%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP419-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 01:33:52 PM UTC 2026
% Result : Unsatisfiable 18.63s 3.33s
% Output : CNFRefutation 18.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 5
% Syntax : Number of formulae : 99 ( 99 unt; 3 def)
% Number of atoms : 443 ( 98 equ)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 12 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 104 !; 0 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/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] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1,
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_66,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1,
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(iPr_def_10,inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(X0,X1))) = b2,
inference(superposition,[status(thm)],[c_62,c_66]) ).
tcf(c_106,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(multiply(inverse(b2),b2)))))))),iPr_def_11)) = X0,
inference(superposition,[status(thm)],[c_63,c_66]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(superposition,[status(thm)],[c_66,c_66]) ).
tcf(c_110,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(iPr_def_11))))))),iPr_def_11)) = X0,
inference(demodulation,[status(thm)],[c_106,c_62,c_63]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = iPr_def_13(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_108]) ).
tcf(c_115,plain,
! [X0: $i] : iPr_def_13(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_66,c_112]) ).
tcf(c_136,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(iPr_def_11))))))),iPr_def_11) = iPr_def_13(X0),
inference(superposition,[status(thm)],[c_110,c_115]) ).
tcf(c_138,plain,
! [X0: $i] : inverse(iPr_def_13(X0)) = X0,
inference(demodulation,[status(thm)],[c_110,c_136]) ).
tcf(c_157,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_10,inverse(multiply(X0,inverse(multiply(b2,inverse(iPr_def_11))))))),iPr_def_11) = iPr_def_13(iPr_def_13(X0)),
inference(superposition,[status(thm)],[c_138,c_136]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(multiply(iPr_def_10,inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(X0,X1)) = iPr_def_13(b2),
inference(superposition,[status(thm)],[c_103,c_115]) ).
tcf(c_291,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(X0,inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(iPr_def_10,inverse(multiply(iPr_def_11,inverse(multiply(inverse(iPr_def_11),iPr_def_11)))))))),iPr_def_13(iPr_def_13(X0))) = iPr_def_13(b2),
inference(superposition,[status(thm)],[c_157,c_270]) ).
tcf(c_457,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(iPr_def_10,inverse(multiply(iPr_def_11,inverse(multiply(inverse(iPr_def_11),iPr_def_11)))))))),iPr_def_13(X0)) = iPr_def_13(b2),
inference(superposition,[status(thm)],[c_115,c_291]) ).
tcf(c_475,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(iPr_def_10,inverse(multiply(iPr_def_11,inverse(multiply(inverse(iPr_def_11),iPr_def_11)))))))),X0) = iPr_def_13(b2),
inference(superposition,[status(thm)],[c_115,c_457]) ).
tcf(c_505,plain,
iPr_def_13(iPr_def_13(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(inverse(inverse(multiply(b2,inverse(iPr_def_11))))),inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(iPr_def_10,inverse(multiply(iPr_def_11,inverse(multiply(inverse(iPr_def_11),iPr_def_11)))))))))) = multiply(inverse(multiply(iPr_def_10,inverse(iPr_def_13(b2)))),iPr_def_11),
inference(superposition,[status(thm)],[c_475,c_157]) ).
tcf(c_511,plain,
iPr_def_13(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(inverse(inverse(multiply(b2,inverse(iPr_def_11))))),inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(iPr_def_10,inverse(multiply(iPr_def_11,inverse(multiply(inverse(iPr_def_11),iPr_def_11)))))))) = multiply(inverse(iPr_def_11),iPr_def_11),
inference(demodulation,[status(thm)],[c_505,c_63,c_115,c_138]) ).
tcf(c_793,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(iPr_def_10,inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(X0,X1))) = b2,
inference(superposition,[status(thm)],[c_62,c_66]) ).
tcf(c_795,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(b2,inverse(multiply(iPr_def_10,b2)))))))),multiply(X0,b2))) = X1,
inference(superposition,[status(thm)],[c_62,c_66]) ).
tcf(c_796,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(multiply(inverse(b2),b2)))))))),iPr_def_11)) = X0,
inference(superposition,[status(thm)],[c_63,c_66]) ).
tcf(c_798,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(superposition,[status(thm)],[c_66,c_66]) ).
tcf(c_800,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(iPr_def_11))))))),iPr_def_11)) = X0,
inference(demodulation,[status(thm)],[c_796,c_62,c_63]) ).
