TSTP Solution File: GRP669-1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : GRP669-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 : Tue May 7 07:45:13 EDT 2024
% Result : Unsatisfiable 15.63s 4.09s
% Output : Refutation 15.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 101 ( 53 unt; 7 typ; 0 def)
% Number of atoms : 190 ( 189 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 892 ( 136 ~; 96 |; 0 &; 660 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 139 ( 0 ^ 139 !; 0 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
thf(mult_type,type,
mult: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(ld_type,type,
ld: $i > $i > $i ).
thf(rd_type,type,
rd: $i > $i > $i ).
thf(unit_type,type,
unit: $i ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[19]) ).
thf(1,negated_conjecture,
( ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) )
!= ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(12,plain,
( ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) )
!= ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,plain,
( ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) )
!= ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b ) ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
( ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b )
!= ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(291,plain,
! [B: $i,A: $i] :
( ( A
!= ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b ) ) ),
inference(paramod_ordered,[status(thm)],[20,14]) ).
thf(316,plain,
! [A: $i] :
( ( ( rd @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) @ A )
!= ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) )
| ( A != b ) ),
inference(simp,[status(thm)],[291]) ).
thf(384,plain,
( ( rd @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) @ b )
!= ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) ),
inference(simp,[status(thm)],[316]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A )
= ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(1237,plain,
( ( rd @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) @ b )
!= ( mult @ ( mult @ a @ b ) @ ( mult @ c @ a ) ) ),
inference(rewrite,[status(thm)],[384,32]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[17]) ).
thf(305,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ld @ C @ A )
= D )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,18]) ).
thf(306,plain,
! [B: $i,A: $i] :
( ( ld @ ( rd @ A @ B ) @ A )
= B ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( rd @ E @ F )),bind(D,$thf( F ))]]) ).
thf(379,plain,
! [B: $i,A: $i] :
( ( ld @ ( rd @ A @ B ) @ A )
= B ),
inference(simp,[status(thm)],[306]) ).
thf(6,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
thf(23,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(lifteq,[status(thm)],[23]) ).
thf(53,plain,
( ( ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a )
!= ( mult @ a @ b ) )
| ( ( mult @ c @ ( mult @ a @ b ) )
!= b ) ),
inference(simp,[status(thm)],[14]) ).
thf(122,plain,
! [A: $i] :
( ( ( mult @ A @ a )
!= ( mult @ a @ b ) )
| ( ( mult @ c @ ( mult @ a @ b ) )
!= b )
| ( ( mult @ A @ unit )
!= ( mult @ a @ ( mult @ b @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,53]) ).
thf(156,plain,
! [A: $i] :
( ( A != a )
| ( b != a )
| ( ( mult @ c @ ( mult @ a @ b ) )
!= b )
| ( A != a )
| ( ( mult @ b @ c )
!= unit ) ),
inference(simp,[status(thm)],[122]) ).
thf(194,plain,
( ( b != a )
| ( ( mult @ c @ ( mult @ a @ b ) )
!= b )
| ( ( mult @ b @ c )
!= unit ) ),
inference(simp,[status(thm)],[156]) ).
thf(209,plain,
! [A: $i] :
( ( b != a )
| ( A != b )
| ( ( mult @ b @ c )
!= unit )
| ( ( mult @ A @ unit )
!= ( mult @ c @ ( mult @ a @ b ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,194]) ).
thf(223,plain,
( ( b != a )
| ( ( mult @ b @ c )
!= unit )
| ( c != b )
| ( ( mult @ a @ b )
!= unit ) ),
inference(simp,[status(thm)],[209]) ).
thf(243,plain,
( ( b != a )
| ( c != b )
| ( ( mult @ a @ b )
!= unit )
| ( ( mult @ b @ c )
!= ( mult @ a @ b ) )
| ( unit != unit ) ),
inference(eqfactor_ordered,[status(thm)],[223]) ).
thf(247,plain,
( ( b != a )
| ( c != b )
| ( ( mult @ a @ b )
!= unit )
| ( b != a )
| ( c != b ) ),
inference(simp,[status(thm)],[243]) ).
thf(258,plain,
( ( b != a )
| ( c != b )
| ( ( mult @ a @ b )
!= unit ) ),
inference(simp,[status(thm)],[247]) ).
thf(392,plain,
! [A: $i] :
( ( b != a )
| ( c != b )
| ( A != unit )
| ( ( mult @ A @ unit )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[24,258]) ).
