TSTP Solution File: GRP118-1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : GRP118-1 : TPTP v8.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 21:03:10 EDT 2024
% Result : Unsatisfiable 119.28s 22.55s
% Output : Refutation 119.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 7
% Syntax : Number of formulae : 75 ( 48 unt; 5 typ; 0 def)
% Number of atoms : 94 ( 93 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1019 ( 49 ~; 24 |; 0 &; 946 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 127 ( 0 ^ 127 !; 0 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(identity_type,type,
identity: $i ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
= B ),
inference(lifteq,[status(thm)],[6]) ).
thf(17,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ D @ ( multiply @ ( multiply @ D @ ( multiply @ ( multiply @ D @ E ) @ F ) ) @ B ) )
= E )
| ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
!= ( multiply @ identity @ ( multiply @ F @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ C ) @ ( multiply @ identity @ C ) ) ) ) ) @ C ) )
= B ),
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( identity )),bind(B,$thf( N )),bind(C,$thf( multiply @ identity @ N )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( multiply @ identity @ ( multiply @ ( multiply @ identity @ N ) @ ( multiply @ identity @ N ) ) ))]]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ C ) @ ( multiply @ identity @ C ) ) ) ) ) @ C ) )
= B ),
inference(simp,[status(thm)],[18]) ).
thf(194,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ D @ ( multiply @ B @ F ) )
= E )
| ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
!= ( multiply @ D @ ( multiply @ ( multiply @ D @ E ) @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ F ) @ ( multiply @ identity @ F ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,29]) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( multiply @ identity @ L )),bind(D,$thf( I )),bind(E,$thf( multiply @ ( multiply @ I @ J ) @ ( multiply @ identity @ L ) )),bind(F,$thf( L ))]]) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(15,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ D @ ( multiply @ B @ ( multiply @ identity @ ( multiply @ F @ F ) ) ) )
= E )
| ( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) )
!= ( multiply @ D @ ( multiply @ ( multiply @ D @ E ) @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,7]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ B @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ C @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) ) ) )
= ( multiply @ ( multiply @ A @ B ) @ C ) ),
inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( N )),bind(D,$thf( I )),bind(E,$thf( multiply @ ( multiply @ I @ J ) @ N )),bind(F,$thf( multiply @ identity @ ( multiply @ N @ N ) ))]]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ B @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ C @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) ) ) )
= ( multiply @ ( multiply @ A @ B ) @ C ) ),
inference(simp,[status(thm)],[16]) ).
thf(392,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ D @ ( multiply @ ( multiply @ ( multiply @ A @ B ) @ C ) @ F ) )
= E )
| ( ( multiply @ A @ ( multiply @ B @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ C @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) ) ) )
!= ( multiply @ D @ ( multiply @ ( multiply @ D @ E ) @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ F ) @ ( multiply @ identity @ F ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,29]) ).
thf(393,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ ( multiply @ A @ ( multiply @ A @ B ) ) @ C ) @ ( multiply @ C @ C ) ) )
= B ),
inference(pattern_uni,[status(thm)],[392:[bind(A,$thf( G )),bind(B,$thf( multiply @ G @ H )),bind(C,$thf( J )),bind(D,$thf( G )),bind(E,$thf( H )),bind(F,$thf( multiply @ J @ J ))]]) ).
thf(737,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ ( multiply @ A @ ( multiply @ A @ B ) ) @ C ) @ ( multiply @ C @ C ) ) )
= B ),
inference(simp,[status(thm)],[393]) ).
thf(2204,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ D @ ( multiply @ A @ ( multiply @ B @ C ) ) )
= E )
| ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
!= ( multiply @ ( multiply @ ( multiply @ D @ ( multiply @ D @ E ) ) @ F ) @ ( multiply @ F @ F ) ) ) ),
inference(paramod_ordered,[status(thm)],[290,737]) ).
thf(2205,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ A @ B ) ) @ ( multiply @ identity @ identity ) ) )
= B ),
inference(pattern_uni,[status(thm)],[2204:[bind(A,$thf( multiply @ I @ ( multiply @ I @ J ) )),bind(B,$thf( identity )),bind(C,$thf( identity )),bind(D,$thf( I )),bind(E,$thf( J )),bind(F,$thf( identity ))]]) ).
thf(2411,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ A @ ( multiply @ A @ B ) ) @ ( multiply @ identity @ identity ) ) )
= B ),
inference(simp,[status(thm)],[2205]) ).
thf(2804,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) ) )
= B ),
inference(rewrite,[status(thm)],[2411,290]) ).