tcf(c_801,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(b2,inverse(iPr_def_11))))))),multiply(X0,b2))) = X1,
inference(demodulation,[status(thm)],[c_795,c_63]) ).
tcf(c_802,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)) = iPr_def_13(X1),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_798]) ).
tcf(c_804,plain,
! [X0: $i] : iPr_def_13(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_66,c_112]) ).
tcf(c_805,plain,
iPr_def_13(iPr_def_10) = b2,
inference(superposition,[status(thm)],[c_62,c_804]) ).
tcf(c_809,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(iPr_def_11))))))),iPr_def_11) = iPr_def_13(X0),
inference(superposition,[status(thm)],[c_800,c_804]) ).
tcf(c_811,plain,
! [X0: $i] : inverse(iPr_def_13(X0)) = X0,
inference(demodulation,[status(thm)],[c_800,c_809]) ).
tcf(c_818,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_10,inverse(multiply(X0,inverse(multiply(b2,inverse(iPr_def_11))))))),iPr_def_11) = iPr_def_13(iPr_def_13(X0)),
inference(superposition,[status(thm)],[c_811,c_809]) ).
tcf(c_825,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(b2,inverse(iPr_def_11))))))),multiply(X0,b2))) = iPr_def_13(X1),
inference(superposition,[status(thm)],[c_811,c_801]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(b2,inverse(iPr_def_11))))))),multiply(X0,b2)) = iPr_def_13(iPr_def_13(X1)),
inference(superposition,[status(thm)],[c_825,c_804]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(multiply(iPr_def_10,inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),multiply(X0,X1)) = iPr_def_13(b2),
inference(superposition,[status(thm)],[c_793,c_804]) ).
tcf(c_880,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(X0,inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(iPr_def_10,inverse(multiply(iPr_def_11,inverse(multiply(inverse(iPr_def_11),iPr_def_11)))))))),iPr_def_13(iPr_def_13(X0))) = iPr_def_13(b2),
inference(superposition,[status(thm)],[c_818,c_872]) ).
tcf(c_897,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)) = iPr_def_13(iPr_def_13(X1)),
inference(superposition,[status(thm)],[c_112,c_804]) ).
tcf(c_910,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(X0,inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(inverse(X1),inverse(multiply(iPr_def_11,inverse(multiply(inverse(iPr_def_11),iPr_def_11)))))))),iPr_def_13(iPr_def_13(X0))) = iPr_def_13(X1),
inference(superposition,[status(thm)],[c_818,c_802]) ).
tcf(c_955,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(iPr_def_10,inverse(multiply(iPr_def_11,inverse(multiply(inverse(iPr_def_11),iPr_def_11)))))))),iPr_def_13(X0)) = iPr_def_13(b2),
inference(superposition,[status(thm)],[c_804,c_880]) ).
tcf(c_966,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(inverse(X0)),inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(iPr_def_10,inverse(multiply(iPr_def_11,inverse(multiply(inverse(iPr_def_11),iPr_def_11)))))))),X0) = iPr_def_13(b2),
inference(superposition,[status(thm)],[c_804,c_955]) ).
tcf(c_985,plain,
! [X0: $i] : iPr_def_13(iPr_def_13(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(inverse(inverse(multiply(b2,inverse(iPr_def_11))))),inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(iPr_def_10,inverse(multiply(iPr_def_11,inverse(multiply(inverse(iPr_def_11),iPr_def_11)))))))))) = multiply(inverse(multiply(X0,inverse(iPr_def_13(b2)))),multiply(X0,b2)),
inference(superposition,[status(thm)],[c_966,c_836]) ).
tcf(c_991,plain,
! [X0: $i] : multiply(inverse(multiply(X0,b2)),multiply(X0,b2)) = multiply(inverse(iPr_def_11),iPr_def_11),
inference(demodulation,[status(thm)],[c_985,c_804,c_811,c_511]) ).
tcf(c_998,plain,
multiply(inverse(iPr_def_13(b2)),iPr_def_13(b2)) = multiply(inverse(iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_966,c_991]) ).
tcf(c_1004,plain,
multiply(inverse(iPr_def_11),iPr_def_11) = multiply(b2,iPr_def_13(b2)),
inference(demodulation,[status(thm)],[c_998,c_811]) ).
