%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP056-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 01:30:24 PM UTC 2026
% Result : Unsatisfiable 22.23s 3.83s
% Output : CNFRefutation 22.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 2
% Syntax : Number of formulae : 88 ( 84 unt; 0 def)
% Number of atoms : 95 ( 94 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 16 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 231 ( 0 sgn 231 !; 0 ?; 228 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X2),X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f3,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(reorient_equations,[],[f2]) ).
tcf(c_51,negated_conjecture,
( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X2),X2))) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),X2)))),multiply(X3,inverse(X2))),
inference(superposition,[status(thm)],[c_52,c_52]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(X0),multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),X2)))),multiply(X1,inverse(X2)))),inverse(X2)))),inverse(multiply(inverse(X2),X2))) = X2,
inference(superposition,[status(thm)],[c_52,c_52]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X3),multiply(inverse(X2),X2))))),X1)),inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2)))) = X3,
inference(superposition,[status(thm)],[c_52,c_52]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(X0),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X3)))),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X0),multiply(inverse(X3),X3))))),X2)),inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(X3),X3)))) = multiply(inverse(X3),X3),
inference(superposition,[status(thm)],[c_52,c_109]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X3)))),multiply(X1,inverse(X3)))))),multiply(X0,inverse(inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))))) = multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(inverse(multiply(inverse(X3),X3))))),
inference(superposition,[status(thm)],[c_108,c_52]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(X2),X2)))),X2)))),multiply(X0,inverse(X2))) = X1,
inference(superposition,[status(thm)],[c_108,c_52]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),X2)))),multiply(X3,inverse(X2))),
inference(superposition,[status(thm)],[c_108,c_108]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(X2),X2))) = X1,
inference(superposition,[status(thm)],[c_108,c_52]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2)))),inverse(multiply(inverse(multiply(inverse(X3),inverse(multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))))),multiply(inverse(X2),X2))))),X1) = X3,
inference(superposition,[status(thm)],[c_52,c_317]) ).
tcf(c_540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,inverse(X3)))))),inverse(multiply(inverse(multiply(X2,inverse(X3))),multiply(X2,inverse(X3))))) = multiply(X2,inverse(multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(X3),X3)))),X3))),
inference(superposition,[status(thm)],[c_317,c_52]) ).
tcf(c_1345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(X2))),
inference(superposition,[status(thm)],[c_533,c_322]) ).
tcf(c_1721,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X1),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X2),X2)))),X2))) = X1,
inference(superposition,[status(thm)],[c_540,c_52]) ).
tcf(c_1951,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(X0),multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),X2)))),multiply(X1,inverse(X2)))),inverse(X3))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),X2)))),multiply(X4,inverse(X3))),
inference(superposition,[status(thm)],[c_52,c_1345]) ).
tcf(c_2260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X3),X3)))),X3))) = multiply(X0,inverse(X2)),
inference(superposition,[status(thm)],[c_1345,c_1721]) ).
tcf(c_2474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X1),multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X1),X3)))),multiply(X2,inverse(X3)))),inverse(X4)))),inverse(multiply(inverse(X4),X4)))),X4))) = multiply(X0,inverse(multiply(inverse(X3),X3))),
inference(superposition,[status(thm)],[c_52,c_2260]) ).
tcf(c_2530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(X2),X2))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(X4)))),inverse(multiply(inverse(X4),X4)))),X4),
inference(superposition,[status(thm)],[c_2260,c_332]) ).
tcf(c_2553,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X2),X2)))),X2) = X1,
inference(light_normalisation,[status(thm)],[c_2530,c_332]) ).
tcf(c_3449,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X1)))),multiply(X0,inverse(multiply(inverse(X1),X1)))) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[c_52,c_1951]) ).
tcf(c_4096,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_3449,c_3449]) ).
tcf(c_4164,plain,
( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_51,c_4096]) ).
