TSTP Solution File: GRP670-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP670-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 : Fri May 19 11:15:05 EDT 2023
% Result : Unsatisfiable 201.82s 38.87s
% Output : Refutation 201.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 18
% Syntax : Number of formulae : 161 ( 68 unt; 8 typ; 0 def)
% Number of atoms : 278 ( 277 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1327 ( 200 ~; 125 |; 0 &;1002 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 199 ( 0 ^; 199 !; 0 ?; 199 :)
% 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(i_type,type,
i: $i > $i ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[26]) ).
thf(513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( mult @ ( i @ C ) @ A )
= D )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[19,27]) ).
thf(514,plain,
! [B: $i,A: $i] :
( ( mult @ ( i @ ( rd @ A @ B ) ) @ A )
= B ),
inference(pattern_uni,[status(thm)],[513:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( rd @ E @ F )),bind(D,$thf( F ))]]) ).
thf(563,plain,
! [B: $i,A: $i] :
( ( mult @ ( i @ ( rd @ A @ B ) ) @ A )
= B ),
inference(simp,[status(thm)],[514]) ).
thf(7,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
thf(24,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
inference(lifteq,[status(thm)],[24]) ).
thf(1,negated_conjecture,
( ( mult @ ( mult @ a @ b ) @ ( mult @ ( mult @ c @ b ) @ c ) )
!= ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(11,plain,
( ( mult @ ( mult @ a @ b ) @ ( mult @ ( mult @ c @ b ) @ c ) )
!= ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( mult @ ( mult @ a @ b ) @ ( mult @ ( mult @ c @ b ) @ c ) )
!= ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c ) ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( mult @ ( mult @ a @ b ) @ ( mult @ ( mult @ c @ b ) @ c ) )
!= ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(54,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ A )
!= ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c ) )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ c @ b ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(132,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) )
!= ( mult @ a @ b ) )
| ( A != c )
| ( ( mult @ c @ b )
!= unit )
| ( A != c ) ),
inference(simp,[status(thm)],[54]) ).
thf(144,plain,
( ( ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) )
!= ( mult @ a @ b ) )
| ( ( mult @ c @ b )
!= unit ) ),
inference(simp,[status(thm)],[132]) ).
thf(189,plain,
! [A: $i] :
( ( ( mult @ a @ A )
!= ( mult @ a @ b ) )
| ( ( mult @ c @ b )
!= unit )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ b @ c ) @ b ) ) ),
inference(paramod_ordered,[status(thm)],[25,144]) ).
thf(207,plain,
! [A: $i] :
( ( a != a )
| ( A != b )
| ( ( mult @ c @ b )
!= unit )
| ( ( mult @ b @ c )
!= unit )
| ( A != b ) ),
inference(simp,[status(thm)],[189]) ).
thf(241,plain,
( ( ( mult @ c @ b )
!= unit )
| ( ( mult @ b @ c )
!= unit ) ),
inference(simp,[status(thm)],[207]) ).
thf(2210,plain,
! [B: $i,A: $i] :
( ( B != unit )
| ( ( mult @ b @ c )
!= unit )
| ( ( mult @ ( i @ ( rd @ A @ B ) ) @ A )
!= ( mult @ c @ b ) ) ),
inference(paramod_ordered,[status(thm)],[563,241]) ).
thf(2231,plain,
! [A: $i] :
( ( ( mult @ b @ c )
!= unit )
| ( ( i @ ( rd @ A @ unit ) )
!= c )
| ( A != b ) ),
inference(simp,[status(thm)],[2210]) ).
thf(2339,plain,
( ( ( mult @ b @ c )
!= unit )
| ( ( i @ ( rd @ b @ unit ) )
!= c ) ),
inference(simp,[status(thm)],[2231]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( i @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( i @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( i @ B ) )
= A ),
inference(lifteq,[status(thm)],[28]) ).
thf(825,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( mult @ A @ ( i @ D ) )
= C )
| ( ( mult @ ( rd @ A @ B ) @ B )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[19,29]) ).
