multiply(X1,multiply(multiply(multiply(inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(multiply(multiply(X1,multiply(X3,sFlat0)),inverse(sFlat1)),b2)))))),multiply(X2,sFlat0)),inverse(sFlat1)),sFlat0)),
inference(cp,[status(thm)],[t1035,t413]) ).
cnf(t3001,plain,
multiply(inverse(sFlat1),multiply(sFlat0,sFlat0)) = multiply(X1,multiply(multiply(multiply(inverse(multiply(X2,X1)),multiply(X2,sFlat0)),inverse(sFlat1)),sFlat0)),
inference(step,[status(thm)],[t1036,t413]) ).
cnf(t1065,plain,
multiply(X1,multiply(multiply(multiply(inverse(multiply(X2,X1)),multiply(X2,sFlat0)),inverse(sFlat1)),sFlat0)) = multiply(inverse(sFlat1),multiply(sFlat0,sFlat0)),
inference(orient,[status(thm)],[t3001]) ).
cnf(t1110,plain,
X1 = inverse(multiply(multiply(multiply(inverse(multiply(X2,X1)),multiply(X2,sFlat0)),inverse(sFlat1)),inverse(multiply(multiply(multiply(inverse(sFlat1),multiply(sFlat0,sFlat0)),inverse(sFlat1)),b2)))),
inference(cp,[status(thm)],[t413,t1065]) ).
cnf(t622,plain,
inverse(multiply(X1,b2)) = multiply(multiply(inverse(multiply(X2,inverse(multiply(inverse(sFlat1),multiply(sFlat0,sFlat0))))),multiply(X2,inverse(multiply(X1,sFlat0)))),inverse(multiply(inverse(multiply(X1,sFlat0)),multiply(X1,sFlat0)))),
inference(cp,[status(thm)],[t4,t619]) ).
cnf(t2994,plain,
inverse(multiply(X1,b2)) = inverse(multiply(X1,inverse(multiply(multiply(multiply(inverse(sFlat1),multiply(sFlat0,sFlat0)),inverse(sFlat1)),b2)))),
inference(step,[status(thm)],[t622,t385]) ).
cnf(t633,plain,
inverse(multiply(X1,inverse(multiply(multiply(multiply(inverse(sFlat1),multiply(sFlat0,sFlat0)),inverse(sFlat1)),b2)))) = inverse(multiply(X1,b2)),
inference(orient,[status(thm)],[t2994]) ).
cnf(t3002,plain,
X1 = inverse(multiply(multiply(multiply(inverse(multiply(X2,X1)),multiply(X2,sFlat0)),inverse(sFlat1)),b2)),
inference(step,[status(thm)],[t1110,t633]) ).
cnf(t1116,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X1,X2)),multiply(X1,sFlat0)),inverse(sFlat1)),b2)) = X2,
inference(orient,[status(thm)],[t3002]) ).
cnf(t2218,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,sFlat0)) = multiply(inverse(sFlat1),multiply(inverse(X2),sFlat0)),
inference(cp,[status(thm)],[t571,t2156]) ).
cnf(t2283,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,sFlat0)) = multiply(inverse(sFlat1),multiply(inverse(X2),sFlat0)),
inference(orient,[status(thm)],[t2218]) ).
cnf(t3045,plain,
inverse(multiply(multiply(multiply(inverse(sFlat1),multiply(inverse(X2),sFlat0)),inverse(sFlat1)),b2)) = X2,
inference(step,[status(thm)],[t1116,t2283]) ).
cnf(t2316,plain,
inverse(multiply(multiply(multiply(inverse(sFlat1),multiply(inverse(X2),sFlat0)),inverse(sFlat1)),b2)) = X2,
inference(rw,[status(thm)],[t3045]) ).
cnf(t2387,plain,
inverse(multiply(multiply(multiply(inverse(sFlat1),multiply(inverse(X1),sFlat0)),inverse(sFlat1)),b2)) = X1,
inference(orient,[status(thm)],[t2316]) ).
cnf(t2197,plain,
X1 = inverse(multiply(inverse(sFlat0),inverse(multiply(multiply(multiply(X1,sFlat1),inverse(sFlat1)),b2)))),
inference(cp,[status(thm)],[t413,t2156]) ).
