TSTP Solution File: ALG176+1 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : ALG176+1 : TPTP v8.2.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n009.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 Jun 24 04:03:14 EDT 2024
% Result : Theorem 202.34s 30.10s
% Output : Refutation 202.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 8 unt; 8 typ; 0 def)
% Number of atoms : 136 ( 47 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 428 ( 51 ~; 31 |; 17 &; 297 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 0 ^ 57 !; 5 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(sorti1_type,type,
sorti1: $i > $o ).
thf(sorti2_type,type,
sorti2: $i > $o ).
thf(h_type,type,
h: $i > $i ).
thf(j_type,type,
j: $i > $i ).
thf(op1_type,type,
op1: $i > $i > $i ).
thf(op2_type,type,
op2: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(5,axiom,
? [A: $i] :
( ( sorti1 @ A )
& ! [B: $i] :
( ( sorti1 @ B )
=> ( ( op1 @ B @ A )
!= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(27,plain,
? [A: $i] :
( ( sorti1 @ A )
& ! [B: $i] :
( ( sorti1 @ B )
=> ( ( op1 @ B @ A )
!= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,plain,
sorti1 @ sk1,
inference(cnf,[status(esa)],[27]) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( sorti1 @ A )
=> ( sorti2 @ ( h @ A ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( sorti1 @ ( j @ A ) ) ) )
=> ~ ( ! [A: $i] :
( ( sorti1 @ A )
=> ! [B: $i] :
( ( sorti1 @ B )
=> ( ( h @ ( op1 @ A @ B ) )
= ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ! [B: $i] :
( ( sorti2 @ B )
=> ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( ( h @ ( j @ A ) )
= A ) )
& ! [A: $i] :
( ( sorti1 @ A )
=> ( ( j @ ( h @ A ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( sorti1 @ A )
=> ( sorti2 @ ( h @ A ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( sorti1 @ ( j @ A ) ) ) )
=> ~ ( ! [A: $i] :
( ( sorti1 @ A )
=> ! [B: $i] :
( ( sorti1 @ B )
=> ( ( h @ ( op1 @ A @ B ) )
= ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ! [B: $i] :
( ( sorti2 @ B )
=> ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( ( h @ ( j @ A ) )
= A ) )
& ! [A: $i] :
( ( sorti1 @ A )
=> ( ( j @ ( h @ A ) )
= A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ( ! [A: $i] :
( ( sorti1 @ A )
=> ( sorti2 @ ( h @ A ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( sorti1 @ ( j @ A ) ) ) )
=> ~ ( ! [A: $i] :
( ( sorti1 @ A )
=> ! [B: $i] :
( ( sorti1 @ B )
=> ( ( h @ ( op1 @ A @ B ) )
= ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ! [B: $i] :
( ( sorti2 @ B )
=> ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( ( h @ ( j @ A ) )
= A ) )
& ! [A: $i] :
( ( sorti1 @ A )
=> ( ( j @ ( h @ A ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
! [A: $i] :
( ~ ( sorti1 @ A )
| ( sorti2 @ ( h @ A ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(36,plain,
! [A: $i] :
( ( sorti2 @ ( h @ A ) )
| ( ( sorti1 @ sk1 )
!= ( sorti1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,10]) ).
thf(37,plain,
sorti2 @ ( h @ sk1 ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( sk1 ))]]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ ( sorti2 @ A )
| ~ ( sorti2 @ B )
| ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) )
| ~ ( sorti2 @ A )
| ~ ( sorti2 @ B ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) )
| ~ ( sorti2 @ A )
| ~ ( sorti2 @ B ) ),
inference(simp,[status(thm)],[14]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) )
| ~ ( sorti2 @ A )
| ( ( sorti2 @ ( h @ sk1 ) )
!= ( sorti2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[37,15]) ).
thf(64,plain,
! [A: $i] :
( ( ( j @ ( op2 @ A @ ( h @ sk1 ) ) )
= ( op1 @ ( j @ A ) @ ( j @ ( h @ sk1 ) ) ) )
| ~ ( sorti2 @ A ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( A )),bind(B,$thf( h @ sk1 ))]]) ).
thf(8,plain,
! [A: $i] :
( ~ ( sorti1 @ A )
| ( ( j @ ( h @ A ) )
= A ) ),
inference(cnf,[status(esa)],[7]) ).
thf(21,plain,
! [A: $i] :
( ( ( j @ ( h @ A ) )
= A )
| ~ ( sorti1 @ A ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(22,plain,
! [A: $i] :
( ( ( j @ ( h @ A ) )
= A )
| ~ ( sorti1 @ A ) ),
inference(simp,[status(thm)],[21]) ).
thf(451,plain,
! [A: $i] :
( ( ( j @ ( h @ A ) )
= A )
| ( ( sorti1 @ sk1 )
!= ( sorti1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,22]) ).
thf(452,plain,
( ( j @ ( h @ sk1 ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[451:[bind(A,$thf( sk1 ))]]) ).
thf(1429,plain,
! [A: $i] :
( ( ( j @ ( op2 @ A @ ( h @ sk1 ) ) )
= ( op1 @ ( j @ A ) @ sk1 ) )
| ~ ( sorti2 @ A ) ),
inference(rewrite,[status(thm)],[64,452]) ).