thf(826,plain,
! [B: $i,A: $i] :
( ( rd @ A @ B )
= ( mult @ A @ ( i @ B ) ) ),
inference(pattern_uni,[status(thm)],[825:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( rd @ E @ F )),bind(D,$thf( F ))]]) ).
thf(890,plain,
! [B: $i,A: $i] :
( ( rd @ A @ B )
= ( mult @ A @ ( i @ B ) ) ),
inference(simp,[status(thm)],[826]) ).
thf(8347,plain,
( ( ( mult @ b @ c )
!= unit )
| ( ( i @ ( mult @ b @ ( i @ unit ) ) )
!= c ) ),
inference(rewrite,[status(thm)],[2339,890]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[16]) ).
thf(805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ld @ C @ A )
= D )
| ( ( mult @ ( mult @ A @ B ) @ ( i @ B ) )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[29,17]) ).
thf(806,plain,
! [B: $i,A: $i] :
( ( ld @ ( mult @ A @ B ) @ A )
= ( i @ B ) ),
inference(pattern_uni,[status(thm)],[805:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( mult @ E @ G )),bind(D,$thf( i @ G ))]]) ).
thf(886,plain,
! [B: $i,A: $i] :
( ( ld @ ( mult @ A @ B ) @ A )
= ( i @ B ) ),
inference(simp,[status(thm)],[806]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[14]) ).
thf(501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( mult @ ( i @ C ) @ B )
= D )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15,27]) ).
thf(502,plain,
! [B: $i,A: $i] :
( ( ld @ A @ B )
= ( mult @ ( i @ A ) @ B ) ),
inference(pattern_uni,[status(thm)],[501:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( ld @ E @ F ))]]) ).
thf(586,plain,
! [B: $i,A: $i] :
( ( ld @ A @ B )
= ( mult @ ( i @ A ) @ B ) ),
inference(simp,[status(thm)],[502]) ).
thf(4589,plain,
! [B: $i,A: $i] :
( ( mult @ ( i @ ( mult @ A @ B ) ) @ A )
= ( i @ B ) ),
inference(rewrite,[status(thm)],[886,586]) ).
thf(796,plain,
! [C: $i,B: $i,A: $i] :
( ( ( mult @ A @ ( i @ C ) )
= B )
| ( ( mult @ unit @ A )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25,29]) ).
thf(797,plain,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
inference(pattern_uni,[status(thm)],[796:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(1239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ unit @ C )
= B )
| ( ( mult @ A @ ( i @ A ) )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[797,21]) ).
thf(1240,plain,
! [A: $i] :
( ( rd @ unit @ ( i @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[1239:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( i @ D ))]]) ).
thf(1339,plain,
! [A: $i] :
( ( rd @ unit @ ( i @ A ) )
= A ),
inference(simp,[status(thm)],[1240]) ).
thf(6,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
thf(22,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
inference(lifteq,[status(thm)],[22]) ).
thf(497,plain,
! [C: $i,B: $i,A: $i] :
( ( ( mult @ ( i @ B ) @ A )
= C )
| ( ( mult @ A @ unit )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,27]) ).
thf(498,plain,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
inference(pattern_uni,[status(thm)],[497:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( unit ))]]) ).
thf(604,plain,
! [C: $i,B: $i,A: $i] :
( ( ( rd @ unit @ C )
= B )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[498,21]) ).
thf(605,plain,
! [A: $i] :
( ( rd @ unit @ A )
= ( i @ A ) ),
inference(pattern_uni,[status(thm)],[604:[bind(A,$thf( D )),bind(B,$thf( i @ D )),bind(C,$thf( D ))]]) ).
thf(702,plain,
! [A: $i] :
( ( rd @ unit @ A )
= ( i @ A ) ),
inference(simp,[status(thm)],[605]) ).
thf(1365,plain,
! [A: $i] :
( ( i @ ( i @ A ) )
= A ),
inference(rewrite,[status(thm)],[1339,702]) ).
thf(2163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( rd @ B @ D )
= C )
| ( ( mult @ ( i @ ( rd @ A @ B ) ) @ A )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[563,21]) ).
