%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP407-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 01:33:40 PM UTC 2026
% Result : Unsatisfiable 12.40s 9.83s
% Output : CNFRefutation 12.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 5
% Syntax : Number of formulae : 108 ( 108 unt; 3 def)
% Number of atoms : 511 ( 107 equ)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 99 !; 0 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f3,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f2]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = X2,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[],[f3]) ).
tcf(c_62,definition,
iPr_def_10 = inverse(b2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_63,definition,
iPr_def_11 = multiply(iPr_def_10,b2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_64,definition,
iPr_def_12 = multiply(iPr_def_11,a2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_65,negated_conjecture,
iPr_def_12 != a2,
inference(demodulation,[status(thm)],[c_52,c_62,c_63,c_64]) ).
tcf(c_117,plain,
! [X0: $i] : multiply(iPr_def_10,inverse(multiply(inverse(multiply(inverse(iPr_def_11),X0)),multiply(inverse(b2),multiply(inverse(b2),b2))))) = X0,
inference(superposition,[status(thm)],[c_63,c_51]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,b2)),X1)),multiply(iPr_def_10,multiply(iPr_def_10,b2))))) = X1,
inference(superposition,[status(thm)],[c_62,c_51]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,b2)),X1)),multiply(iPr_def_10,iPr_def_11)))) = X1,
inference(light_normalisation,[status(thm)],[c_119,c_63]) ).
tcf(c_124,plain,
! [X0: $i] : multiply(iPr_def_10,inverse(multiply(inverse(multiply(inverse(iPr_def_11),X0)),multiply(iPr_def_10,iPr_def_11)))) = X0,
inference(light_normalisation,[status(thm)],[c_117,c_62,c_63]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),b2)),X2)),multiply(iPr_def_10,iPr_def_11))) = multiply(X0,inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X1),X1))))),
inference(superposition,[status(thm)],[c_123,c_51]) ).
tcf(c_148,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(iPr_def_11),b2)),X0)),multiply(iPr_def_10,iPr_def_11))) = multiply(iPr_def_10,inverse(multiply(inverse(X0),multiply(iPr_def_10,iPr_def_11)))),
inference(superposition,[status(thm)],[c_123,c_124]) ).
tcf(c_179,plain,
! [X0: $i] : multiply(inverse(iPr_def_11),multiply(iPr_def_10,inverse(multiply(inverse(X0),multiply(iPr_def_10,iPr_def_11))))) = X0,
inference(superposition,[status(thm)],[c_148,c_123]) ).
tcf(c_226,plain,
! [X0: $i] : multiply(inverse(iPr_def_11),multiply(iPr_def_10,multiply(iPr_def_10,inverse(multiply(inverse(X0),multiply(iPr_def_10,iPr_def_11)))))) = multiply(inverse(multiply(inverse(iPr_def_11),b2)),X0),
inference(superposition,[status(thm)],[c_148,c_179]) ).
tcf(c_227,plain,
multiply(inverse(iPr_def_11),multiply(iPr_def_10,inverse(multiply(iPr_def_10,multiply(iPr_def_10,iPr_def_11))))) = b2,
inference(superposition,[status(thm)],[c_62,c_179]) ).
tcf(c_333,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(iPr_def_11),b2)),multiply(inverse(iPr_def_11),X0)) = multiply(inverse(iPr_def_11),multiply(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_124,c_226]) ).
tcf(c_351,plain,
! [X0: $i] : multiply(iPr_def_10,inverse(multiply(inverse(multiply(inverse(iPr_def_11),X0)),multiply(iPr_def_10,iPr_def_11)))) = inverse(multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,X0))),multiply(iPr_def_10,iPr_def_11))),
inference(superposition,[status(thm)],[c_333,c_148]) ).
tcf(c_353,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,X0))),multiply(iPr_def_10,iPr_def_11))) = X0,
inference(light_normalisation,[status(thm)],[c_351,c_124]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(inverse(multiply(iPr_def_10,X0)),X1)),multiply(inverse(X0),multiply(inverse(X0),X0)))) = inverse(multiply(inverse(multiply(inverse(iPr_def_11),X1)),multiply(iPr_def_10,iPr_def_11))),
inference(superposition,[status(thm)],[c_51,c_353]) ).
