TSTP Solution File: SYN726+1 by Leo-III-SAT---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SYN726+1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 11:02:31 EDT 2024
% Result : Theorem 73.87s 11.32s
% Output : Refutation 74.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of formulae : 78 ( 13 unt; 6 typ; 0 def)
% Number of atoms : 237 ( 22 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 624 ( 87 ~; 94 |; 15 &; 416 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 159 ( 0 ^ 159 !; 0 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
thf(p_type,type,
p: $i > $i > $o ).
thf(q_type,type,
q: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
( ( ( ! [A: $i,B: $i,C: $i] :
( ( ( p @ A @ B )
& ( p @ B @ C ) )
=> ( p @ A @ C ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( q @ A @ B )
& ( q @ B @ C ) )
=> ( q @ A @ C ) )
& ! [A: $i,B: $i] :
( ( q @ A @ B )
=> ( q @ B @ A ) )
& ! [A: $i,B: $i] :
( ( p @ A @ B )
| ( q @ A @ B ) ) )
=> ! [A: $i,B: $i] : ( p @ A @ B ) )
| ! [A: $i,B: $i] : ( q @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm400) ).
thf(2,negated_conjecture,
~ ( ( ( ! [A: $i,B: $i,C: $i] :
( ( ( p @ A @ B )
& ( p @ B @ C ) )
=> ( p @ A @ C ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( q @ A @ B )
& ( q @ B @ C ) )
=> ( q @ A @ C ) )
& ! [A: $i,B: $i] :
( ( q @ A @ B )
=> ( q @ B @ A ) )
& ! [A: $i,B: $i] :
( ( p @ A @ B )
| ( q @ A @ B ) ) )
=> ! [A: $i,B: $i] : ( p @ A @ B ) )
| ! [A: $i,B: $i] : ( q @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( ! [A: $i,B: $i,C: $i] :
( ( ( p @ A @ B )
& ( p @ B @ C ) )
=> ( p @ A @ C ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( q @ A @ B )
& ( q @ B @ C ) )
=> ( q @ A @ C ) )
& ! [A: $i,B: $i] :
( ( q @ A @ B )
=> ( q @ B @ A ) )
& ! [A: $i,B: $i] :
( ( p @ A @ B )
| ( q @ A @ B ) ) )
=> ! [A: $i,B: $i] : ( p @ A @ B ) )
| ! [A: $i,B: $i] : ( q @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( p @ A @ B )
| ( q @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( p @ A @ B )
| ( q @ A @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ~ ( q @ A @ B )
| ( q @ B @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( q @ A @ B )
| ( q @ B @ A ) ),
inference(simp,[status(thm)],[6]) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ( q @ D @ C )
| ( ( q @ A @ B )
!= ( q @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[11,10]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( p @ A @ B )
| ( q @ B @ A ) ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(5,plain,
~ ( q @ sk3 @ sk4 ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( p @ A @ B )
| ( ( q @ A @ B )
!= ( q @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[11,5]) ).
thf(17,plain,
p @ sk3 @ sk4,
inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(4,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( p @ A @ B )
| ~ ( p @ B @ C )
| ( p @ A @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( p @ A @ B )
| ( p @ A @ C )
| ( ( p @ sk3 @ sk4 )
!= ( p @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17,4]) ).
thf(46,plain,
! [A: $i] :
( ~ ( p @ A @ sk3 )
| ( p @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( q @ A @ B )
| ~ ( q @ B @ C )
| ( q @ A @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( q @ A @ B )
| ~ ( q @ B @ C )
| ( q @ A @ C ) ),
inference(simp,[status(thm)],[7]) ).
thf(72,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ~ ( q @ C @ D )
| ( q @ C @ E )
| ( ( q @ A @ B )
!= ( q @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[11,12]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ~ ( q @ C @ A )
| ( q @ C @ B ) ),
inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(310,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ( p @ C @ D )
| ( q @ E @ D )
| ( ( q @ B @ A )
!= ( q @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[19,73]) ).
thf(311,plain,
! [C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ( p @ A @ C )
| ( q @ B @ C ) ),
inference(pattern_uni,[status(thm)],[310:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ( p @ A @ C )
| ( q @ B @ C ) ),
inference(simp,[status(thm)],[311]) ).