thf(2164,plain,
! [B: $i,A: $i] :
( ( rd @ B @ A )
= ( i @ ( rd @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[2163:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( i @ ( rd @ F @ G ) )),bind(D,$thf( F ))]]) ).
thf(2328,plain,
! [B: $i,A: $i] :
( ( rd @ B @ A )
= ( i @ ( rd @ A @ B ) ) ),
inference(simp,[status(thm)],[2164]) ).
thf(7806,plain,
! [B: $i,A: $i] :
( ( mult @ B @ ( i @ A ) )
= ( i @ ( mult @ A @ ( i @ B ) ) ) ),
inference(rewrite,[status(thm)],[2328,890]) ).
thf(632,plain,
! [A: $i] :
( ( ( mult @ b @ c )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ c @ b ) ) ),
inference(paramod_ordered,[status(thm)],[498,241]) ).
thf(651,plain,
! [A: $i] :
( ( ( mult @ b @ c )
!= unit )
| ( ( i @ A )
!= c )
| ( A != b ) ),
inference(simp,[status(thm)],[632]) ).
thf(686,plain,
( ( ( mult @ b @ c )
!= unit )
| ( ( i @ b )
!= c ) ),
inference(simp,[status(thm)],[651]) ).
thf(1243,plain,
! [A: $i] :
( ( ( i @ b )
!= c )
| ( ( mult @ A @ ( i @ A ) )
!= ( mult @ b @ c ) ) ),
inference(paramod_ordered,[status(thm)],[797,686]) ).
thf(1270,plain,
! [A: $i] :
( ( ( i @ b )
!= c )
| ( A != b )
| ( ( i @ A )
!= c ) ),
inference(simp,[status(thm)],[1243]) ).
thf(1349,plain,
( ( i @ b )
!= c ),
inference(simp,[status(thm)],[1270]) ).
thf(614,plain,
! [B: $i,A: $i] :
( ( unit = B )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ B @ unit ) ) ),
inference(paramod_ordered,[status(thm)],[498,23]) ).
thf(615,plain,
( ( i @ unit )
= unit ),
inference(pattern_uni,[status(thm)],[614:[bind(A,$thf( unit )),bind(B,$thf( i @ unit ))]]) ).
thf(622,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ld @ B @ unit )
= C )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[498,17]) ).
thf(623,plain,
! [A: $i] :
( ( ld @ ( i @ A ) @ unit )
= A ),
inference(pattern_uni,[status(thm)],[622:[bind(A,$thf( D )),bind(B,$thf( i @ D )),bind(C,$thf( D ))]]) ).
thf(710,plain,
! [A: $i] :
( ( ld @ ( i @ A ) @ unit )
= A ),
inference(simp,[status(thm)],[623]) ).
thf(272,plain,
( ( ( mult @ b @ c )
!= unit )
| ( ( mult @ c @ b )
!= ( mult @ b @ c ) )
| ( unit != unit ) ),
inference(eqfactor_ordered,[status(thm)],[241]) ).
thf(284,plain,
( ( ( mult @ b @ c )
!= unit )
| ( c != b )
| ( c != b ) ),
inference(simp,[status(thm)],[272]) ).
thf(289,plain,
( ( ( mult @ b @ c )
!= unit )
| ( c != b ) ),
inference(simp,[status(thm)],[284]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ( B != unit )
| ( c != b )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ b @ c ) ) ),
inference(paramod_ordered,[status(thm)],[15,289]) ).
thf(298,plain,
! [A: $i] :
( ( c != b )
| ( A != b )
| ( ( ld @ A @ unit )
!= c ) ),
inference(simp,[status(thm)],[292]) ).
thf(299,plain,
( ( c != b )
| ( ( ld @ b @ unit )
!= c ) ),
inference(simp,[status(thm)],[298]) ).
thf(959,plain,
! [A: $i] :
( ( c != b )
| ( A != c )
| ( ( ld @ ( i @ A ) @ unit )
!= ( ld @ b @ unit ) ) ),
inference(paramod_ordered,[status(thm)],[710,299]) ).