tcf(c_365,plain,
inverse(multiply(inverse(multiply(inverse(iPr_def_11),iPr_def_11)),multiply(iPr_def_10,iPr_def_11))) = b2,
inference(superposition,[status(thm)],[c_63,c_353]) ).
tcf(c_371,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,X0))),multiply(iPr_def_10,iPr_def_11)) = multiply(inverse(iPr_def_11),multiply(iPr_def_10,inverse(multiply(X0,multiply(iPr_def_10,iPr_def_11))))),
inference(superposition,[status(thm)],[c_353,c_179]) ).
tcf(c_375,plain,
! [X0: $i] : inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,inverse(multiply(X0,multiply(iPr_def_10,iPr_def_11)))))) = X0,
inference(demodulation,[status(thm)],[c_353,c_371]) ).
tcf(c_431,plain,
multiply(inverse(iPr_def_11),multiply(iPr_def_10,inverse(multiply(b2,multiply(iPr_def_10,iPr_def_11))))) = multiply(inverse(multiply(inverse(iPr_def_11),iPr_def_11)),multiply(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_365,c_179]) ).
tcf(c_432,plain,
multiply(iPr_def_10,b2) = iPr_def_11,
inference(superposition,[status(thm)],[c_365,c_124]) ).
tcf(c_699,plain,
inverse(b2) = iPr_def_10,
inference(superposition,[status(thm)],[c_227,c_375]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(inverse(iPr_def_11),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(iPr_def_10,X0)),X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1)))))),multiply(iPr_def_10,iPr_def_11))) = inverse(multiply(inverse(X2),multiply(inverse(X0),multiply(inverse(X0),X0)))),
inference(superposition,[status(thm)],[c_51,c_364]) ).
tcf(c_873,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X1),X1)))))) = X2,
inference(superposition,[status(thm)],[c_147,c_123]) ).
tcf(c_883,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),b2)),multiply(inverse(multiply(X0,X1)),X2))),multiply(iPr_def_10,iPr_def_11))) = X2,
inference(superposition,[status(thm)],[c_147,c_51]) ).
tcf(c_1129,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(inverse(multiply(X0,b2)),multiply(X0,X1))),multiply(iPr_def_10,iPr_def_11))) = X1,
inference(superposition,[status(thm)],[c_883,c_883]) ).
tcf(c_1149,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1)))) = inverse(multiply(inverse(multiply(inverse(multiply(X0,b2)),X2)),multiply(iPr_def_10,iPr_def_11))),
inference(superposition,[status(thm)],[c_51,c_1129]) ).
tcf(c_1166,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,b2)),inverse(multiply(X1,multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(X0,X1)),multiply(X0,X1)))))) = multiply(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1129,c_51]) ).
tcf(c_1176,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,b2)),multiply(X0,X1)) = multiply(inverse(iPr_def_11),multiply(iPr_def_10,X1)),
inference(superposition,[status(thm)],[c_1129,c_179]) ).
tcf(c_1339,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,b2)),multiply(X0,inverse(X1)))),b2)),X1)),multiply(iPr_def_10,iPr_def_11))) = multiply(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1166,c_147]) ).
tcf(c_1666,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(multiply(X0,b2)),b2)),multiply(inverse(iPr_def_11),multiply(iPr_def_10,X1))) = multiply(inverse(iPr_def_11),multiply(iPr_def_10,multiply(X0,X1))),
inference(superposition,[status(thm)],[c_1176,c_1176]) ).
tcf(c_2656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X2,b2)),X3)),multiply(iPr_def_10,iPr_def_11))))) = multiply(inverse(multiply(X2,X1)),X3),
inference(superposition,[status(thm)],[c_1149,c_873]) ).
tcf(c_2657,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,multiply(inverse(X1),X1)))))) = multiply(inverse(X1),b2),
inference(superposition,[status(thm)],[c_1176,c_873]) ).