thf(397,plain,
( ( b != a )
| ( c != b )
| ( unit != a )
| ( unit != b ) ),
inference(simp,[status(thm)],[392]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[15]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B
!= ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ b ) ) ),
inference(paramod_ordered,[status(thm)],[16,14]) ).
thf(96,plain,
! [A: $i] :
( ( A
!= ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) )
| ( ( ld @ A @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) )
!= b ) ),
inference(simp,[status(thm)],[58]) ).
thf(120,plain,
( ( ld @ ( mult @ ( mult @ a @ ( mult @ b @ c ) ) @ a ) @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) )
!= b ),
inference(simp,[status(thm)],[96]) ).
thf(1106,plain,
( ( ld @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ a ) ) @ ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) )
!= b ),
inference(rewrite,[status(thm)],[120,32]) ).
thf(7,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
thf(25,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(lifteq,[status(thm)],[25]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[21]) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ A @ C )
= B )
| ( ( mult @ unit @ A )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[26,22]) ).
thf(420,plain,
! [A: $i] :
( ( rd @ A @ A )
= unit ),
inference(pattern_uni,[status(thm)],[419:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(210,plain,
! [A: $i] :
( ( b != a )
| ( ( mult @ c @ ( mult @ a @ b ) )
!= b )
| ( A != unit )
| ( ( mult @ A @ unit )
!= ( mult @ b @ c ) ) ),
inference(paramod_ordered,[status(thm)],[24,194]) ).
thf(226,plain,
( ( b != a )
| ( ( mult @ c @ ( mult @ a @ b ) )
!= b )
| ( unit != b )
| ( unit != c ) ),
inference(simp,[status(thm)],[210]) ).
thf(1041,plain,
! [A: $i] :
( ( b != a )
| ( ( mult @ c @ A )
!= b )
| ( unit != b )
| ( unit != c )
| ( ( mult @ A @ unit )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[24,226]) ).
thf(1051,plain,
! [A: $i] :
( ( b != a )
| ( ( mult @ c @ A )
!= b )
| ( unit != b )
| ( unit != c )
| ( A != a )
| ( unit != b ) ),
inference(simp,[status(thm)],[1041]) ).
thf(1078,plain,
( ( b != a )
| ( ( mult @ c @ a )
!= b )
| ( unit != b )
| ( unit != c ) ),
inference(simp,[status(thm)],[1051]) ).
thf(1086,plain,
! [A: $i] :
( ( b != a )
| ( A != b )
| ( unit != b )
| ( unit != c )
| ( ( mult @ unit @ A )
!= ( mult @ c @ a ) ) ),
inference(paramod_ordered,[status(thm)],[26,1078]) ).
thf(1093,plain,
( ( b != a )
| ( unit != b )
| ( unit != c )
| ( unit != c )
| ( b != a ) ),
inference(simp,[status(thm)],[1086]) ).
thf(1102,plain,
( ( b != a )
| ( unit != b )
| ( unit != c ) ),
inference(simp,[status(thm)],[1093]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ A ) @ C )
= ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( mult @ ( mult @ A @ B ) @ D )
= ( mult @ B @ ( mult @ C @ ( mult @ B @ D ) ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[26,28]) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( mult @ ( mult @ A @ unit ) @ B )
= ( mult @ unit @ ( mult @ A @ ( mult @ unit @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[474:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(512,plain,
! [B: $i,A: $i] :
( ( mult @ ( mult @ A @ unit ) @ B )
= ( mult @ unit @ ( mult @ A @ ( mult @ unit @ B ) ) ) ),
inference(simp,[status(thm)],[475]) ).
thf(1737,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ unit @ B ) )
= ( mult @ A @ B ) ),
inference(rewrite,[status(thm)],[512,24,26]) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( b != a )
| ( c != b )
| ( B != unit )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[16,258]) ).
thf(401,plain,
! [A: $i] :
( ( b != a )
| ( c != b )
| ( A != a )
| ( ( ld @ A @ unit )
!= b ) ),
inference(simp,[status(thm)],[394]) ).
thf(404,plain,
( ( b != a )
| ( c != b )
| ( ( ld @ a @ unit )
!= b ) ),
inference(simp,[status(thm)],[401]) ).
thf(215,plain,
! [A: $i] :
( ( b != a )
| ( A != b )
| ( ( mult @ b @ c )
!= unit )
| ( ( mult @ unit @ A )
!= ( mult @ c @ ( mult @ a @ b ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,194]) ).