thf(963,plain,
( ( c != b )
| ( ( ld @ ( i @ c ) @ unit )
!= ( ld @ b @ unit ) ) ),
inference(simp,[status(thm)],[959]) ).
thf(5342,plain,
( ( c != b )
| ( ( mult @ ( i @ ( i @ c ) ) @ unit )
!= ( mult @ ( i @ b ) @ unit ) ) ),
inference(rewrite,[status(thm)],[963,586]) ).
thf(5356,plain,
( ( c != b )
| ( ( mult @ ( i @ b ) @ unit )
!= ( mult @ unit @ unit ) )
| ( ( i @ ( i @ c ) )
!= ( i @ unit ) ) ),
inference(paramod_ordered,[status(thm)],[615,5342]) ).
thf(5386,plain,
( ( c != b )
| ( ( i @ b )
!= unit )
| ( unit != unit )
| ( ( i @ c )
!= unit ) ),
inference(simp,[status(thm)],[5356]) ).
thf(5396,plain,
( ( c != b )
| ( ( i @ b )
!= unit )
| ( ( i @ c )
!= unit ) ),
inference(simp,[status(thm)],[5386]) ).
thf(5415,plain,
( ( c != b )
| ( ( i @ b )
!= unit )
| ( ( i @ c )
!= ( i @ b ) )
| ( unit != unit ) ),
inference(eqfactor_ordered,[status(thm)],[5396]) ).
thf(5421,plain,
( ( c != b )
| ( ( i @ b )
!= unit )
| ( c != b ) ),
inference(simp,[status(thm)],[5415]) ).
thf(5424,plain,
( ( c != b )
| ( ( i @ b )
!= unit ) ),
inference(simp,[status(thm)],[5421]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ ( mult @ A @ B ) ) )
= ( mult @ ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( 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)],[10]) ).
thf(56,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ A ) @ c )
!= ( mult @ ( mult @ a @ b ) @ ( mult @ ( mult @ c @ b ) @ c ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ b @ c ) @ b ) ) ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(78,plain,
! [A: $i] :
( ( ( mult @ a @ A )
!= ( mult @ a @ b ) )
| ( ( mult @ ( mult @ c @ b ) @ c )
!= c )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ b @ c ) @ b ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(2404,plain,
! [A: $i] :
( ( ( mult @ a @ A )
!= ( mult @ a @ b ) )
| ( ( mult @ ( mult @ c @ b ) @ c )
!= c )
| ( A
!= ( mult @ ( mult @ b @ c ) @ b ) ) ),
inference(rewrite,[status(thm)],[78,25]) ).
thf(57,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ ( mult @ A @ b ) ) @ c )
!= ( mult @ ( mult @ a @ b ) @ ( mult @ ( mult @ c @ b ) @ c ) ) )
| ( ( mult @ unit @ A )
!= ( mult @ b @ c ) ) ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(83,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ A @ b ) )
!= ( mult @ a @ b ) )
| ( ( mult @ ( mult @ c @ b ) @ c )
!= c )
| ( ( mult @ unit @ A )
!= ( mult @ b @ c ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(3817,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ A @ b ) )
!= ( mult @ a @ b ) )
| ( ( mult @ ( mult @ c @ b ) @ c )
!= c )
| ( A
!= ( mult @ b @ c ) ) ),
inference(rewrite,[status(thm)],[83,25]) ).
thf(53,plain,
! [A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ ( mult @ A @ c ) )
!= ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c ) )
| ( ( mult @ unit @ A )
!= ( mult @ c @ b ) ) ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(94,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) )
!= ( mult @ a @ b ) )
| ( ( mult @ A @ c )
!= c )
| ( ( mult @ unit @ A )
!= ( mult @ c @ b ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(5425,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) )
!= ( mult @ a @ b ) )
| ( ( mult @ A @ c )
!= c )
| ( A
!= ( mult @ c @ b ) ) ),
inference(rewrite,[status(thm)],[94,25]) ).
