TSTP Solution File: SEU807^2 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEU807^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n025.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 15:33:13 EDT 2024
% Result : Theorem 42.84s 7.11s
% Output : Refutation 42.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 19 unt; 0 typ; 5 def)
% Number of atoms : 142 ( 50 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 408 ( 50 ~; 36 |; 4 &; 290 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 115 ( 0 ^ 109 !; 6 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(foundationAx_type,type,
foundationAx: $o ).
thf(foundationAx_def,definition,
( foundationAx
= ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [C: $i] :
( ( in @ C @ B )
& ( in @ C @ A ) ) ) ) ) ) ).
thf(setadjoinIL_type,type,
setadjoinIL: $o ).
thf(setadjoinIL_def,definition,
( setadjoinIL
= ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ) ).
thf(setadjoinIR_type,type,
setadjoinIR: $o ).
thf(setadjoinIR_def,definition,
( setadjoinIR
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ B )
=> ( in @ C @ ( setadjoin @ A @ B ) ) ) ) ) ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(in__Cong_def,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ) ) ).
thf(upairset2E_type,type,
upairset2E: $o ).
thf(upairset2E_def,definition,
( upairset2E
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ( ( C = A )
| ( C = B ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( foundationAx
=> ( setadjoinIL
=> ( setadjoinIR
=> ( in__Cong
=> ( upairset2E
=> ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinself2) ).
thf(2,negated_conjecture,
~ ( foundationAx
=> ( setadjoinIL
=> ( setadjoinIR
=> ( in__Cong
=> ( upairset2E
=> ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [C: $i] :
( ( in @ C @ B )
& ( in @ C @ A ) ) ) )
=> ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ B )
=> ( in @ C @ ( setadjoin @ A @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ( ( C = A )
| ( C = B ) ) )
=> ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
! [B: $i,A: $i] : ( in @ A @ ( setadjoin @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [B: $i,A: $i] : ( in @ A @ ( setadjoin @ A @ B ) ),
inference(simp,[status(thm)],[10]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( in @ ( sk1 @ A ) @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ ( sk1 @ C ) @ C )
| ( ( in @ A @ ( setadjoin @ A @ B ) )
!= ( in @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[14,11]) ).
thf(25,plain,
! [B: $i,A: $i] : ( in @ ( sk1 @ ( setadjoin @ A @ B ) ) @ ( setadjoin @ A @ B ) ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( setadjoin @ E @ F )),bind(D,$thf( E ))]]) ).
thf(27,plain,
! [B: $i,A: $i] : ( in @ ( sk1 @ ( setadjoin @ A @ B ) ) @ ( setadjoin @ A @ B ) ),
inference(simp,[status(thm)],[25]) ).
thf(5,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
| ( C = A )
| ( C = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C = B )
| ~ ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( C = A )
| ( C = B )
| ~ ( in @ C @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(417,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = C )
| ( E = D )
| ( ( in @ ( sk1 @ ( setadjoin @ A @ B ) ) @ ( setadjoin @ A @ B ) )
!= ( in @ E @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,13]) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
= A )
| ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
= B ) ),
inference(pattern_uni,[status(thm)],[417:[bind(A,$thf( G )),bind(B,$thf( setadjoin @ I @ emptyset )),bind(C,$thf( G )),bind(D,$thf( I )),bind(E,$thf( sk1 @ ( setadjoin @ G @ ( setadjoin @ I @ emptyset ) ) ))]]) ).
thf(453,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
= A )
| ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
= B ) ),
inference(simp,[status(thm)],[418]) ).
thf(9,plain,
in @ sk3 @ sk2,
inference(cnf,[status(esa)],[3]) ).
thf(4,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ A )
| ~ ( in @ C @ ( sk1 @ A ) )
| ~ ( in @ C @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( sk1 @ A ) )
| ~ ( in @ C @ A )
| ( ( in @ B @ A )
!= ( in @ C @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[4]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( sk1 @ A ) )
| ~ ( in @ B @ A ) ),
inference(pattern_uni,[status(thm)],[49:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1613,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ sk3 @ sk2 )
!= ( in @ B @ ( sk1 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,52]) ).
thf(1675,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( sk3 != B )
| ( ( sk1 @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[1613]) ).