tcf(c_7146,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(multiply(X0,b2)),b2)),multiply(inverse(iPr_def_11),iPr_def_11)) = multiply(inverse(iPr_def_11),multiply(iPr_def_10,multiply(X0,b2))),
inference(superposition,[status(thm)],[c_432,c_1666]) ).
tcf(c_8011,plain,
inverse(multiply(inverse(multiply(inverse(iPr_def_11),inverse(multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,multiply(iPr_def_10,b2)))),multiply(inverse(b2),multiply(inverse(b2),b2)))))),multiply(iPr_def_10,iPr_def_11))) = inverse(multiply(inverse(multiply(inverse(iPr_def_11),iPr_def_11)),multiply(inverse(b2),multiply(inverse(b2),b2)))),
inference(superposition,[status(thm)],[c_7146,c_728]) ).
tcf(c_8014,plain,
inverse(multiply(inverse(multiply(inverse(iPr_def_11),inverse(multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_11))),multiply(iPr_def_10,iPr_def_11))))),multiply(iPr_def_10,iPr_def_11))) = b2,
inference(light_normalisation,[status(thm)],[c_8011,c_365,c_432,c_699]) ).
tcf(c_8984,plain,
inverse(multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_11))),multiply(iPr_def_10,iPr_def_11))) = multiply(iPr_def_10,b2),
inference(superposition,[status(thm)],[c_8014,c_124]) ).
tcf(c_8989,plain,
inverse(multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_11))),multiply(iPr_def_10,iPr_def_11))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_8984,c_432]) ).
tcf(c_14509,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,inverse(X0)))),b2)),X0)),multiply(iPr_def_10,iPr_def_11))) = multiply(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_432,c_1339]) ).
tcf(c_18124,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(iPr_def_11),iPr_def_11)),multiply(iPr_def_10,iPr_def_11))),b2)),multiply(b2,multiply(iPr_def_10,iPr_def_11)))),multiply(iPr_def_10,iPr_def_11))) = multiply(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_431,c_14509]) ).
tcf(c_18136,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_10))),b2)),b2)),multiply(iPr_def_10,iPr_def_11))) = multiply(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_699,c_14509]) ).
tcf(c_18200,plain,
inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),multiply(b2,multiply(iPr_def_10,iPr_def_11)))),multiply(iPr_def_10,iPr_def_11))) = multiply(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_18124,c_365]) ).
tcf(c_18309,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(iPr_def_10,iPr_def_11))) = multiply(inverse(multiply(b2,X1)),multiply(b2,multiply(iPr_def_10,iPr_def_11))),
inference(superposition,[status(thm)],[c_18200,c_2656]) ).
tcf(c_18703,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(iPr_def_10,iPr_def_11))) = multiply(inverse(multiply(X2,X1)),multiply(X2,multiply(iPr_def_10,iPr_def_11))),
inference(superposition,[status(thm)],[c_18309,c_18309]) ).
tcf(c_18802,plain,
! [X0: $i] : multiply(inverse(multiply(X0,multiply(iPr_def_10,iPr_def_11))),multiply(X0,multiply(iPr_def_10,iPr_def_11))) = multiply(b2,multiply(inverse(multiply(inverse(iPr_def_11),iPr_def_11)),multiply(iPr_def_10,iPr_def_11))),
inference(superposition,[status(thm)],[c_365,c_18703]) ).
tcf(c_19556,plain,
multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_10))),multiply(iPr_def_10,iPr_def_11)) = b2,
inference(superposition,[status(thm)],[c_18136,c_123]) ).
tcf(c_20440,plain,
! [X0: $i] : multiply(inverse(multiply(X0,multiply(iPr_def_10,iPr_def_11))),multiply(X0,multiply(iPr_def_10,iPr_def_11))) = multiply(inverse(b2),b2),
inference(superposition,[status(thm)],[c_19556,c_18703]) ).
tcf(c_20445,plain,
! [X0: $i] : multiply(inverse(multiply(X0,multiply(iPr_def_10,iPr_def_11))),multiply(X0,multiply(iPr_def_10,iPr_def_11))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_20440,c_432,c_699,c_18802]) ).