thf(7590,plain,
! [C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ( p @ A @ C )
| ( ( q @ B @ C )
!= ( q @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[319,5]) ).
thf(7591,plain,
! [A: $i] :
( ( p @ A @ sk3 )
| ( p @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[7590:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( p @ A @ B )
| ( ( q @ B @ A )
!= ( q @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[19,5]) ).
thf(123,plain,
p @ sk4 @ sk3,
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( p @ A @ B )
| ( p @ A @ C )
| ( ( p @ sk4 @ sk3 )
!= ( p @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[123,4]) ).
thf(141,plain,
! [A: $i] :
( ~ ( p @ A @ sk4 )
| ( p @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( sk3 ))]]) ).
thf(11354,plain,
! [B: $i,A: $i] :
( ( p @ A @ sk3 )
| ( p @ B @ sk3 )
| ( ( p @ A @ sk4 )
!= ( p @ B @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[7591,141]) ).
thf(11355,plain,
! [A: $i] :
( ( p @ A @ sk3 )
| ( p @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[11354:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(11430,plain,
! [A: $i] : ( p @ A @ sk3 ),
inference(simp,[status(thm)],[11355]) ).
thf(11440,plain,
! [A: $i] :
( ~ $true
| ( p @ A @ sk4 ) ),
inference(rewrite,[status(thm)],[46,11430]) ).
thf(11441,plain,
! [A: $i] : ( p @ A @ sk4 ),
inference(simp,[status(thm)],[11440]) ).
thf(7802,plain,
! [C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ( q @ B @ C )
| ( ( p @ A @ C )
!= ( p @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[319]) ).
thf(7803,plain,
! [B: $i,A: $i] :
( ( p @ A @ B )
| ( q @ B @ B ) ),
inference(pattern_uni,[status(thm)],[7802:[bind(A,$thf( A )),bind(B,$thf( C ))]]) ).
thf(7840,plain,
! [B: $i,A: $i] :
( ( p @ A @ B )
| ( q @ B @ B ) ),
inference(simp,[status(thm)],[7803]) ).
thf(8,plain,
~ ( p @ sk1 @ sk2 ),
inference(cnf,[status(esa)],[3]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( p @ A @ B )
| ~ ( p @ B @ C )
| ( ( p @ A @ C )
!= ( p @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[4,8]) ).
thf(21,plain,
! [A: $i] :
( ~ ( p @ sk1 @ A )
| ~ ( p @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(28,plain,
! [A: $i] :
( ~ ( p @ sk1 @ A )
| ~ ( p @ A @ sk2 ) ),
inference(simp,[status(thm)],[21]) ).
thf(10189,plain,
! [C: $i,B: $i,A: $i] :
( ( q @ B @ B )
| ~ ( p @ sk1 @ C )
| ( ( p @ A @ B )
!= ( p @ C @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[7840,28]) ).
thf(10190,plain,
! [A: $i] :
( ( q @ sk2 @ sk2 )
| ~ ( p @ sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[10189:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(17925,plain,
! [B: $i,A: $i] :
( ( q @ sk2 @ sk2 )
| ( ( p @ A @ sk4 )
!= ( p @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11441,10190]) ).
thf(17926,plain,
q @ sk2 @ sk2,
inference(pattern_uni,[status(thm)],[17925:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(70,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ~ ( q @ D @ E )
| ( q @ C @ E )
| ( ( q @ A @ B )
!= ( q @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[11,12]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ~ ( q @ B @ C )
| ( q @ A @ C ) ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ~ ( q @ B @ C )
| ( q @ A @ C ) ),
inference(simp,[status(thm)],[71]) ).
thf(18040,plain,
! [C: $i,B: $i,A: $i] :
( ( p @ A @ B )
| ( q @ A @ C )
| ( ( q @ sk2 @ sk2 )
!= ( q @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[17926,77]) ).
thf(18041,plain,
! [A: $i] :
( ( p @ A @ sk2 )
| ( q @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[18040:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk2 ))]]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( q @ A @ B )
| ~ ( q @ B @ C )
| ( ( q @ A @ C )
!= ( q @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[12,5]) ).