tcf(c_4248,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X1)))),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X1),X1))) = X2,
inference(superposition,[status(thm)],[c_4096,c_52]) ).
tcf(c_4254,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(inverse(X0)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(X1),multiply(inverse(X2),X2))),inverse(multiply(inverse(X0),X0)))),X0))) = X1,
inference(superposition,[status(thm)],[c_4096,c_1721]) ).
tcf(c_4263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X1),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X3),X3)))),X2))) = X1,
inference(superposition,[status(thm)],[c_4096,c_1721]) ).
tcf(c_4266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(X2),X2)))),X3)))),multiply(X0,inverse(X3))) = X1,
inference(superposition,[status(thm)],[c_4096,c_317]) ).
tcf(c_4270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X3),X3))) = X1,
inference(superposition,[status(thm)],[c_4096,c_52]) ).
tcf(c_4292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X3),multiply(inverse(X2),X2))))),X1)),inverse(multiply(inverse(X4),X4))) = X3,
inference(superposition,[status(thm)],[c_4096,c_110]) ).
tcf(c_4300,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),X2)))),multiply(X0,inverse(X2))) = inverse(multiply(inverse(X2),X2)),
inference(superposition,[status(thm)],[c_4096,c_317]) ).
tcf(c_4304,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(X1),X1)))),X1) = X1,
inference(superposition,[status(thm)],[c_4096,c_2553]) ).
tcf(c_4597,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X1),X1)))) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[c_118,c_4292]) ).
tcf(c_4602,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(X1),X1))) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[c_4096,c_4597]) ).
tcf(c_4619,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(inverse(X1),X1))) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_4096,c_4248]) ).
tcf(c_4693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(inverse(X0),multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X0),X2)))),multiply(X1,inverse(X2)))),inverse(X3)))),inverse(multiply(inverse(X4),X4))) = X3,
inference(superposition,[status(thm)],[c_4270,c_4248]) ).
tcf(c_4791,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(X0),X0)),X0) = X0,
inference(light_normalisation,[status(thm)],[c_4304,c_4619]) ).
tcf(c_4792,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(X0),X0)),X1) = X1,
inference(superposition,[status(thm)],[c_4096,c_4791]) ).
tcf(c_4817,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(inverse(multiply(inverse(X0),X1))),inverse(X1))),inverse(multiply(inverse(X2),X2))) = X0,
inference(superposition,[status(thm)],[c_4792,c_4270]) ).
tcf(c_4825,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2))) = multiply(inverse(inverse(X1)),inverse(X2)),
inference(superposition,[status(thm)],[c_4792,c_1345]) ).
tcf(c_4984,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X0)) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[c_4602,c_4792]) ).
tcf(c_5002,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[status(thm)],[c_4984,c_4792]) ).
tcf(c_5003,plain,
! [X0: $i,X1: $i] : inverse(inverse(multiply(inverse(X0),X0))) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_4984,c_4984]) ).
tcf(c_5004,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(multiply(inverse(X0),X0))),X1) = X1,
inference(superposition,[status(thm)],[c_4984,c_4792]) ).
tcf(c_5009,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[c_4164,c_5002]) ).
tcf(c_5033,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(inverse(multiply(inverse(X0),X0)))),X1) = X1,
inference(superposition,[status(thm)],[c_5004,c_5004]) ).
tcf(c_5072,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(inverse(inverse(multiply(inverse(X0),X0))))),X1) = X1,
inference(superposition,[status(thm)],[c_5003,c_5004]) ).
tcf(c_5077,plain,
! [X0: $i,X1: $i] : inverse(inverse(multiply(inverse(X0),X0))) = inverse(inverse(multiply(inverse(X1),X1))),
inference(superposition,[status(thm)],[c_5003,c_5003]) ).
tcf(c_6423,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X1),X1))))),X2) = X2,
inference(superposition,[status(thm)],[c_5077,c_5004]) ).