thf(2888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ C @ ( multiply @ C @ ( multiply @ B @ identity ) ) )
= D )
| ( ( multiply @ A @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) ) )
!= ( multiply @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2804,2804]) ).
thf(2889,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) )
= ( multiply @ A @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) ),
inference(pattern_uni,[status(thm)],[2888:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( I )),bind(D,$thf( multiply @ I @ ( multiply @ ( multiply @ I @ J ) @ identity ) ))]]) ).
thf(3161,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) )
= ( multiply @ A @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) ),
inference(simp,[status(thm)],[2889]) ).
thf(3529,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) )
= B ),
inference(rewrite,[status(thm)],[2804,3161]) ).
thf(4845,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ D @ ( multiply @ D @ ( multiply @ A @ ( multiply @ B @ C ) ) ) )
= E )
| ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
!= ( multiply @ D @ ( multiply @ E @ identity ) ) ) ),
inference(paramod_ordered,[status(thm)],[290,3529]) ).
thf(4846,plain,
! [B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ ( multiply @ A @ B ) @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) )
= identity ),
inference(pattern_uni,[status(thm)],[4845:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( identity )),bind(D,$thf( multiply @ F @ G )),bind(E,$thf( identity ))]]) ).
thf(5102,plain,
! [B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ ( multiply @ A @ B ) @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) )
= identity ),
inference(simp,[status(thm)],[4846]) ).
thf(6632,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ ( multiply @ D @ E ) @ ( multiply @ A @ ( multiply @ B @ C ) ) )
= identity )
| ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
!= ( multiply @ ( multiply @ D @ E ) @ ( multiply @ D @ ( multiply @ E @ identity ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[290,5102]) ).
thf(6633,plain,
! [A: $i] :
( ( multiply @ ( multiply @ identity @ A ) @ ( multiply @ identity @ ( multiply @ A @ ( multiply @ A @ identity ) ) ) )
= identity ),
inference(pattern_uni,[status(thm)],[6632:[bind(A,$thf( identity )),bind(B,$thf( F )),bind(C,$thf( multiply @ F @ identity )),bind(D,$thf( identity )),bind(E,$thf( F ))]]) ).
thf(7091,plain,
! [A: $i] :
( ( multiply @ ( multiply @ identity @ A ) @ ( multiply @ identity @ ( multiply @ A @ ( multiply @ A @ identity ) ) ) )
= identity ),
inference(simp,[status(thm)],[6633]) ).
thf(7601,plain,
! [A: $i] :
( ( multiply @ identity @ ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) ) )
= identity ),
inference(rewrite,[status(thm)],[7091,290]) ).
thf(7740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ B @ ( multiply @ ( multiply @ identity @ D ) @ ( multiply @ D @ D ) ) )
= C )
| ( ( multiply @ identity @ ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) ) )
!= ( multiply @ B @ ( multiply @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[7601,737]) ).
thf(7741,plain,
! [A: $i] :
( ( multiply @ identity @ ( multiply @ ( multiply @ identity @ A ) @ ( multiply @ A @ A ) ) )
= ( multiply @ identity @ ( multiply @ identity @ identity ) ) ),
inference(pattern_uni,[status(thm)],[7740:[bind(A,$thf( identity )),bind(B,$thf( identity )),bind(C,$thf( multiply @ identity @ ( multiply @ identity @ identity ) )),bind(D,$thf( D ))]]) ).
thf(8183,plain,
! [A: $i] :
( ( multiply @ identity @ ( multiply @ ( multiply @ identity @ A ) @ ( multiply @ A @ A ) ) )
= ( multiply @ identity @ ( multiply @ identity @ identity ) ) ),
inference(simp,[status(thm)],[7741]) ).
thf(9542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ identity @ ( multiply @ A @ ( multiply @ B @ C ) ) )
= ( multiply @ identity @ ( multiply @ identity @ identity ) ) )
| ( ( multiply @ ( multiply @ A @ B ) @ ( multiply @ identity @ C ) )
!= ( multiply @ ( multiply @ identity @ D ) @ ( multiply @ D @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[290,8183]) ).
thf(9543,plain,
( ( multiply @ identity @ ( multiply @ identity @ ( multiply @ identity @ identity ) ) )
= ( multiply @ identity @ ( multiply @ identity @ identity ) ) ),
inference(pattern_uni,[status(thm)],[9542:[bind(A,$thf( identity )),bind(B,$thf( identity )),bind(C,$thf( identity )),bind(D,$thf( identity ))]]) ).