cnf(t2350,plain,
inverse(multiply(inverse(sFlat0),inverse(multiply(multiply(multiply(X1,sFlat1),inverse(sFlat1)),b2)))) = X1,
inference(orient,[status(thm)],[t2197]) ).
cnf(t3,axiom,
sFlat2 = multiply(multiply(inverse(b2),b2),a2),
introduced(definition) ).
cnf(t8,plain,
multiply(multiply(inverse(b2),b2),a2) = sFlat2,
inference(orient,[status(thm)],[t3]) ).
cnf(t2982,plain,
multiply(sFlat1,a2) = sFlat2,
inference(step,[status(thm)],[t8,t10]) ).
cnf(t13,plain,
multiply(sFlat1,a2) = sFlat2,
inference(rw,[status(thm)],[t2982]) ).
cnf(t18,plain,
multiply(sFlat1,a2) = sFlat2,
inference(orient,[status(thm)],[t13]) ).
cnf(t19,plain,
sFlat1 = multiply(multiply(inverse(multiply(X1,inverse(sFlat2))),multiply(X1,inverse(a2))),inverse(multiply(inverse(a2),a2))),
inference(cp,[status(thm)],[t4,t18]) ).
cnf(t31,plain,
multiply(multiply(inverse(multiply(X1,inverse(sFlat2))),multiply(X1,inverse(a2))),inverse(multiply(inverse(a2),a2))) = sFlat1,
inference(orient,[status(thm)],[t19]) ).
cnf(t3023,plain,
multiply(multiply(inverse(multiply(X1,inverse(sFlat2))),multiply(X1,inverse(a2))),inverse(sFlat1)) = sFlat1,
inference(step,[status(thm)],[t31,t2156]) ).
cnf(t2236,plain,
multiply(multiply(inverse(multiply(X1,inverse(sFlat2))),multiply(X1,inverse(a2))),inverse(sFlat1)) = sFlat1,
inference(rw,[status(thm)],[t3023]) ).
cnf(t2360,plain,
multiply(multiply(inverse(multiply(X1,inverse(sFlat2))),multiply(X1,inverse(a2))),inverse(sFlat1)) = sFlat1,
inference(orient,[status(thm)],[t2236]) ).
cnf(t2362,plain,
sFlat1 = multiply(multiply(inverse(multiply(inverse(inverse(a2)),inverse(sFlat2))),sFlat1),inverse(sFlat1)),
inference(cp,[status(thm)],[t2360,t2156]) ).
cnf(t2376,plain,
multiply(multiply(inverse(multiply(inverse(inverse(a2)),inverse(sFlat2))),sFlat1),inverse(sFlat1)) = sFlat1,
inference(orient,[status(thm)],[t2362]) ).
cnf(t2378,plain,
inverse(multiply(inverse(inverse(a2)),inverse(sFlat2))) = inverse(multiply(inverse(sFlat0),inverse(multiply(sFlat1,b2)))),
inference(cp,[status(thm)],[t2350,t2376]) ).
cnf(t2381,plain,
inverse(multiply(inverse(sFlat0),inverse(multiply(sFlat1,b2)))) = inverse(multiply(inverse(inverse(a2)),inverse(sFlat2))),
inference(orient,[status(thm)],[t2378]) ).
cnf(t2389,plain,
multiply(inverse(sFlat0),inverse(multiply(sFlat1,b2))) = inverse(multiply(multiply(multiply(inverse(sFlat1),multiply(inverse(multiply(inverse(inverse(a2)),inverse(sFlat2))),sFlat0)),inverse(sFlat1)),b2)),
inference(cp,[status(thm)],[t2387,t2381]) ).
cnf(t3057,plain,
multiply(inverse(sFlat0),inverse(multiply(sFlat1,b2))) = multiply(inverse(inverse(a2)),inverse(sFlat2)),
inference(step,[status(thm)],[t2389,t2387]) ).
cnf(t2408,plain,
multiply(inverse(sFlat0),inverse(multiply(sFlat1,b2))) = multiply(inverse(inverse(a2)),inverse(sFlat2)),
inference(orient,[status(thm)],[t3057]) ).