tcf(c_8523,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(X1),X1))) = multiply(X0,inverse(multiply(inverse(X2),X2))),
inference(demodulation,[status(thm)],[c_2474,c_4693]) ).
tcf(c_8595,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(X1),X1))) = multiply(X0,multiply(inverse(X2),X2)),
inference(superposition,[status(thm)],[c_4984,c_8523]) ).
tcf(c_8610,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(inverse(multiply(inverse(X1),X1)))) = multiply(X0,inverse(multiply(inverse(X2),X2))),
inference(superposition,[status(thm)],[c_5004,c_8523]) ).
tcf(c_9458,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(inverse(multiply(inverse(X1),X1)))) = multiply(X0,multiply(inverse(X2),X2)),
inference(superposition,[status(thm)],[c_5004,c_8595]) ).
tcf(c_9459,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(inverse(inverse(multiply(inverse(X1),X1))))) = multiply(X0,multiply(inverse(X2),X2)),
inference(superposition,[status(thm)],[c_5033,c_8595]) ).
tcf(c_16611,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(inverse(multiply(inverse(X1),X1)))) = multiply(X0,inverse(inverse(multiply(inverse(X2),X2)))),
inference(superposition,[status(thm)],[c_9458,c_9458]) ).
tcf(c_25569,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(inverse(X0)),inverse(X1))),inverse(inverse(inverse(multiply(inverse(X2),X2))))) = multiply(inverse(inverse(X1)),inverse(X0)),
inference(superposition,[status(thm)],[c_4825,c_9459]) ).
tcf(c_47191,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(inverse(multiply(inverse(X0),X1))),inverse(X1))) = multiply(inverse(inverse(X0)),inverse(inverse(multiply(inverse(X1),X1)))),
inference(demodulation,[status(thm)],[c_312,c_4825,c_5004,c_5072,c_6423,c_25569]) ).
tcf(c_47206,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),inverse(inverse(multiply(inverse(X0),X0)))) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_5004,c_47191]) ).
tcf(c_49025,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),inverse(inverse(multiply(inverse(X1),X1)))) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_47206,c_16611]) ).
tcf(c_49038,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(inverse(multiply(inverse(X0),X1))),inverse(X1))) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[c_47191,c_49025]) ).
tcf(c_49337,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),inverse(multiply(inverse(X1),X1))) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_49025,c_8610]) ).
tcf(c_49338,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),multiply(inverse(X1),X1)) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_49025,c_9458]) ).
tcf(c_54442,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),inverse(multiply(inverse(X1),X1))) = X0,
inference(light_normalisation,[status(thm)],[c_4817,c_49038]) ).
tcf(c_54443,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_49337,c_54442]) ).
tcf(c_54445,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2))) = multiply(X1,inverse(X2)),
inference(demodulation,[status(thm)],[c_4825,c_54443]) ).
tcf(c_54449,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(demodulation,[status(thm)],[c_49338,c_54443]) ).
tcf(c_54469,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),X1))) = X0,
inference(demodulation,[status(thm)],[c_8595,c_54449]) ).
tcf(c_54514,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(multiply(inverse(X1),multiply(X0,inverse(X2))),X2))) = X1,
inference(demodulation,[status(thm)],[c_4263,c_54443,c_54469]) ).
tcf(c_54518,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),X1)),X2))) = multiply(X0,inverse(X2)),
inference(superposition,[status(thm)],[c_4984,c_54514]) ).
tcf(c_54554,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(demodulation,[status(thm)],[c_4266,c_54443,c_54445,c_54469]) ).
tcf(c_54566,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),inverse(multiply(multiply(inverse(X2),X0),X1))) = X2,
inference(superposition,[status(thm)],[c_54554,c_54514]) ).
tcf(c_54575,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X1))) = inverse(multiply(inverse(X1),X1)),
inference(light_normalisation,[status(thm)],[c_4300,c_54518]) ).
tcf(c_54576,plain,
! [X0: $i] : inverse(multiply(inverse(X0),X0)) = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[c_54575,c_54445]) ).