thf(59,plain,
! [A: $i] :
( ~ ( q @ sk3 @ A )
| ~ ( q @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(78,plain,
! [A: $i] :
( ~ ( q @ sk3 @ A )
| ~ ( q @ A @ sk4 ) ),
inference(simp,[status(thm)],[59]) ).
thf(18826,plain,
! [B: $i,A: $i] :
( ( p @ A @ sk2 )
| ~ ( q @ B @ sk4 )
| ( ( q @ A @ sk2 )
!= ( q @ sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18041,78]) ).
thf(18827,plain,
( ( p @ sk3 @ sk2 )
| ~ ( q @ sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[18826:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( p @ A @ B )
| ~ ( p @ B @ C )
| ~ ( p @ sk1 @ D )
| ( ( p @ A @ C )
!= ( p @ D @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[4,28]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( p @ A @ B )
| ~ ( p @ B @ sk2 )
| ~ ( p @ sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( A ))]]) ).
thf(651,plain,
! [B: $i,A: $i] :
( ~ ( p @ B @ sk2 )
| ~ ( p @ sk1 @ A )
| ( ( p @ sk4 @ sk3 )
!= ( p @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[123,34]) ).
thf(652,plain,
( ~ ( p @ sk3 @ sk2 )
| ~ ( p @ sk1 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[651:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).
thf(782,plain,
! [A: $i] :
( ~ ( p @ A @ sk3 )
| ~ ( p @ sk3 @ sk2 )
| ( ( p @ A @ sk4 )
!= ( p @ sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[46,652]) ).
thf(783,plain,
( ~ ( p @ sk1 @ sk3 )
| ~ ( p @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[782:[bind(A,$thf( sk1 ))]]) ).
thf(11434,plain,
( ~ $true
| ~ ( p @ sk3 @ sk2 ) ),
inference(rewrite,[status(thm)],[783,11430]) ).
thf(11435,plain,
~ ( p @ sk3 @ sk2 ),
inference(simp,[status(thm)],[11434]) ).
thf(18873,plain,
( $false
| ~ ( q @ sk2 @ sk4 ) ),
inference(rewrite,[status(thm)],[18827,11435]) ).
thf(18874,plain,
~ ( q @ sk2 @ sk4 ),
inference(simp,[status(thm)],[18873]) ).
thf(18908,plain,
! [B: $i,A: $i] :
( ( p @ A @ B )
| ( ( q @ B @ A )
!= ( q @ sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[19,18874]) ).
thf(18909,plain,
p @ sk4 @ sk2,
inference(pattern_uni,[status(thm)],[18908:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ~ ( p @ A @ sk3 )
| ~ ( p @ B @ sk2 )
| ( ( p @ A @ sk4 )
!= ( p @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[46,28]) ).
thf(93,plain,
( ~ ( p @ sk1 @ sk3 )
| ~ ( p @ sk4 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(11442,plain,
( ~ $true
| ~ ( p @ sk4 @ sk2 ) ),
inference(rewrite,[status(thm)],[93,11430]) ).
thf(11443,plain,
~ ( p @ sk4 @ sk2 ),
inference(simp,[status(thm)],[11442]) ).
thf(18930,plain,
$false,
inference(rewrite,[status(thm)],[18909,11443]) ).
thf(18931,plain,
$false,
inference(simp,[status(thm)],[18930]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN726+1 : TPTP v8.1.2. Released v2.5.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n002.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 : Mon May 6 21:10:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.98/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.98 % [INFO] Parsing done (111ms).
% 1.17/0.99 % [INFO] Running in sequential loop mode.
% 1.68/1.21 % [INFO] nitpick registered as external prover.
% 1.68/1.21 % [INFO] Scanning for conjecture ...
% 1.81/1.27 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 1.81/1.29 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.81/1.29 % [INFO] Problem is first-order (TPTP FOF).
% 1.81/1.30 % [INFO] Type checking passed.
% 1.81/1.30 % [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 ...
% 73.87/11.31 % [INFO] Killing All external provers ...
% 73.87/11.32 % Time passed: 10777ms (effective reasoning time: 10326ms)
% 73.87/11.32 % 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)>
% 73.87/11.32 % Axioms used in derivation (0):
% 73.87/11.32 % No. of inferences in proof: 72
% 73.87/11.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10777 ms resp. 10326 ms w/o parsing
% 74.13/11.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 74.13/11.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------