thf(4671,plain,
! [C: $i,B: $i,A: $i] :
( ( ( mult @ ( i @ unit ) @ B )
= ( i @ C ) )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[498,4589]) ).
thf(4672,plain,
! [A: $i] :
( ( mult @ ( i @ unit ) @ ( i @ A ) )
= ( i @ A ) ),
inference(pattern_uni,[status(thm)],[4671:[bind(A,$thf( D )),bind(B,$thf( i @ D )),bind(C,$thf( D ))]]) ).
thf(4861,plain,
! [A: $i] :
( ( mult @ ( i @ unit ) @ ( i @ A ) )
= ( i @ A ) ),
inference(simp,[status(thm)],[4672]) ).
thf(5005,plain,
! [A: $i] :
( ( mult @ unit @ ( i @ A ) )
= ( i @ A ) ),
inference(rewrite,[status(thm)],[4861,615]) ).
thf(63,plain,
! [A: $i] :
( ( A
!= ( mult @ ( mult @ a @ b ) @ ( mult @ ( mult @ c @ b ) @ c ) ) )
| ( ( mult @ A @ unit )
!= ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[23,13]) ).
thf(110,plain,
( ( ( mult @ ( mult @ a @ b ) @ ( mult @ ( mult @ c @ b ) @ c ) )
!= ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) )
| ( unit != c ) ),
inference(simp,[status(thm)],[63]) ).
thf(792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( mult @ B @ ( i @ D ) )
= C )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[15,29]) ).
thf(793,plain,
! [B: $i,A: $i] :
( ( mult @ B @ ( i @ ( ld @ A @ B ) ) )
= A ),
inference(pattern_uni,[status(thm)],[792:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( ld @ E @ F ))]]) ).
thf(883,plain,
! [B: $i,A: $i] :
( ( mult @ B @ ( i @ ( ld @ A @ B ) ) )
= A ),
inference(simp,[status(thm)],[793]) ).
thf(3413,plain,
! [B: $i,A: $i] :
( ( mult @ B @ ( i @ ( mult @ ( i @ A ) @ B ) ) )
= A ),
inference(rewrite,[status(thm)],[883,586]) ).
thf(3446,plain,
! [B: $i,A: $i] :
( ( A != unit )
| ( c != b )
| ( ( mult @ B @ ( i @ ( mult @ ( i @ A ) @ B ) ) )
!= ( mult @ b @ c ) ) ),
inference(paramod_ordered,[status(thm)],[3413,289]) ).
thf(3530,plain,
! [A: $i] :
( ( c != b )
| ( A != b )
| ( ( i @ ( mult @ ( i @ unit ) @ A ) )
!= c ) ),
inference(simp,[status(thm)],[3446]) ).
thf(3733,plain,
( ( c != b )
| ( ( i @ ( mult @ ( i @ unit ) @ b ) )
!= c ) ),
inference(simp,[status(thm)],[3530]) ).
thf(3784,plain,
( ( c != b )
| ( ( i @ ( mult @ unit @ b ) )
!= c ) ),
inference(rewrite,[status(thm)],[3733,615]) ).
thf(633,plain,
! [A: $i] :
( ( ( mult @ c @ b )
!= unit )
| ( ( mult @ ( i @ A ) @ A )
!= ( mult @ b @ c ) ) ),
inference(paramod_ordered,[status(thm)],[498,241]) ).
thf(642,plain,
! [A: $i] :
( ( ( mult @ c @ b )
!= unit )
| ( ( i @ A )
!= b )
| ( A != c ) ),
inference(simp,[status(thm)],[633]) ).
thf(679,plain,
( ( ( mult @ c @ b )
!= unit )
| ( ( i @ c )
!= b ) ),
inference(simp,[status(thm)],[642]) ).
thf(725,plain,
! [A: $i] :
( ( A != unit )
| ( ( i @ c )
!= b )
| ( ( mult @ A @ unit )
!= ( mult @ c @ b ) ) ),
inference(paramod_ordered,[status(thm)],[23,679]) ).