tcf(c_1007,plain,
! [X0: $i] : multiply(inverse(multiply(X0,b2)),multiply(X0,b2)) = multiply(b2,iPr_def_13(b2)),
inference(demodulation,[status(thm)],[c_991,c_1004]) ).
tcf(c_1199,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(X0,inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(inverse(X1),inverse(multiply(iPr_def_11,inverse(multiply(b2,iPr_def_13(b2))))))))),iPr_def_13(iPr_def_13(X0))) = iPr_def_13(X1),
inference(light_normalisation,[status(thm)],[c_910,c_1004]) ).
tcf(c_1205,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(X0),inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(inverse(X1),inverse(multiply(iPr_def_11,inverse(multiply(b2,iPr_def_13(b2))))))))),iPr_def_13(X0)) = iPr_def_13(X1),
inference(superposition,[status(thm)],[c_804,c_1199]) ).
tcf(c_1445,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(multiply(iPr_def_10,inverse(multiply(inverse(iPr_def_10),inverse(multiply(b2,inverse(iPr_def_11))))))),inverse(multiply(inverse(X0),inverse(multiply(iPr_def_11,inverse(multiply(b2,iPr_def_13(b2))))))))),b2) = iPr_def_13(X0),
inference(superposition,[status(thm)],[c_805,c_1205]) ).
tcf(c_1471,plain,
! [X0: $i] : multiply(inverse(iPr_def_13(X0)),iPr_def_13(X0)) = multiply(b2,iPr_def_13(b2)),
inference(superposition,[status(thm)],[c_1445,c_1007]) ).
tcf(c_1474,plain,
! [X0: $i] : multiply(X0,iPr_def_13(X0)) = multiply(b2,iPr_def_13(b2)),
inference(demodulation,[status(thm)],[c_1471,c_811]) ).
tcf(c_1499,plain,
! [X0: $i] : multiply(inverse(X0),X0) = multiply(b2,iPr_def_13(b2)),
inference(superposition,[status(thm)],[c_804,c_1474]) ).
tcf(c_1501,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_13(X0),inverse(multiply(inverse(iPr_def_13(X0)),iPr_def_13(X0))))))))),multiply(b2,iPr_def_13(b2))) = iPr_def_13(iPr_def_13(X1)),
inference(superposition,[status(thm)],[c_1474,c_897]) ).
tcf(c_1507,plain,
! [X0: $i,X1: $i] : multiply(X0,iPr_def_13(X0)) = multiply(X1,iPr_def_13(X1)),
inference(superposition,[status(thm)],[c_1474,c_1474]) ).
tcf(c_1517,plain,
! [X0: $i] : multiply(X0,iPr_def_13(X0)) = iPr_def_14,
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_1507]) ).
tcf(c_1519,plain,
! [X0: $i] : multiply(inverse(X0),X0) = iPr_def_14,
inference(demodulation,[status(thm)],[c_1499,c_1517]) ).
tcf(c_1525,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_13(X0),inverse(iPr_def_14))))))),iPr_def_14) = iPr_def_13(iPr_def_13(X1)),
inference(demodulation,[status(thm)],[c_1501,c_1517,c_1519]) ).
tcf(c_1553,plain,
multiply(iPr_def_10,b2) = iPr_def_14,
inference(superposition,[status(thm)],[c_805,c_1517]) ).
tcf(c_1554,plain,
iPr_def_11 = iPr_def_14,
inference(demodulation,[status(thm)],[c_1553,c_63]) ).
tcf(c_1555,plain,
! [X0: $i] : multiply(X0,iPr_def_13(X0)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1517,c_1554]) ).
tcf(c_1557,plain,
! [X0: $i] : multiply(inverse(X0),X0) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1519,c_1554]) ).
tcf(c_1619,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_13(X0),inverse(iPr_def_11))))))),iPr_def_11) = iPr_def_13(iPr_def_13(X1)),
inference(light_normalisation,[status(thm)],[c_1525,c_1554]) ).
tcf(c_1620,plain,
! [X0: $i] : iPr_def_13(iPr_def_13(inverse(inverse(multiply(iPr_def_13(X0),inverse(iPr_def_11)))))) = multiply(inverse(multiply(X0,inverse(iPr_def_11))),iPr_def_11),
inference(superposition,[status(thm)],[c_1557,c_1619]) ).
