TSTP Solution File: SEU807^2 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---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 THM
% Computer : n024.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 15:28:58 EDT 2024
% Result : Theorem 3.10s 1.82s
% Output : Refutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 9 ( 6 unt; 0 typ; 5 def)
% Number of atoms : 57 ( 15 equ; 0 cnn)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 109 ( 7 ~; 2 |; 4 &; 68 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 38 ( 0 ^ 32 !; 6 ?; 38 :)
% 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(1,conjecture,
( foundationAx
=> ( setadjoinIL
=> ( setadjoinIR
=> ( in__Cong
=> ( upairset2E
=> ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/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(18,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU807^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n024.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 17:04:25 EDT 2024
% 0.13/0.34 % CPUTime :
% 1.01/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.10/1.01 % [INFO] Parsing done (111ms).
% 1.34/1.02 % [INFO] Running in sequential loop mode.
% 1.83/1.31 % [INFO] eprover registered as external prover.
% 1.83/1.32 % [INFO] Scanning for conjecture ...
% 1.99/1.41 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.99/1.43 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.99/1.43 % [INFO] Problem is higher-order (TPTP THF).
% 1.99/1.43 % [INFO] Type checking passed.
% 1.99/1.44 % [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 ...
% 3.10/1.81 % External prover 'e' found a proof!
% 3.10/1.81 % [INFO] Killing All external provers ...
% 3.10/1.82 % Time passed: 1278ms (effective reasoning time: 792ms)
% 3.10/1.82 % 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)>
% 3.10/1.82 % Axioms used in derivation (0):
% 3.10/1.82 % No. of inferences in proof: 4
% 3.10/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1278 ms resp. 792 ms w/o parsing
% 3.13/1.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.13/1.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------