%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP328-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 01:32:51 PM UTC 2026
% Result : Unsatisfiable 3.71s 1.19s
% Output : CNFRefutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 45
% Syntax : Number of formulae : 236 ( 90 unt; 11 def)
% Number of atoms : 633 ( 425 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 322 ( 110 ~; 212 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c6 = inverse(sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c8)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c4)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( sk_c8 != inverse(X4)
| multiply(X4,sk_c8) != X3
| sk_c7 != multiply(sk_c8,X3)
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c8 != inverse(X2)
| multiply(X2,sk_c8) != X1
| sk_c7 != multiply(sk_c8,X1)
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( sk_c8 != inverse(X4)
| multiply(X4,sk_c8) != X3
| sk_c7 != multiply(sk_c8,X3)
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X2,X0,X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c6 != inverse(sk_c8)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(equality_resolution,[],[f67]) ).
tcf(c_83,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c8,sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c8,sk_c3) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c8) != sk_c6 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(X0,sk_c7) != sk_c8 )
| ( multiply(sk_c8,multiply(X2,sk_c8)) != sk_c7 )
| ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_405,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_406,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_407,negated_conjecture,
( iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_408,definition,
iPr_def_12 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_409,definition,
iPr_def_13 = multiply(sk_c7,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_410,definition,
iPr_def_14 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_411,definition,
iPr_def_15 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_412,definition,
iPr_def_16 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_413,definition,
iPr_def_17 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_414,definition,
iPr_def_18 = multiply(sk_c8,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_415,definition,
iPr_def_19 = multiply(sk_c2,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_416,definition,
iPr_def_20 = multiply(sk_c8,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_417,definition,
iPr_def_21 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_418,definition,
iPr_def_22 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_419,negated_conjecture,
( iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c6 )
| ( iPr_def_13 != sk_c8 )
| ( iPr_def_12 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_407,c_410,c_409,c_408]) ).
tcf(c_421,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_406]) ).
tcf(c_422,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_405]) ).
tcf(c_423,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115,c_412,c_411]) ).
tcf(c_424,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_114,c_413]) ).
tcf(c_425,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_113,c_414]) ).
tcf(c_426,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_427,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_13 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_428,negated_conjecture,
( ( iPr_def_19 = sk_c3 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110,c_415]) ).
tcf(c_429,negated_conjecture,
( ( iPr_def_19 = sk_c3 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_19 = sk_c3 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_19 = sk_c3 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_19 = sk_c3 )
| ( iPr_def_13 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105,c_416]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_13 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100,c_417]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_13 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_95,c_418]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_13 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_12 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_12 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_12 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_12 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_13 = sk_c8 )
| ( iPr_def_12 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_848,plain,
multiply(iPr_def_14,sk_c8) = identity,
inference(superposition,[status(thm)],[c_410,c_84]) ).
tcf(c_849,plain,
multiply(iPr_def_15,sk_c4) = identity,
inference(superposition,[status(thm)],[c_411,c_84]) ).
tcf(c_850,plain,
multiply(iPr_def_21,sk_c1) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_851,plain,
multiply(iPr_def_16,sk_c2) = identity,
inference(superposition,[status(thm)],[c_412,c_84]) ).
tcf(c_892,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_440,c_435]) ).
tcf(c_1589,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_22 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_418,c_422]) ).
tcf(c_1590,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c8 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_422]) ).
tcf(c_1591,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_422]) ).
tcf(c_1604,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_22 )
| ( sk_c7 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_1589,c_417]) ).
tcf(c_1788,plain,
( ~ iPr_def_11
| ( inverse(sk_c7) != sk_c8 )
| ( multiply(sk_c8,iPr_def_12) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_408,c_421]) ).
tcf(c_1789,plain,
( ~ iPr_def_11
| ( inverse(sk_c4) != sk_c8 )
| ( multiply(sk_c8,iPr_def_17) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_413,c_421]) ).