cnf(t3070,plain,
multiply(inverse(sFlat1),b2) = b2,
inference(step,[status(thm)],[t2107,t2670]) ).
cnf(t2679,plain,
multiply(inverse(sFlat1),b2) = b2,
inference(rw,[status(thm)],[t3070]) ).
cnf(t3184,plain,
multiply(sFlat1,b2) = b2,
inference(step,[status(thm)],[t2679,t2682]) ).
cnf(t2732,plain,
multiply(sFlat1,b2) = b2,
inference(orient,[status(thm)],[t3184]) ).
cnf(t3185,plain,
multiply(inverse(sFlat0),inverse(b2)) = multiply(inverse(inverse(a2)),inverse(sFlat2)),
inference(step,[status(thm)],[t2408,t2732]) ).
cnf(t3186,plain,
multiply(inverse(sFlat0),sFlat0) = multiply(inverse(inverse(a2)),inverse(sFlat2)),
inference(step,[status(thm)],[t3185,t14]) ).
cnf(t3187,plain,
sFlat1 = multiply(inverse(inverse(a2)),inverse(sFlat2)),
inference(step,[status(thm)],[t3186,t2156]) ).
cnf(t2734,plain,
sFlat1 = multiply(inverse(inverse(a2)),inverse(sFlat2)),
inference(rw,[status(thm)],[t3187]) ).
cnf(t2735,plain,
multiply(inverse(inverse(a2)),inverse(sFlat2)) = sFlat1,
inference(orient,[status(thm)],[t2734]) ).
cnf(t2924,plain,
multiply(sFlat1,multiply(inverse(inverse(sFlat2)),sFlat1)) = multiply(inverse(sFlat1),multiply(inverse(inverse(a2)),sFlat1)),
inference(cp,[status(thm)],[t2918,t2735]) ).
cnf(t3240,plain,
multiply(sFlat1,multiply(inverse(inverse(sFlat2)),sFlat1)) = multiply(sFlat1,multiply(inverse(inverse(a2)),sFlat1)),
inference(step,[status(thm)],[t2924,t2682]) ).
cnf(t2958,plain,
multiply(sFlat1,multiply(inverse(inverse(a2)),sFlat1)) = multiply(sFlat1,multiply(inverse(inverse(sFlat2)),sFlat1)),
inference(orient,[status(thm)],[t3240]) ).
cnf(t2961,plain,
multiply(inverse(inverse(a2)),sFlat1) = multiply(multiply(sFlat1,multiply(sFlat1,multiply(inverse(inverse(sFlat2)),sFlat1))),sFlat1),
inference(cp,[status(thm)],[t2804,t2958]) ).
cnf(t3241,plain,
multiply(inverse(inverse(a2)),sFlat1) = multiply(inverse(inverse(sFlat2)),sFlat1),
inference(step,[status(thm)],[t2961,t2804]) ).
cnf(t2964,plain,
multiply(inverse(inverse(a2)),sFlat1) = multiply(inverse(inverse(sFlat2)),sFlat1),
inference(orient,[status(thm)],[t3241]) ).
cnf(t2967,plain,
inverse(a2) = multiply(multiply(inverse(multiply(inverse(inverse(sFlat2)),sFlat1)),sFlat1),sFlat1),
inference(cp,[status(thm)],[t2817,t2964]) ).
cnf(t3242,plain,
inverse(a2) = inverse(sFlat2),
inference(step,[status(thm)],[t2967,t2817]) ).
cnf(t2968,plain,
inverse(a2) = inverse(sFlat2),
inference(orient,[status(thm)],[t3242]) ).
cnf(t2974,plain,
a2 = multiply(multiply(inverse(multiply(inverse(sFlat2),sFlat1)),sFlat1),sFlat1),
inference(cp,[status(thm)],[t2817,t2968]) ).
cnf(t3250,plain,
a2 = sFlat2,
inference(step,[status(thm)],[t2974,t2817]) ).
cnf(t2978,plain,
a2 = sFlat2,
inference(orient,[status(thm)],[t3250]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(multiply(inverse(b2),b2),a2) != sFlat2,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_0,t2978]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP410-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 14:43:19 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.58/3.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.58/3.55 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------