thf(6,axiom,
~ ? [A: $i] :
( ( sorti2 @ A )
& ! [B: $i] :
( ( sorti2 @ B )
=> ( ( op2 @ B @ A )
!= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(31,plain,
~ ? [A: $i] :
( ( sorti2 @ A )
& ! [B: $i] :
( ( sorti2 @ B )
=> ( ( op2 @ B @ A )
!= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
~ ? [A: $i] :
( ( sorti2 @ A )
& ! [B: $i] :
( ( sorti2 @ B )
=> ( ( op2 @ B @ A )
!= B ) ) ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(33,plain,
! [A: $i] :
( ~ ( sorti2 @ A )
| ( sorti2 @ ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(832,plain,
! [A: $i] :
( ( sorti2 @ ( sk2 @ A ) )
| ( ( sorti2 @ ( h @ sk1 ) )
!= ( sorti2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[37,33]) ).
thf(833,plain,
sorti2 @ ( sk2 @ ( h @ sk1 ) ),
inference(pattern_uni,[status(thm)],[832:[bind(A,$thf( h @ sk1 ))]]) ).
thf(13,plain,
! [A: $i] :
( ~ ( sorti2 @ A )
| ( sorti1 @ ( j @ A ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(16,plain,
! [A: $i] :
( ~ ( sorti2 @ A )
| ( sorti1 @ ( j @ A ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(862,plain,
! [A: $i] :
( ( sorti1 @ ( j @ A ) )
| ( ( sorti2 @ ( sk2 @ ( h @ sk1 ) ) )
!= ( sorti2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[833,16]) ).
thf(863,plain,
sorti1 @ ( j @ ( sk2 @ ( h @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[862:[bind(A,$thf( sk2 @ ( h @ sk1 ) ))]]) ).
thf(28,plain,
! [A: $i] :
( ~ ( sorti1 @ A )
| ( ( op1 @ A @ sk1 )
!= A ) ),
inference(cnf,[status(esa)],[27]) ).
thf(30,plain,
! [A: $i] :
( ( ( op1 @ A @ sk1 )
!= A )
| ~ ( sorti1 @ A ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(921,plain,
! [A: $i] :
( ( ( op1 @ A @ sk1 )
!= A )
| ( ( sorti1 @ ( j @ ( sk2 @ ( h @ sk1 ) ) ) )
!= ( sorti1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[863,30]) ).
thf(922,plain,
( ( op1 @ ( j @ ( sk2 @ ( h @ sk1 ) ) ) @ sk1 )
!= ( j @ ( sk2 @ ( h @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[921:[bind(A,$thf( j @ ( sk2 @ ( h @ sk1 ) ) ))]]) ).
thf(1490,plain,
! [A: $i] :
( ~ ( sorti2 @ A )
| ( ( j @ ( op2 @ A @ ( h @ sk1 ) ) )
!= ( j @ ( sk2 @ ( h @ sk1 ) ) ) )
| ( ( op1 @ ( j @ A ) @ sk1 )
!= ( op1 @ ( j @ ( sk2 @ ( h @ sk1 ) ) ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1429,922]) ).
thf(1491,plain,
( ~ ( sorti2 @ ( sk2 @ ( h @ sk1 ) ) )
| ( ( j @ ( op2 @ ( sk2 @ ( h @ sk1 ) ) @ ( h @ sk1 ) ) )
!= ( j @ ( sk2 @ ( h @ sk1 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1490:[bind(A,$thf( sk2 @ ( h @ sk1 ) ))]]) ).
thf(34,plain,
! [A: $i] :
( ~ ( sorti2 @ A )
| ( ( op2 @ ( sk2 @ A ) @ A )
= ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(35,plain,
! [A: $i] :
( ( ( op2 @ ( sk2 @ A ) @ A )
= ( sk2 @ A ) )
| ~ ( sorti2 @ A ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(1044,plain,
! [A: $i] :
( ( ( op2 @ ( sk2 @ A ) @ A )
= ( sk2 @ A ) )
| ( ( sorti2 @ ( h @ sk1 ) )
!= ( sorti2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[37,35]) ).
thf(1045,plain,
( ( op2 @ ( sk2 @ ( h @ sk1 ) ) @ ( h @ sk1 ) )
= ( sk2 @ ( h @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1044:[bind(A,$thf( h @ sk1 ))]]) ).
thf(48951,plain,
( ~ $true
| ( ( j @ ( sk2 @ ( h @ sk1 ) ) )
!= ( j @ ( sk2 @ ( h @ sk1 ) ) ) ) ),
inference(rewrite,[status(thm)],[1491,833,1045]) ).
thf(48952,plain,
$false,
inference(simp,[status(thm)],[48951]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.16 % Problem : ALG176+1 : TPTP v8.2.0. Released v2.7.0.
% 0.04/0.16 % Command : run_Leo-III %s %d SAT
% 0.15/0.38 % Computer : n009.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Wed Jun 19 15:39:40 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.98/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.05 % [INFO] Parsing done (115ms).
% 1.31/1.06 % [INFO] Running in sequential loop mode.
% 1.65/1.29 % [INFO] nitpick registered as external prover.
% 1.65/1.30 % [INFO] Scanning for conjecture ...
% 1.86/1.37 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.93/1.40 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.93/1.41 % [INFO] Problem is first-order (TPTP FOF).
% 1.93/1.42 % [INFO] Type checking passed.
% 1.93/1.42 % [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 ...
% 202.34/30.09 % [INFO] Killing All external provers ...
% 202.34/30.10 % Time passed: 29516ms (effective reasoning time: 29032ms)
% 202.34/30.10 % 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)>
% 202.34/30.10 % Axioms used in derivation (2): ax3, ax4
% 202.34/30.10 % No. of inferences in proof: 42
% 202.34/30.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 29516 ms resp. 29032 ms w/o parsing
% 202.34/30.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 202.34/30.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------