thf(736,plain,
( ( ( i @ c )
!= b )
| ( unit != c )
| ( unit != b ) ),
inference(simp,[status(thm)],[725]) ).
thf(978,plain,
( ( unit != b )
| ( unit != c )
| ( ( i @ unit )
!= ( i @ c ) ) ),
inference(paramod_ordered,[status(thm)],[615,736]) ).
thf(979,plain,
( ( unit != b )
| ( unit != c )
| ( unit != c ) ),
inference(simp,[status(thm)],[978]) ).
thf(980,plain,
( ( unit != b )
| ( unit != c ) ),
inference(simp,[status(thm)],[979]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( mult @ ( mult @ a @ b ) @ ( mult @ B @ c ) )
!= ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c ) )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ c @ b ) ) ),
inference(paramod_ordered,[status(thm)],[15,13]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) )
!= ( mult @ a @ b ) )
| ( ( mult @ B @ c )
!= c )
| ( ( mult @ A @ ( ld @ A @ B ) )
!= ( mult @ c @ b ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(1825,plain,
! [A: $i] :
( ( ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) )
!= ( mult @ a @ b ) )
| ( ( mult @ A @ c )
!= c )
| ( A
!= ( mult @ c @ b ) ) ),
inference(rewrite,[status(thm)],[75,15]) ).
thf(1369,plain,
! [C: $i,B: $i,A: $i] :
( ( ( mult @ ( mult @ B @ C ) @ A )
= B )
| ( ( i @ ( i @ A ) )
!= ( i @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1365,29]) ).
thf(1370,plain,
! [B: $i,A: $i] :
( ( mult @ ( mult @ A @ ( i @ B ) ) @ B )
= A ),
inference(pattern_uni,[status(thm)],[1369:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( i @ D ))]]) ).
thf(1393,plain,
! [B: $i,A: $i] :
( ( mult @ ( mult @ A @ ( i @ B ) ) @ B )
= A ),
inference(simp,[status(thm)],[1370]) ).
thf(2211,plain,
! [B: $i,A: $i] :
( ( ( mult @ c @ b )
!= unit )
| ( B != unit )
| ( ( mult @ ( i @ ( rd @ A @ B ) ) @ A )
!= ( mult @ b @ c ) ) ),
inference(paramod_ordered,[status(thm)],[563,241]) ).
thf(2269,plain,
! [A: $i] :
( ( ( mult @ c @ b )
!= unit )
| ( ( i @ ( rd @ A @ unit ) )
!= b )
| ( A != c ) ),
inference(simp,[status(thm)],[2211]) ).
thf(2373,plain,
( ( ( mult @ c @ b )
!= unit )
| ( ( i @ ( rd @ c @ unit ) )
!= b ) ),
inference(simp,[status(thm)],[2269]) ).
thf(8441,plain,
( ( ( mult @ c @ b )
!= unit )
| ( ( i @ ( mult @ c @ ( i @ unit ) ) )
!= b ) ),
inference(rewrite,[status(thm)],[2373,890]) ).
thf(50,plain,
( ( ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) )
!= ( mult @ a @ b ) )
| ( ( mult @ ( mult @ c @ b ) @ c )
!= c ) ),
inference(simp,[status(thm)],[13]) ).
thf(1244,plain,
! [A: $i] :
( ( ( i @ c )
!= b )
| ( ( mult @ A @ ( i @ A ) )
!= ( mult @ c @ b ) ) ),
inference(paramod_ordered,[status(thm)],[797,679]) ).
thf(1309,plain,
! [A: $i] :
( ( ( i @ c )
!= b )
| ( A != c )
| ( ( i @ A )
!= b ) ),
inference(simp,[status(thm)],[1244]) ).
thf(1336,plain,
( ( i @ c )
!= b ),
inference(simp,[status(thm)],[1309]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A ) @ B )
= ( mult @ ( mult @ A @ B ) @ ( mult @ C @ ( mult @ A @ B ) ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(60,plain,
! [A: $i] :
( ( A
!= ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c ) )
| ( ( mult @ A @ unit )
!= ( mult @ ( mult @ a @ b ) @ ( mult @ ( mult @ c @ b ) @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,13]) ).