thf(228,plain,
( ( b != a )
| ( ( mult @ b @ c )
!= unit )
| ( unit != c )
| ( ( mult @ a @ b )
!= b ) ),
inference(simp,[status(thm)],[215]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ A ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ C @ unit ) ) ),
inference(paramod_ordered,[status(thm)],[16,24]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A != C )
| ( ( ld @ A @ B )
!= unit ) ),
inference(simp,[status(thm)],[39]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( ld @ B @ A )
!= unit ) ),
inference(simp,[status(thm)],[45]) ).
thf(393,plain,
! [B: $i,A: $i] :
( ( b != a )
| ( c != b )
| ( A != unit )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[20,258]) ).
thf(399,plain,
! [A: $i] :
( ( b != a )
| ( c != b )
| ( ( rd @ unit @ A )
!= a )
| ( A != b ) ),
inference(simp,[status(thm)],[393]) ).
thf(406,plain,
( ( b != a )
| ( c != b )
| ( ( rd @ unit @ b )
!= a ) ),
inference(simp,[status(thm)],[399]) ).
thf(287,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ C @ unit ) ) ),
inference(paramod_ordered,[status(thm)],[20,24]) ).
thf(288,plain,
! [A: $i] :
( ( rd @ A @ unit )
= A ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( D )),bind(B,$thf( unit )),bind(C,$thf( rd @ D @ unit ))]]) ).
thf(377,plain,
! [A: $i] :
( ( rd @ A @ unit )
= A ),
inference(simp,[status(thm)],[288]) ).
thf(434,plain,
( ( mult @ a @ ( mult @ ( mult @ b @ c ) @ ( mult @ a @ b ) ) )
!= ( mult @ ( mult @ a @ b ) @ ( mult @ c @ ( mult @ a @ b ) ) ) ),
inference(rewrite,[status(thm)],[14,28]) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ld @ B @ A )
= C )
| ( ( mult @ A @ unit )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[24,18]) ).
thf(262,plain,
! [A: $i] :
( ( ld @ A @ A )
= unit ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( unit ))]]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
= ( mult @ A @ ( mult @ B @ ( mult @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( rd @ B @ D )
= C )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16,22]) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( rd @ B @ ( ld @ A @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[417:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( ld @ E @ F ))]]) ).
thf(422,plain,
! [B: $i,A: $i] :
( ( rd @ B @ ( ld @ A @ B ) )
= A ),
inference(simp,[status(thm)],[418]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ unit @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16,26]) ).
thf(42,plain,
! [A: $i] :
( ( ld @ unit @ A )
= A ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( unit )),bind(B,$thf( E )),bind(C,$thf( ld @ unit @ E ))]]) ).
thf(47,plain,
! [A: $i] :
( ( ld @ unit @ A )
= A ),
inference(simp,[status(thm)],[42]) ).
thf(3246,plain,
$false,
inference(cvc4,[status(thm)],[1237,379,397,1106,420,1102,194,18,1737,404,24,25,20,228,29,28,21,33,17,32,34,22,27,12,49,406,377,434,16,31,26,258,23,262,30,19,422,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GRP669-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : run_Leo-III %s %d
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Mon May 6 16:12:24 EDT 2024
% 0.10/0.28 % CPUTime :
% 0.69/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.97/0.80 % [INFO] Parsing done (108ms).
% 0.97/0.80 % [INFO] Running in sequential loop mode.
% 1.43/1.01 % [INFO] eprover registered as external prover.
% 1.43/1.01 % [INFO] cvc4 registered as external prover.
% 1.43/1.02 % [INFO] Scanning for conjecture ...
% 1.59/1.07 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.59/1.09 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.59/1.11 % [INFO] Problem is propositional (TPTP CNF).
% 1.59/1.11 % [INFO] Type checking passed.
% 1.59/1.11 % [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 ...
% 15.63/4.08 % External prover 'cvc4' found a proof!
% 15.63/4.08 % [INFO] Killing All external provers ...
% 15.63/4.08 % Time passed: 3684ms (effective reasoning time: 3275ms)
% 15.63/4.08 % Solved by 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)>
% 15.63/4.08 % Axioms used in derivation (10): c05, c08, c01, c03, c06, c02, c07, c10, c09, c04
% 15.63/4.08 % No. of inferences in proof: 94
% 15.63/4.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3684 ms resp. 3275 ms w/o parsing
% 15.63/4.15 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.63/4.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------