thf(11767,plain,
! [A: $i] :
( ( ( multiply @ identity @ ( multiply @ identity @ ( multiply @ identity @ identity ) ) )
= identity )
| ( ( multiply @ identity @ ( multiply @ identity @ ( multiply @ identity @ identity ) ) )
!= ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9543,7601]) ).
thf(11768,plain,
( ( multiply @ identity @ ( multiply @ identity @ ( multiply @ identity @ identity ) ) )
= identity ),
inference(pattern_uni,[status(thm)],[11767:[bind(A,$thf( identity ))]]) ).
thf(12692,plain,
( ( multiply @ identity @ ( multiply @ identity @ identity ) )
= identity ),
inference(rewrite,[status(thm)],[11768,9543]) ).
thf(12693,plain,
( ( multiply @ identity @ identity )
= identity ),
inference(rewrite,[status(thm)],[9543,12692]) ).
thf(13832,plain,
! [B: $i,A: $i] :
( ( ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) )
= B )
| ( ( multiply @ identity @ identity )
!= ( multiply @ B @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[12693,3529]) ).
thf(13833,plain,
! [A: $i] :
( ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) )
= identity ),
inference(pattern_uni,[status(thm)],[13832:[bind(A,$thf( A )),bind(B,$thf( identity ))]]) ).
thf(20270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ B @ identity )
= C )
| ( ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ identity ) ) )
!= ( multiply @ B @ ( multiply @ B @ ( multiply @ C @ identity ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13833,3529]) ).
thf(20271,plain,
! [A: $i] :
( ( multiply @ A @ identity )
= A ),
inference(pattern_uni,[status(thm)],[20270:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(21052,plain,
! [A: $i] :
( ( multiply @ A @ ( multiply @ A @ A ) )
= identity ),
inference(rewrite,[status(thm)],[13833,20271]) ).
thf(1,negated_conjecture,
( ( multiply @ ( multiply @ a @ b ) @ c )
!= ( multiply @ a @ ( multiply @ b @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_order3) ).
thf(3,plain,
( ( multiply @ ( multiply @ a @ b ) @ c )
!= ( multiply @ a @ ( multiply @ b @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,plain,
( ( multiply @ ( multiply @ a @ b ) @ c )
!= ( multiply @ a @ ( multiply @ b @ c ) ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( multiply @ ( multiply @ a @ b ) @ c )
!= ( multiply @ a @ ( multiply @ b @ c ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(385,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ ( multiply @ B @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ C @ C ) ) @ ( multiply @ identity @ ( multiply @ C @ C ) ) ) ) ) )
!= ( multiply @ a @ ( multiply @ b @ c ) ) )
| ( ( multiply @ ( multiply @ A @ B ) @ C )
!= ( multiply @ ( multiply @ a @ b ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[28,5]) ).
thf(386,plain,
( ( multiply @ a @ ( multiply @ b @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ c @ c ) ) @ ( multiply @ identity @ ( multiply @ c @ c ) ) ) ) ) )
!= ( multiply @ a @ ( multiply @ b @ c ) ) ),
inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( a )),bind(B,$thf( b )),bind(C,$thf( c ))]]) ).
thf(775,plain,
( ( a != a )
| ( ( multiply @ b @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ c @ c ) ) @ ( multiply @ identity @ ( multiply @ c @ c ) ) ) ) )
!= ( multiply @ b @ c ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(898,plain,
( ( multiply @ b @ ( multiply @ identity @ ( multiply @ ( multiply @ identity @ ( multiply @ c @ c ) ) @ ( multiply @ identity @ ( multiply @ c @ c ) ) ) ) )
!= ( multiply @ b @ c ) ),
inference(simp,[status(thm)],[775]) ).
thf(1249,plain,
( ( multiply @ b @ ( multiply @ identity @ ( multiply @ identity @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) ) ) )
!= ( multiply @ b @ c ) ),
inference(rewrite,[status(thm)],[898,290]) ).
thf(2838,plain,
! [B: $i,A: $i] :
( ( ( multiply @ b @ B )
!= ( multiply @ b @ c ) )
| ( ( multiply @ A @ ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) ) )
!= ( multiply @ identity @ ( multiply @ identity @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2804,1249]) ).
thf(3080,plain,
! [B: $i,A: $i] :
( ( b != b )
| ( B != c )
| ( A != identity )
| ( ( multiply @ A @ ( multiply @ ( multiply @ A @ B ) @ identity ) )
!= ( multiply @ identity @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) ) ) ),
inference(simp,[status(thm)],[2838]) ).
thf(3122,plain,
( ( multiply @ identity @ ( multiply @ ( multiply @ identity @ c ) @ identity ) )
!= ( multiply @ identity @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) ) ),
inference(simp,[status(thm)],[3080]) ).