tcf(c_20465,plain,
multiply(b2,multiply(inverse(multiply(inverse(iPr_def_11),iPr_def_11)),multiply(iPr_def_10,iPr_def_11))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_18802,c_20445]) ).
tcf(c_20473,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(inverse(iPr_def_11),X0)),multiply(inverse(multiply(inverse(multiply(inverse(iPr_def_11),iPr_def_11)),multiply(iPr_def_10,iPr_def_11))),multiply(inverse(multiply(inverse(multiply(inverse(iPr_def_11),iPr_def_11)),multiply(iPr_def_10,iPr_def_11))),multiply(inverse(multiply(inverse(iPr_def_11),iPr_def_11)),multiply(iPr_def_10,iPr_def_11)))))) = inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),X0)),multiply(iPr_def_10,iPr_def_11))),
inference(superposition,[status(thm)],[c_20465,c_1149]) ).
tcf(c_20476,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(inverse(multiply(b2,b2)),X0)),multiply(iPr_def_10,iPr_def_11))) = inverse(multiply(inverse(multiply(inverse(iPr_def_11),X0)),multiply(b2,iPr_def_11))),
inference(light_normalisation,[status(thm)],[c_20473,c_365,c_20465]) ).
tcf(c_20519,plain,
multiply(iPr_def_11,multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_11))),multiply(iPr_def_10,iPr_def_11))) = iPr_def_11,
inference(superposition,[status(thm)],[c_8989,c_20445]) ).
tcf(c_20526,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,inverse(multiply(X0,multiply(iPr_def_10,iPr_def_11)))))),multiply(inverse(iPr_def_11),multiply(iPr_def_10,inverse(multiply(X0,multiply(iPr_def_10,iPr_def_11)))))) = iPr_def_11,
inference(superposition,[status(thm)],[c_371,c_20445]) ).
tcf(c_20564,plain,
! [X0: $i] : multiply(X0,multiply(inverse(iPr_def_11),multiply(iPr_def_10,inverse(multiply(X0,multiply(iPr_def_10,iPr_def_11)))))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_20526,c_375]) ).
tcf(c_20608,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(inverse(iPr_def_11),X0)),multiply(inverse(multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_11))),multiply(iPr_def_10,iPr_def_11))),multiply(inverse(multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_11))),multiply(iPr_def_10,iPr_def_11))),multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_11))),multiply(iPr_def_10,iPr_def_11)))))) = inverse(multiply(inverse(multiply(inverse(multiply(iPr_def_11,b2)),X0)),multiply(iPr_def_10,iPr_def_11))),
inference(superposition,[status(thm)],[c_20519,c_1149]) ).
tcf(c_20614,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(inverse(multiply(iPr_def_11,b2)),X0)),multiply(iPr_def_10,iPr_def_11))) = inverse(multiply(inverse(multiply(inverse(iPr_def_11),X0)),multiply(iPr_def_11,iPr_def_11))),
inference(light_normalisation,[status(thm)],[c_20608,c_8989,c_20519]) ).
tcf(c_20628,plain,
! [X0: $i] : multiply(inverse(X0),X0) = iPr_def_11,
inference(superposition,[status(thm)],[c_179,c_20564]) ).
tcf(c_20715,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_11))))) = multiply(inverse(X1),b2),
inference(demodulation,[status(thm)],[c_2657,c_20628]) ).
tcf(c_20732,plain,
inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_11))) = b2,
inference(demodulation,[status(thm)],[c_365,c_20628]) ).
tcf(c_20745,plain,
inverse(multiply(b2,multiply(iPr_def_10,iPr_def_11))) = iPr_def_11,
inference(demodulation,[status(thm)],[c_8989,c_20732]) ).
tcf(c_20831,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_11))))) = multiply(inverse(multiply(X2,X1)),multiply(X2,b2)),
inference(superposition,[status(thm)],[c_20628,c_2656]) ).