tcf(c_1790,plain,
( ~ iPr_def_11
| ( inverse(sk_c2) != sk_c8 )
| ( multiply(sk_c8,iPr_def_19) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_415,c_421]) ).
tcf(c_1811,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_15 )
| ( multiply(sk_c8,iPr_def_17) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_1789,c_411]) ).
tcf(c_2062,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_408,c_85]) ).
tcf(c_2063,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_409,c_85]) ).
tcf(c_2064,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c5,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_2065,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_413,c_85]) ).
tcf(c_2066,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_418,c_85]) ).
tcf(c_2068,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c8,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2070,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2073,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_848,c_85]) ).
tcf(c_2074,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_849,c_85]) ).
tcf(c_2075,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_850,c_85]) ).
tcf(c_2076,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_851,c_85]) ).
tcf(c_2080,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2076,c_83]) ).
tcf(c_2081,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2075,c_83]) ).
tcf(c_2082,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2074,c_83]) ).
tcf(c_2083,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2073,c_83]) ).
tcf(c_2178,plain,
multiply(iPr_def_16,iPr_def_19) = sk_c8,
inference(superposition,[status(thm)],[c_415,c_2080]) ).
tcf(c_2209,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_418,c_2081]) ).
tcf(c_2251,plain,
multiply(iPr_def_15,iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_413,c_2082]) ).
tcf(c_2609,plain,
multiply(iPr_def_14,iPr_def_18) = sk_c5,
inference(superposition,[status(thm)],[c_414,c_2083]) ).
tcf(c_2610,plain,
multiply(iPr_def_14,iPr_def_20) = sk_c3,
inference(superposition,[status(thm)],[c_416,c_2083]) ).
tcf(c_2659,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_18,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2609,c_85]) ).
tcf(c_2661,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_20,X0)) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2610,c_85]) ).
tcf(c_9193,plain,
multiply(sk_c7,iPr_def_20) = multiply(iPr_def_12,sk_c3),
inference(superposition,[status(thm)],[c_416,c_2062]) ).
tcf(c_9653,plain,
( ~ iPr_def_11
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(iPr_def_18,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_2064,c_421]) ).
tcf(c_9936,plain,
multiply(sk_c1,iPr_def_12) = multiply(iPr_def_22,sk_c8),
inference(superposition,[status(thm)],[c_408,c_2066]) ).
tcf(c_9937,plain,
multiply(sk_c1,iPr_def_13) = multiply(iPr_def_22,sk_c6),
inference(superposition,[status(thm)],[c_409,c_2066]) ).
tcf(c_12695,plain,
( ( iPr_def_20 = iPr_def_21 )
| ~ iPr_def_10
| ( sk_c8 != identity )
| ( inverse(inverse(iPr_def_18)) != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_892,c_1591]) ).
tcf(c_12696,plain,
( ( sk_c8 = iPr_def_22 )
| ~ iPr_def_10
| ( sk_c8 != identity )
| ( inverse(inverse(iPr_def_18)) != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_445,c_1591]) ).
tcf(c_12775,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2070,c_83]) ).
tcf(c_12801,plain,
multiply(inverse(sk_c7),iPr_def_13) = sk_c6,
inference(superposition,[status(thm)],[c_409,c_12775]) ).
tcf(c_12803,plain,
multiply(inverse(sk_c4),iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_413,c_12775]) ).
tcf(c_12804,plain,
multiply(inverse(sk_c1),iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_418,c_12775]) ).
tcf(c_12806,plain,
multiply(inverse(sk_c2),iPr_def_19) = sk_c8,
inference(superposition,[status(thm)],[c_415,c_12775]) ).
tcf(c_12807,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_12775]) ).
tcf(c_12808,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_12775]) ).
tcf(c_12865,plain,
multiply(inverse(iPr_def_16),identity) = sk_c2,
inference(superposition,[status(thm)],[c_851,c_12775]) ).
tcf(c_12947,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2083,c_12775]) ).