thf(3528,plain,
( ( multiply @ identity @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) )
!= ( multiply @ identity @ ( multiply @ identity @ ( multiply @ c @ identity ) ) ) ),
inference(rewrite,[status(thm)],[3122,3161]) ).
thf(4259,plain,
( ( identity != identity )
| ( ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) )
!= ( multiply @ identity @ ( multiply @ c @ identity ) ) ) ),
inference(simp,[status(thm)],[3528]) ).
thf(4339,plain,
( ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) )
!= ( multiply @ identity @ ( multiply @ c @ identity ) ) ),
inference(simp,[status(thm)],[4259]) ).
thf(4770,plain,
! [B: $i,A: $i] :
( ( B
!= ( multiply @ identity @ ( multiply @ c @ identity ) ) )
| ( ( multiply @ A @ ( multiply @ A @ ( multiply @ A @ ( multiply @ B @ identity ) ) ) )
!= ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[3529,4339]) ).
thf(5028,plain,
! [A: $i] :
( ( A
!= ( multiply @ c @ c ) )
| ( ( multiply @ A @ ( multiply @ A @ ( multiply @ ( multiply @ identity @ ( multiply @ c @ identity ) ) @ identity ) ) )
!= ( multiply @ c @ c ) ) ),
inference(simp,[status(thm)],[4770]) ).
thf(5261,plain,
( ( multiply @ ( multiply @ c @ c ) @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ ( multiply @ identity @ ( multiply @ c @ identity ) ) @ identity ) ) )
!= ( multiply @ c @ c ) ),
inference(simp,[status(thm)],[5028]) ).
thf(21061,plain,
( ( multiply @ ( multiply @ c @ c ) @ ( multiply @ ( multiply @ c @ c ) @ ( multiply @ identity @ ( multiply @ c @ identity ) ) ) )
!= ( multiply @ c @ c ) ),
inference(rewrite,[status(thm)],[5261,20271]) ).
thf(36953,plain,
( ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ ( multiply @ c @ ( multiply @ c @ identity ) ) ) )
!= ( multiply @ c @ c ) ),
inference(rewrite,[status(thm)],[21061,290]) ).
thf(36996,plain,
! [A: $i] :
( ( A
!= ( multiply @ c @ c ) )
| ( ( multiply @ A @ identity )
!= ( multiply @ ( multiply @ c @ c ) @ ( multiply @ c @ ( multiply @ c @ ( multiply @ c @ identity ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[20271,36953]) ).
thf(37052,plain,
( ( ( multiply @ c @ c )
!= ( multiply @ c @ c ) )
| ( ( multiply @ c @ ( multiply @ c @ ( multiply @ c @ identity ) ) )
!= identity ) ),
inference(simp,[status(thm)],[36996]) ).
thf(37235,plain,
( ( multiply @ c @ ( multiply @ c @ ( multiply @ c @ identity ) ) )
!= identity ),
inference(simp,[status(thm)],[37052]) ).
thf(39491,plain,
( ( multiply @ c @ ( multiply @ c @ c ) )
!= identity ),
inference(rewrite,[status(thm)],[37235,20271]) ).
thf(39500,plain,
! [A: $i] :
( ( multiply @ A @ ( multiply @ A @ A ) )
!= ( multiply @ c @ ( multiply @ c @ c ) ) ),
inference(paramod_ordered,[status(thm)],[21052,39491]) ).
thf(39501,plain,
$false,
inference(pattern_uni,[status(thm)],[39500:[bind(A,$thf( c ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP118-1 : TPTP v8.2.0. Released v1.2.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n007.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun May 19 04:19:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.14/0.97 % [INFO] Parsing done (93ms).
% 1.14/0.98 % [INFO] Running in sequential loop mode.
% 1.65/1.18 % [INFO] nitpick registered as external prover.
% 1.65/1.19 % [INFO] Scanning for conjecture ...
% 1.77/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.80/1.25 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.80/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 1.80/1.26 % [INFO] Type checking passed.
% 1.80/1.26 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 119.28/22.55 % [INFO] Killing All external provers ...
% 119.28/22.55 % Time passed: 22012ms (effective reasoning time: 21567ms)
% 119.28/22.55 % Axioms used in derivation (1): single_axiom
% 119.28/22.55 % No. of inferences in proof: 70
% 119.28/22.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 22012 ms resp. 21567 ms w/o parsing
% 119.28/22.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 119.28/22.59 % [INFO] Killing All external provers ...
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