tcf(c_20854,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,b2)) = multiply(inverse(X1),b2),
inference(light_normalisation,[status(thm)],[c_20831,c_20715]) ).
tcf(c_20917,plain,
inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,b2))) = inverse(iPr_def_11),
inference(superposition,[status(thm)],[c_20732,c_375]) ).
tcf(c_20918,plain,
inverse(multiply(inverse(iPr_def_11),iPr_def_11)) = inverse(iPr_def_11),
inference(light_normalisation,[status(thm)],[c_20917,c_432]) ).
tcf(c_21129,plain,
multiply(inverse(multiply(iPr_def_10,iPr_def_11)),b2) = multiply(iPr_def_11,multiply(b2,b2)),
inference(superposition,[status(thm)],[c_20745,c_20854]) ).
tcf(c_21138,plain,
! [X0: $i] : multiply(inverse(inverse(multiply(inverse(multiply(inverse(iPr_def_11),X0)),multiply(iPr_def_10,iPr_def_11)))),b2) = multiply(inverse(X0),multiply(iPr_def_10,b2)),
inference(superposition,[status(thm)],[c_124,c_20854]) ).
tcf(c_21144,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,inverse(multiply(X0,multiply(iPr_def_10,iPr_def_11)))))),b2) = multiply(inverse(iPr_def_11),multiply(X0,b2)),
inference(superposition,[status(thm)],[c_20564,c_20854]) ).
tcf(c_21171,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_10,X0)),iPr_def_11) = multiply(inverse(X0),b2),
inference(superposition,[status(thm)],[c_432,c_20854]) ).
tcf(c_21195,plain,
! [X0: $i] : multiply(inverse(inverse(multiply(inverse(multiply(inverse(iPr_def_11),X0)),multiply(iPr_def_10,iPr_def_11)))),b2) = multiply(inverse(X0),iPr_def_11),
inference(light_normalisation,[status(thm)],[c_21138,c_432]) ).
tcf(c_21196,plain,
! [X0: $i] : multiply(inverse(iPr_def_11),multiply(X0,b2)) = multiply(X0,b2),
inference(light_normalisation,[status(thm)],[c_21144,c_375]) ).
tcf(c_21351,plain,
! [X0: $i] : multiply(iPr_def_10,inverse(multiply(inverse(multiply(X0,b2)),multiply(iPr_def_10,iPr_def_11)))) = multiply(X0,b2),
inference(superposition,[status(thm)],[c_21196,c_124]) ).
tcf(c_21395,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_10,iPr_def_11)),inverse(multiply(inverse(multiply(inverse(multiply(iPr_def_11,multiply(b2,b2))),X0)),multiply(iPr_def_10,iPr_def_11)))) = X0,
inference(superposition,[status(thm)],[c_21129,c_123]) ).
tcf(c_21421,plain,
multiply(inverse(iPr_def_11),b2) = b2,
inference(superposition,[status(thm)],[c_21351,c_124]) ).
tcf(c_21441,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(inverse(b2),X0)),multiply(iPr_def_10,iPr_def_11))) = multiply(iPr_def_10,inverse(multiply(inverse(X0),multiply(iPr_def_10,iPr_def_11)))),
inference(demodulation,[status(thm)],[c_148,c_21421]) ).
tcf(c_21442,plain,
! [X0: $i] : multiply(iPr_def_10,inverse(multiply(inverse(X0),multiply(iPr_def_10,iPr_def_11)))) = inverse(multiply(inverse(multiply(iPr_def_10,X0)),multiply(iPr_def_10,iPr_def_11))),
inference(light_normalisation,[status(thm)],[c_21441,c_699]) ).
tcf(c_21456,plain,
multiply(iPr_def_10,inverse(multiply(inverse(b2),multiply(iPr_def_10,iPr_def_11)))) = b2,
inference(superposition,[status(thm)],[c_21421,c_124]) ).
tcf(c_21463,plain,
! [X0: $i] : multiply(inverse(b2),multiply(inverse(iPr_def_11),X0)) = multiply(inverse(iPr_def_11),multiply(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_21421,c_1176]) ).