tcf(c_1623,plain,
! [X0: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_11))),iPr_def_11) = multiply(iPr_def_13(X0),inverse(iPr_def_11)),
inference(demodulation,[status(thm)],[c_1620,c_804]) ).
tcf(c_1637,plain,
multiply(iPr_def_13(inverse(inverse(iPr_def_11))),inverse(iPr_def_11)) = multiply(inverse(iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_1557,c_1623]) ).
tcf(c_1638,plain,
multiply(inverse(iPr_def_11),inverse(iPr_def_11)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1637,c_804,c_1557]) ).
tcf(c_1639,plain,
multiply(iPr_def_13(inverse(iPr_def_11)),inverse(iPr_def_11)) = multiply(inverse(iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_1638,c_1623]) ).
tcf(c_1641,plain,
multiply(iPr_def_11,inverse(iPr_def_11)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1639,c_804,c_1557]) ).
tcf(c_1643,plain,
multiply(iPr_def_13(iPr_def_11),inverse(iPr_def_11)) = multiply(inverse(iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_1641,c_1623]) ).
tcf(c_1645,plain,
multiply(iPr_def_13(iPr_def_11),inverse(iPr_def_11)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1643,c_1557]) ).
tcf(c_1655,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_11,inverse(multiply(X0,inverse(iPr_def_11))))),iPr_def_11) = iPr_def_13(iPr_def_13(X0)),
inference(superposition,[status(thm)],[c_1645,c_1619]) ).
tcf(c_1802,plain,
multiply(inverse(iPr_def_11),iPr_def_11) = iPr_def_13(iPr_def_13(iPr_def_11)),
inference(superposition,[status(thm)],[c_1641,c_1655]) ).
tcf(c_1804,plain,
multiply(inverse(multiply(iPr_def_11,inverse(iPr_def_11))),iPr_def_11) = iPr_def_13(iPr_def_13(iPr_def_13(iPr_def_11))),
inference(superposition,[status(thm)],[c_1645,c_1655]) ).
tcf(c_1811,plain,
iPr_def_13(iPr_def_13(iPr_def_11)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1802,c_1557]) ).
tcf(c_1812,plain,
multiply(inverse(multiply(iPr_def_11,inverse(iPr_def_11))),iPr_def_11) = iPr_def_13(iPr_def_11),
inference(demodulation,[status(thm)],[c_1804,c_1811]) ).
tcf(c_1813,plain,
iPr_def_13(iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1812,c_1623,c_1645]) ).
tcf(c_1833,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_11,inverse(multiply(X0,inverse(multiply(iPr_def_11,inverse(iPr_def_11))))))),iPr_def_11) = iPr_def_13(iPr_def_13(X0)),
inference(superposition,[status(thm)],[c_1813,c_1619]) ).
tcf(c_1834,plain,
multiply(iPr_def_11,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_1813,c_1555]) ).
tcf(c_1835,plain,
inverse(iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_1813,c_811]) ).
tcf(c_1836,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_11,inverse(multiply(X0,iPr_def_11)))),iPr_def_11) = iPr_def_13(iPr_def_13(X0)),
inference(demodulation,[status(thm)],[c_1833,c_1834,c_1835]) ).
tcf(c_1843,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_11)),iPr_def_11) = multiply(iPr_def_13(X0),iPr_def_11),
inference(demodulation,[status(thm)],[c_1623,c_1835]) ).
tcf(c_2422,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_11,inverse(multiply(iPr_def_13(X0),iPr_def_11)))),iPr_def_11) = iPr_def_13(iPr_def_13(inverse(multiply(X0,iPr_def_11)))),
inference(superposition,[status(thm)],[c_1843,c_1836]) ).
tcf(c_2438,plain,
! [X0: $i] : iPr_def_13(iPr_def_13(inverse(multiply(X0,iPr_def_11)))) = iPr_def_13(iPr_def_13(iPr_def_13(X0))),
inference(demodulation,[status(thm)],[c_2422,c_1836]) ).
tcf(c_2439,plain,
! [X0: $i] : iPr_def_13(multiply(X0,iPr_def_11)) = iPr_def_13(iPr_def_13(iPr_def_13(X0))),
inference(demodulation,[status(thm)],[c_2438,c_804]) ).