tcf(c_12953,plain,
multiply(inverse(iPr_def_16),sk_c8) = iPr_def_19,
inference(superposition,[status(thm)],[c_2178,c_12775]) ).
tcf(c_12955,plain,
multiply(inverse(iPr_def_21),sk_c7) = iPr_def_22,
inference(superposition,[status(thm)],[c_2209,c_12775]) ).
tcf(c_12964,plain,
multiply(inverse(iPr_def_15),sk_c8) = iPr_def_17,
inference(superposition,[status(thm)],[c_2251,c_12775]) ).
tcf(c_13024,plain,
multiply(inverse(sk_c1),multiply(iPr_def_22,sk_c6)) = iPr_def_13,
inference(superposition,[status(thm)],[c_9937,c_12775]) ).
tcf(c_13031,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_12775,c_12775]) ).
tcf(c_13949,plain,
( ~ iPr_def_11
| ( inverse(inverse(identity)) != sk_c8 )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_12807,c_421]) ).
tcf(c_13987,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_12808,c_13031]) ).
tcf(c_14000,plain,
multiply(sk_c7,sk_c8) = multiply(iPr_def_12,identity),
inference(superposition,[status(thm)],[c_13987,c_2062]) ).
tcf(c_14002,plain,
multiply(sk_c7,sk_c6) = multiply(iPr_def_13,identity),
inference(superposition,[status(thm)],[c_13987,c_2063]) ).
tcf(c_14003,plain,
multiply(sk_c5,identity) = multiply(iPr_def_14,iPr_def_18),
inference(superposition,[status(thm)],[c_13987,c_2659]) ).
tcf(c_14004,plain,
multiply(sk_c8,sk_c5) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_13987,c_2064]) ).
tcf(c_14009,plain,
multiply(sk_c1,sk_c7) = multiply(iPr_def_22,identity),
inference(superposition,[status(thm)],[c_13987,c_2066]) ).
tcf(c_14010,plain,
multiply(sk_c3,identity) = multiply(iPr_def_14,iPr_def_20),
inference(superposition,[status(thm)],[c_13987,c_2661]) ).
tcf(c_14020,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_13987,c_12807]) ).
tcf(c_14023,plain,
multiply(sk_c3,identity) = sk_c3,
inference(light_normalisation,[status(thm)],[c_14010,c_2610]) ).
tcf(c_14024,plain,
multiply(iPr_def_22,identity) = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_14009,c_418]) ).
tcf(c_14027,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_14004,c_414]) ).
tcf(c_14028,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_14003,c_2609]) ).
tcf(c_14029,plain,
multiply(iPr_def_13,identity) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_14002,c_409]) ).
tcf(c_14030,plain,
multiply(iPr_def_12,identity) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_14000,c_408]) ).
tcf(c_14036,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( sk_c7 != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_1590,c_14020]) ).
tcf(c_14519,plain,
multiply(sk_c8,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_12947,c_84]) ).
tcf(c_14523,plain,
! [X0: $i] : multiply(sk_c8,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_12947,c_12775]) ).
tcf(c_14524,plain,
multiply(sk_c8,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_12947,c_13987]) ).
tcf(c_14561,plain,
multiply(sk_c2,identity) = multiply(iPr_def_19,iPr_def_14),
inference(superposition,[status(thm)],[c_14519,c_2068]) ).
tcf(c_14562,plain,
multiply(sk_c4,identity) = multiply(iPr_def_17,iPr_def_14),
inference(superposition,[status(thm)],[c_14519,c_2065]) ).
tcf(c_14563,plain,
multiply(sk_c7,identity) = multiply(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_14519,c_2062]) ).
tcf(c_14564,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(superposition,[status(thm)],[c_14519,c_2083]) ).
tcf(c_14630,plain,
inverse(iPr_def_14) = sk_c8,
inference(demodulation,[status(thm)],[c_14524,c_13987]) ).
tcf(c_14883,plain,
multiply(sk_c8,sk_c5) = iPr_def_18,
inference(superposition,[status(thm)],[c_2609,c_14523]) ).