tcf(c_21466,plain,
multiply(iPr_def_10,inverse(multiply(iPr_def_10,multiply(iPr_def_10,iPr_def_11)))) = b2,
inference(light_normalisation,[status(thm)],[c_21456,c_699]) ).
tcf(c_21467,plain,
! [X0: $i] : multiply(inverse(iPr_def_11),multiply(iPr_def_10,X0)) = multiply(iPr_def_10,multiply(inverse(iPr_def_11),X0)),
inference(light_normalisation,[status(thm)],[c_21463,c_699]) ).
tcf(c_21487,plain,
inverse(multiply(iPr_def_10,multiply(inverse(iPr_def_11),iPr_def_11))) = b2,
inference(demodulation,[status(thm)],[c_20732,c_21467]) ).
tcf(c_21555,plain,
inverse(multiply(iPr_def_10,iPr_def_11)) = b2,
inference(superposition,[status(thm)],[c_20628,c_21487]) ).
tcf(c_21559,plain,
multiply(inverse(multiply(inverse(iPr_def_11),iPr_def_11)),b2) = multiply(b2,iPr_def_11),
inference(superposition,[status(thm)],[c_21487,c_21171]) ).
tcf(c_21560,plain,
multiply(b2,iPr_def_11) = b2,
inference(light_normalisation,[status(thm)],[c_21559,c_20918,c_21421]) ).
tcf(c_21563,plain,
multiply(iPr_def_11,multiply(b2,b2)) = multiply(b2,b2),
inference(demodulation,[status(thm)],[c_21129,c_21555]) ).
tcf(c_21573,plain,
multiply(b2,multiply(iPr_def_10,iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_21555,c_20628]) ).
tcf(c_21578,plain,
inverse(iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_20745,c_21573]) ).
tcf(c_21580,plain,
multiply(iPr_def_11,b2) = b2,
inference(demodulation,[status(thm)],[c_21421,c_21578]) ).
tcf(c_21718,plain,
! [X0: $i] : multiply(inverse(inverse(multiply(inverse(multiply(iPr_def_11,X0)),multiply(iPr_def_10,iPr_def_11)))),b2) = multiply(inverse(X0),iPr_def_11),
inference(light_normalisation,[status(thm)],[c_21195,c_21578]) ).
tcf(c_21729,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(multiply(inverse(multiply(iPr_def_11,X0)),multiply(iPr_def_10,iPr_def_11)))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(X0),iPr_def_11)),X1)),multiply(iPr_def_10,iPr_def_11)))) = X1,
inference(superposition,[status(thm)],[c_21718,c_123]) ).
tcf(c_21746,plain,
multiply(iPr_def_10,inverse(multiply(inverse(b2),multiply(iPr_def_10,iPr_def_11)))) = inverse(multiply(inverse(iPr_def_11),multiply(iPr_def_10,iPr_def_11))),
inference(superposition,[status(thm)],[c_432,c_21442]) ).
tcf(c_21761,plain,
inverse(multiply(iPr_def_11,multiply(iPr_def_10,iPr_def_11))) = b2,
inference(light_normalisation,[status(thm)],[c_21746,c_699,c_21466,c_21578]) ).
tcf(c_21775,plain,
! [X0: $i] : multiply(b2,inverse(multiply(inverse(multiply(iPr_def_11,X0)),b2))) = X0,
inference(light_normalisation,[status(thm)],[c_21395,c_20476,c_21555,c_21560,c_21563,c_21578]) ).
tcf(c_21778,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(inverse(multiply(iPr_def_11,b2)),X0)),multiply(iPr_def_10,iPr_def_11))) = multiply(b2,inverse(multiply(inverse(X0),b2))),
inference(superposition,[status(thm)],[c_123,c_21775]) ).
tcf(c_21784,plain,
! [X0: $i] : multiply(iPr_def_10,inverse(multiply(inverse(X0),multiply(iPr_def_10,iPr_def_11)))) = multiply(b2,inverse(multiply(inverse(X0),b2))),
inference(light_normalisation,[status(thm)],[c_21778,c_699,c_20614,c_21442,c_21580]) ).