thf(1691,plain,
! [A: $i] :
( ~ ( in @ sk3 @ A )
| ( ( sk1 @ A )
!= sk2 ) ),
inference(simp,[status(thm)],[1675]) ).
thf(9137,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ C )
!= sk2 )
| ( ( in @ A @ ( setadjoin @ A @ B ) )
!= ( in @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[14,1691]) ).
thf(9138,plain,
! [A: $i] :
( ( sk1 @ ( setadjoin @ sk3 @ A ) )
!= sk2 ),
inference(pattern_uni,[status(thm)],[9137:[bind(A,$thf( sk3 )),bind(B,$thf( E )),bind(C,$thf( setadjoin @ sk3 @ E ))]]) ).
thf(9220,plain,
! [A: $i] :
( ( sk1 @ ( setadjoin @ sk3 @ A ) )
!= sk2 ),
inference(simp,[status(thm)],[9138]) ).
thf(9934,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
= A )
| ( B != sk2 )
| ( ( sk1 @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
!= ( sk1 @ ( setadjoin @ sk3 @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[453,9220]) ).
thf(9935,plain,
! [A: $i] :
( ( ( sk1 @ ( setadjoin @ sk3 @ ( setadjoin @ A @ emptyset ) ) )
= sk3 )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[9934:[bind(A,$thf( sk3 )),bind(B,$thf( D )),bind(C,$thf( setadjoin @ D @ emptyset ))]]) ).
thf(9968,plain,
( ( sk1 @ ( setadjoin @ sk3 @ ( setadjoin @ sk2 @ emptyset ) ) )
= sk3 ),
inference(simp,[status(thm)],[9935]) ).
thf(7,plain,
in @ sk2 @ sk3,
inference(cnf,[status(esa)],[3]) ).
thf(1657,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ sk2 @ sk3 )
!= ( in @ B @ ( sk1 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,52]) ).
thf(1683,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( sk2 != B )
| ( ( sk1 @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[1657]) ).
thf(1701,plain,
! [A: $i] :
( ~ ( in @ sk2 @ A )
| ( ( sk1 @ A )
!= sk3 ) ),
inference(simp,[status(thm)],[1683]) ).
thf(11771,plain,
! [A: $i] :
( ~ ( in @ sk2 @ A )
| ( ( sk1 @ ( setadjoin @ sk3 @ ( setadjoin @ sk2 @ emptyset ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9968,1701]) ).
thf(11772,plain,
~ ( in @ sk2 @ ( setadjoin @ sk3 @ ( setadjoin @ sk2 @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[11771:[bind(A,$thf( setadjoin @ sk3 @ ( setadjoin @ sk2 @ emptyset ) ))]]) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ ( setadjoin @ A @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ ( setadjoin @ A @ B ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(657,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( in @ E @ ( setadjoin @ C @ D ) )
| ( ( in @ A @ ( setadjoin @ A @ B ) )
!= ( in @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[14,15]) ).
thf(658,plain,
! [C: $i,B: $i,A: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[657:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( setadjoin @ F @ G )),bind(E,$thf( F ))]]) ).
thf(699,plain,
! [C: $i,B: $i,A: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ C ) ) ),
inference(simp,[status(thm)],[658]) ).
thf(11867,plain,
~ $true,
inference(rewrite,[status(thm)],[11772,699]) ).
thf(11868,plain,
$false,
inference(simp,[status(thm)],[11867]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SEU807^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.13 % Command : run_Leo-III %s %d SAT
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 21 17:05:10 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.14/0.99 % [INFO] Parsing done (109ms).
% 1.14/1.00 % [INFO] Running in sequential loop mode.
% 1.64/1.19 % [INFO] nitpick registered as external prover.
% 1.64/1.20 % [INFO] Scanning for conjecture ...
% 1.81/1.27 % [INFO] Found a conjecture (or negated_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 higher-order (TPTP THF).
% 1.81/1.29 % [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 ...
% 42.84/7.11 % [INFO] Killing All external provers ...
% 42.84/7.11 % Time passed: 6570ms (effective reasoning time: 6112ms)
% 42.84/7.11 % 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)>
% 42.84/7.11 % Axioms used in derivation (0):
% 42.84/7.11 % No. of inferences in proof: 41
% 42.84/7.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6570 ms resp. 6112 ms w/o parsing
% 42.84/7.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 42.84/7.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------