tcf(c_14884,plain,
multiply(sk_c8,sk_c3) = iPr_def_20,
inference(superposition,[status(thm)],[c_2610,c_14523]) ).
tcf(c_16105,plain,
multiply(iPr_def_19,iPr_def_14) = sk_c2,
inference(demodulation,[status(thm)],[c_14561,c_13987]) ).
tcf(c_16113,plain,
multiply(iPr_def_17,iPr_def_14) = sk_c4,
inference(demodulation,[status(thm)],[c_14562,c_13987]) ).
tcf(c_16288,plain,
multiply(iPr_def_12,iPr_def_14) = sk_c7,
inference(demodulation,[status(thm)],[c_14563,c_13987]) ).
tcf(c_16289,plain,
multiply(inverse(iPr_def_12),sk_c7) = iPr_def_14,
inference(superposition,[status(thm)],[c_16288,c_12775]) ).
tcf(c_16310,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_14 )
| ( inverse(inverse(iPr_def_12)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_16289,c_422]) ).
tcf(c_16366,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_16310,c_16289,c_16288,c_16113,c_16105,c_14884,c_14883,c_14630,c_14564,c_14524,c_14519,c_14036,c_14030,c_14029,c_14028,c_14027,c_14024,c_14023,c_14010,c_14009,c_14003,c_14002,c_14000,c_14020,c_13949,c_13024,c_12964,c_12955,c_12953,c_12865,c_12806,c_12804,c_12803,c_12801,c_12695,c_12696,c_9936,c_9653,c_9193,c_1811,c_1790,c_1788,c_1604,c_1589,c_848,c_452,c_451,c_450,c_449,c_448,c_447,c_446,c_445,c_444,c_443,c_442,c_441,c_440,c_439,c_438,c_437,c_436,c_435,c_434,c_433,c_432,c_431,c_430,c_429,c_428,c_427,c_426,c_425,c_424,c_423,c_419,c_417,c_412,c_411,c_410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP328-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 14:23:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 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...
% 3.71/1.19 % SZS status Started for theBenchmark.p
% 3.71/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.71/1.19
% 3.71/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.71/1.19
% 3.71/1.19 % ------ iProver source info
% 3.71/1.19
% 3.71/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.71/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.71/1.19 % git: non_committed_changes: false
% 3.71/1.19
% 3.71/1.19 % ------ Parsing...% successful
% 3.71/1.19
% 3.71/1.19
% 3.71/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.71/1.19
% 3.71/1.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.71/1.19
% 3.71/1.19 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.71/1.19
% 3.71/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.71/1.19 % ------ Proving...
% 3.71/1.19 % ------ Problem Properties
% 3.71/1.19
% 3.71/1.19 %
% 3.71/1.19 % clauses 47
% 3.71/1.19 % conjectures 33
% 3.71/1.19 % EPR 31
% 3.71/1.19 % Horn 16
% 3.71/1.19 % unary 14
% 3.71/1.19 % binary 30
% 3.71/1.19 % lits 85
% 3.71/1.19 % lits eq 81
% 3.71/1.19 % fd_pure 0
% 3.71/1.19 % fd_pseudo 0
% 3.71/1.19 % fd_cond 0
% 3.71/1.19 % fd_pseudo_cond 0
% 3.71/1.19 % AC symbols 0
% 3.71/1.19
% 3.71/1.19 % ------ Schedule dynamic 5 is on
% 3.71/1.19
% 3.71/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.71/1.19
% 3.71/1.19
% 3.71/1.19 % ------
% 3.71/1.19 % Current options:
% 3.71/1.19 % ------
% 3.71/1.19
% 3.71/1.19
% 3.71/1.19 %
% 3.71/1.19
% 3.71/1.19 % ------ Proving...
% 3.71/1.19 %
% 3.71/1.19
% 3.71/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.71/1.19
% 3.71/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.71/1.19
% 3.71/1.19
%------------------------------------------------------------------------------