tcf(c_21785,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(iPr_def_10,X0)),multiply(iPr_def_10,iPr_def_11))) = multiply(b2,inverse(multiply(inverse(X0),b2))),
inference(demodulation,[status(thm)],[c_21442,c_21784]) ).
tcf(c_21796,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_11,X0)),b2) = multiply(inverse(X0),b2),
inference(superposition,[status(thm)],[c_21580,c_20854]) ).
tcf(c_21811,plain,
! [X0: $i] : multiply(b2,inverse(multiply(inverse(X0),b2))) = X0,
inference(demodulation,[status(thm)],[c_21775,c_21796]) ).
tcf(c_21901,plain,
! [X0: $i] : multiply(inverse(inverse(multiply(inverse(multiply(iPr_def_11,multiply(iPr_def_10,iPr_def_11))),multiply(iPr_def_10,iPr_def_11)))),inverse(multiply(inverse(multiply(inverse(multiply(b2,iPr_def_11)),X0)),multiply(iPr_def_10,iPr_def_11)))) = X0,
inference(superposition,[status(thm)],[c_21555,c_21729]) ).
tcf(c_21913,plain,
! [X0: $i] : multiply(iPr_def_11,X0) = X0,
inference(light_normalisation,[status(thm)],[c_21901,c_699,c_21560,c_21573,c_21578,c_21761,c_21785,c_21811]) ).
tcf(c_21922,plain,
a2 = iPr_def_12,
inference(demodulation,[status(thm)],[c_64,c_21913]) ).
tcf(c_21927,plain,
iPr_def_12 != iPr_def_12,
inference(demodulation,[status(thm)],[c_65,c_21922]) ).
tcf(c_21928,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_21927]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP407-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 14:44:03 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running UEQ theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 12.40/9.83 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 12.40/9.83 % SZS status Started for theBenchmark.p
% 12.40/9.83 % SZS status Unsatisfiable for theBenchmark.p
% 12.40/9.83
% 12.40/9.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.40/9.83
% 12.40/9.83 % ------ iProver source info
% 12.40/9.83
% 12.40/9.83 % git: date: 2026-07-19 20:42:38 +0200
% 12.40/9.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.40/9.83 % git: non_committed_changes: false
% 12.40/9.83
% 12.40/9.83 % ------ Parsing...% successful
% 12.40/9.83
% 12.40/9.83
% 12.40/9.83 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 12.40/9.83
% 12.40/9.83 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 12.40/9.83
% 12.40/9.83 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 12.40/9.83
% 12.40/9.83 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 12.40/9.83 % ------ Proving...
% 12.40/9.83 % ------ Problem Properties
% 12.40/9.83
% 12.40/9.83 %
% 12.40/9.83 % clauses 5
% 12.40/9.83 % conjectures 1
% 12.40/9.83 % EPR 1
% 12.40/9.83 % Horn 5
% 12.40/9.83 % unary 5
% 12.40/9.83 % binary 0
% 12.40/9.83 % lits 5
% 12.40/9.83 % lits eq 5
% 12.40/9.83 % fd_pure 0
% 12.40/9.83 % fd_pseudo 0
% 12.40/9.83 % fd_cond 0
% 12.40/9.83 % fd_pseudo_cond 0
% 12.40/9.83 % AC symbols 0
% 12.40/9.83
% 12.40/9.83 % ------ Input Options Time Limit: Unbounded
% 12.40/9.83
% 12.40/9.83
% 12.40/9.83 % ------
% 12.40/9.83 % Current options:
% 12.40/9.83 % ------
% 12.40/9.83
% 12.40/9.83
% 12.40/9.83 %
% 12.40/9.83
% 12.40/9.83 % ------ Proving...
% 12.40/9.83 %
% 12.40/9.83
% 12.40/9.83 % SZS status Unsatisfiable for theBenchmark.p
% 12.40/9.83
% 12.40/9.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.40/9.83
% 12.40/9.83
%------------------------------------------------------------------------------