tcf(c_54604,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),multiply(X1,inverse(X1))) = X0,
inference(superposition,[status(thm)],[c_54576,c_54442]) ).
tcf(c_54606,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(light_normalisation,[status(thm)],[c_54604,c_54443]) ).
tcf(c_54630,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(superposition,[status(thm)],[c_54443,c_54554]) ).
tcf(c_55411,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(X1),multiply(inverse(X2),X2))),multiply(X0,inverse(X0)))),X0))) = X1,
inference(light_normalisation,[status(thm)],[c_4254,c_54443,c_54576]) ).
tcf(c_55412,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[c_55411,c_54443,c_54449,c_54606]) ).
tcf(c_55436,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_55412,c_54630]) ).
tcf(c_55567,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_54443,c_55436]) ).
tcf(c_55598,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(superposition,[status(thm)],[c_54554,c_55567]) ).
tcf(c_55678,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_55598,c_54630]) ).
tcf(c_55835,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(multiply(inverse(X0),X1),X2)) = multiply(inverse(X2),multiply(inverse(X1),X0)),
inference(superposition,[status(thm)],[c_55678,c_55678]) ).
tcf(c_55880,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),multiply(inverse(X1),multiply(inverse(X0),X2))) = X2,
inference(demodulation,[status(thm)],[c_54566,c_55835]) ).
tcf(c_55927,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),multiply(inverse(X1),X2)) = multiply(X0,X2),
inference(superposition,[status(thm)],[c_55567,c_55880]) ).
tcf(c_56018,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c_55567,c_55927]) ).
tcf(c_56035,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_5009,c_56018]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP056-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 13:25:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 22.23/3.83 % SZS status Started for theBenchmark.p
% 22.23/3.83 % SZS status Unsatisfiable for theBenchmark.p
% 22.23/3.83
% 22.23/3.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.23/3.83
% 22.23/3.83 % ------ iProver source info
% 22.23/3.83
% 22.23/3.83 % git: date: 2026-07-19 20:42:38 +0200
% 22.23/3.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.23/3.83 % git: non_committed_changes: false
% 22.23/3.83
% 22.23/3.83 % ------ Parsing...% successful
% 22.23/3.83
% 22.23/3.83
% 22.23/3.83 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.23/3.83
% 22.23/3.83 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 22.23/3.83
% 22.23/3.83 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.23/3.83
% 22.23/3.83 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 22.23/3.83 % ------ Proving...
% 22.23/3.83 % ------ Problem Properties
% 22.23/3.83
% 22.23/3.83 %
% 22.23/3.83 % clauses 2
% 22.23/3.83 % conjectures 1
% 22.23/3.83 % EPR 0
% 22.23/3.83 % Horn 2
% 22.23/3.83 % unary 1
% 22.23/3.83 % binary 0
% 22.23/3.83 % lits 4
% 22.23/3.83 % lits eq 4
% 22.23/3.83 % fd_pure 0
% 22.23/3.83 % fd_pseudo 0
% 22.23/3.83 % fd_cond 0
% 22.23/3.83 % fd_pseudo_cond 0
% 22.23/3.83 % AC symbols 0
% 22.23/3.83
% 22.23/3.83 % ------ Schedule dynamic 5 is on
% 22.23/3.83
% 22.23/3.83 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.23/3.83
% 22.23/3.83
% 22.23/3.83 % ------
% 22.23/3.83 % Current options:
% 22.23/3.83 % ------
% 22.23/3.83
% 22.23/3.83
% 22.23/3.83 %
% 22.23/3.83
% 22.23/3.83 % ------ Proving...
% 22.23/3.83 %
% 22.23/3.83
% 22.23/3.83 % SZS status Unsatisfiable for theBenchmark.p
% 22.23/3.83
% 22.23/3.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.23/3.83
% 22.23/3.83
%------------------------------------------------------------------------------