thf(87,plain,
( ( ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c )
!= ( mult @ a @ b ) )
| ( ( mult @ ( mult @ c @ b ) @ c )
!= unit ) ),
inference(simp,[status(thm)],[60]) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ( ( mult @ A @ ( mult @ B @ C ) )
= C )
| ( ( i @ ( i @ A ) )
!= ( i @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1365,27]) ).
thf(1380,plain,
! [B: $i,A: $i] :
( ( mult @ B @ ( mult @ ( i @ B ) @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[1379:[bind(A,$thf( D )),bind(B,$thf( i @ D ))]]) ).
thf(1390,plain,
! [B: $i,A: $i] :
( ( mult @ B @ ( mult @ ( i @ B ) @ A ) )
= A ),
inference(simp,[status(thm)],[1380]) ).
thf(7869,plain,
! [C: $i,B: $i,A: $i] :
( ( ( i @ ( mult @ A @ ( i @ B ) ) )
= ( i @ C ) )
| ( ( mult @ B @ ( i @ A ) )
!= ( mult @ unit @ ( i @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[7806,5005]) ).
thf(7870,plain,
! [A: $i] :
( ( i @ ( mult @ A @ ( i @ unit ) ) )
= ( i @ A ) ),
inference(pattern_uni,[status(thm)],[7869:[bind(A,$thf( A )),bind(B,$thf( unit )),bind(C,$thf( A ))]]) ).
thf(9028,plain,
! [A: $i] :
( ( i @ ( mult @ A @ unit ) )
= ( i @ A ) ),
inference(rewrite,[status(thm)],[7870,615]) ).
thf(52,plain,
! [A: $i] :
( ( A
!= ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c ) )
| ( ( mult @ unit @ A )
!= ( mult @ ( mult @ a @ b ) @ ( mult @ ( mult @ c @ b ) @ c ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,13]) ).
thf(82,plain,
( ( ( mult @ a @ b )
!= unit )
| ( ( mult @ ( mult @ a @ ( mult @ ( mult @ b @ c ) @ b ) ) @ c )
!= ( mult @ ( mult @ c @ b ) @ c ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(5861,plain,
( ( c != b )
| ( ( i @ unit )
!= ( i @ b ) ) ),
inference(paramod_ordered,[status(thm)],[615,5424]) ).
thf(5864,plain,
( ( c != b )
| ( unit != b ) ),
inference(simp,[status(thm)],[5861]) ).
thf(155571,plain,
$false,
inference(e,[status(thm)],[8347,4589,28,1365,7806,586,1349,890,5424,18,11,30,2404,3817,5425,797,5005,24,25,5342,14,110,20,289,29,3784,3413,615,980,1825,13,1393,22,27,144,498,8441,241,50,16,1336,31,87,1390,26,23,9028,82,5864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP670-1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n017.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 : Fri May 19 01:15:01 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (102ms).
% 1.19/0.97 % [INFO] Running in sequential loop mode.
% 1.63/1.16 % [INFO] eprover registered as external prover.
% 1.63/1.16 % [INFO] cvc4 registered as external prover.
% 1.63/1.17 % [INFO] Scanning for conjecture ...
% 1.63/1.22 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.84/1.24 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.84/1.25 % [INFO] Problem is propositional (TPTP CNF).
% 1.84/1.25 % [INFO] Type checking passed.
% 1.84/1.25 % [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 ...
% 201.82/38.86 % External prover 'e' found a proof!
% 201.82/38.86 % [INFO] Killing All external provers ...
% 201.82/38.86 % Time passed: 38340ms (effective reasoning time: 37893ms)
% 201.82/38.86 % 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)>
% 201.82/38.87 % Axioms used in derivation (9): c05, c08, c01, c03, c06, c02, c07, c09, c04
% 201.82/38.87 % No. of inferences in proof: 153
% 201.82/38.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 38340 ms resp. 37893 ms w/o parsing
% 201.82/38.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 201.82/38.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------