tcf(c_2489,plain,
! [X0: $i] : inverse(iPr_def_13(iPr_def_13(iPr_def_13(X0)))) = multiply(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_2439,c_811]) ).
tcf(c_2490,plain,
! [X0: $i] : multiply(X0,iPr_def_11) = iPr_def_13(iPr_def_13(X0)),
inference(demodulation,[status(thm)],[c_2489,c_811]) ).
tcf(c_2499,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_11,inverse(iPr_def_13(iPr_def_13(X0))))),iPr_def_11) = iPr_def_13(iPr_def_13(X0)),
inference(demodulation,[status(thm)],[c_1836,c_2490]) ).
tcf(c_2514,plain,
! [X0: $i] : iPr_def_13(iPr_def_13(inverse(multiply(iPr_def_11,inverse(iPr_def_13(iPr_def_13(X0))))))) = iPr_def_13(iPr_def_13(X0)),
inference(demodulation,[status(thm)],[c_2499,c_2490]) ).
tcf(c_2515,plain,
! [X0: $i] : iPr_def_13(multiply(iPr_def_11,iPr_def_13(X0))) = iPr_def_13(iPr_def_13(X0)),
inference(demodulation,[status(thm)],[c_2514,c_804,c_811]) ).
tcf(c_2546,plain,
! [X0: $i] : iPr_def_13(multiply(iPr_def_11,X0)) = iPr_def_13(X0),
inference(superposition,[status(thm)],[c_804,c_2515]) ).
tcf(c_2563,plain,
! [X0: $i] : inverse(iPr_def_13(X0)) = multiply(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_2546,c_811]) ).
tcf(c_2564,plain,
! [X0: $i] : multiply(iPr_def_11,X0) = X0,
inference(demodulation,[status(thm)],[c_2563,c_811]) ).
tcf(c_2575,plain,
a2 = iPr_def_12,
inference(demodulation,[status(thm)],[c_64,c_2564]) ).
tcf(c_2577,plain,
iPr_def_12 != iPr_def_12,
inference(demodulation,[status(thm)],[c_65,c_2575]) ).
tcf(c_2578,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2577]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP419-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 14:42:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.40 Running UEQ theorem proving
% 0.15/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.43 % Proving...
% 18.63/3.33 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 18.63/3.33 % SZS status Started for theBenchmark.p
% 18.63/3.33 % SZS status Unsatisfiable for theBenchmark.p
% 18.63/3.33
% 18.63/3.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.63/3.33
% 18.63/3.33 % ------ iProver source info
% 18.63/3.33
% 18.63/3.33 % git: date: 2026-07-19 20:42:38 +0200
% 18.63/3.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.63/3.33 % git: non_committed_changes: false
% 18.63/3.33
% 18.63/3.33 % ------ Parsing...% successful
% 18.63/3.33
% 18.63/3.33
% 18.63/3.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.63/3.33
% 18.63/3.33 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 18.63/3.33
% 18.63/3.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.63/3.33
% 18.63/3.33 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 18.63/3.33 % ------ Proving...
% 18.63/3.33 % ------ Problem Properties
% 18.63/3.33
% 18.63/3.33 %
% 18.63/3.33 % clauses 5
% 18.63/3.33 % conjectures 1
% 18.63/3.33 % EPR 1
% 18.63/3.33 % Horn 5
% 18.63/3.33 % unary 5
% 18.63/3.33 % binary 0
% 18.63/3.33 % lits 5
% 18.63/3.33 % lits eq 5
% 18.63/3.33 % fd_pure 0
% 18.63/3.33 % fd_pseudo 0
% 18.63/3.33 % fd_cond 0
% 18.63/3.33 % fd_pseudo_cond 0
% 18.63/3.33 % AC symbols 0
% 18.63/3.33
% 18.63/3.33 % ------ Input Options Time Limit: Unbounded
% 18.63/3.33
% 18.63/3.33
% 18.63/3.33 % ------
% 18.63/3.33 % Current options:
% 18.63/3.33 % ------
% 18.63/3.33
% 18.63/3.33
% 18.63/3.33 %
% 18.63/3.33
% 18.63/3.33 % ------ Proving...
% 18.63/3.33 %
% 18.63/3.33
% 18.63/3.33 % SZS status Unsatisfiable for theBenchmark.p
% 18.63/3.33
% 18.63/3.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.63/3.33
% 18.63/3.33
%------------------------------------------------------------------------------