TSTP Solution File: SET716^4 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SET716^4 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 10:50:24 EDT 2024
% Result : Theorem 3.26s 1.81s
% Output : Refutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 31 ( 13 unt; 8 typ; 2 def)
% Number of atoms : 42 ( 34 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 90 ( 11 ~; 7 |; 3 &; 62 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 32 ( 4 ^ 28 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(fun_composition_type,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(fun_composition_def,definition,
( fun_composition
= ( ^ [A: $i > $i,B: $i > $i,C: $i] : ( B @ ( A @ C ) ) ) ) ).
thf(fun_injective_type,type,
fun_injective: ( $i > $i ) > $o ).
thf(fun_injective_def,definition,
( fun_injective
= ( ^ [A: $i > $i] :
! [B: $i,C: $i] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(1,conjecture,
! [A: $i > $i,B: $i > $i] :
( ( ( fun_injective @ A )
& ( fun_injective @ B ) )
=> ( fun_injective @ ( fun_composition @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i,B: $i > $i] :
( ( ( fun_injective @ A )
& ( fun_injective @ B ) )
=> ( fun_injective @ ( fun_composition @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i,B: $i > $i] :
( ( ! [C: $i,D: $i] :
( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) )
& ! [C: $i,D: $i] :
( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ C ) )
= ( B @ ( A @ D ) ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( sk2 @ ( sk1 @ sk3 ) )
= ( sk2 @ ( sk1 @ sk4 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
( ( sk2 @ ( sk1 @ sk4 ) )
= ( sk2 @ ( sk1 @ sk3 ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ A )
!= ( sk2 @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ A )
!= ( sk2 @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ A )
!= ( sk2 @ B ) )
| ( A = B ) ),
inference(simp,[status(thm)],[10]) ).
thf(12,plain,
! [A: $i] :
( ( sk5 @ ( sk2 @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(sk2),[sk5])]) ).
thf(15,plain,
! [A: $i] :
( ( ( sk5 @ ( sk2 @ ( sk1 @ sk3 ) ) )
= A )
| ( ( sk2 @ ( sk1 @ sk4 ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,12]) ).
thf(16,plain,
( ( sk5 @ ( sk2 @ ( sk1 @ sk3 ) ) )
= ( sk1 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( sk1 @ sk4 ))]]) ).
thf(17,plain,
( ( sk1 @ sk4 )
= ( sk1 @ sk3 ) ),
inference(rewrite,[status(thm)],[16,12]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ A )
!= ( sk1 @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ A )
!= ( sk1 @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(14,plain,
! [A: $i] :
( ( sk6 @ ( sk1 @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(sk1),[sk6])]) ).
thf(29,plain,
! [A: $i] :
( ( ( sk6 @ ( sk1 @ sk3 ) )
= A )
| ( ( sk1 @ sk4 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17,14]) ).
thf(30,plain,
( ( sk6 @ ( sk1 @ sk3 ) )
= sk4 ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( sk4 ))]]) ).
thf(31,plain,
sk4 = sk3,
inference(rewrite,[status(thm)],[30,14]) ).
thf(4,plain,
sk3 != sk4,
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
sk4 != sk3,
inference(lifteq,[status(thm)],[4]) ).
thf(32,plain,
$false,
inference(simplifyReflect,[status(thm)],[31,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET716^4 : TPTP v8.1.2. Released v3.6.0.
% 0.16/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n018.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 20:46:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.99/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.39/1.04 % [INFO] Parsing done (139ms).
% 1.39/1.05 % [INFO] Running in sequential loop mode.
% 1.85/1.27 % [INFO] nitpick registered as external prover.
% 1.85/1.27 % [INFO] Scanning for conjecture ...
% 2.04/1.34 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 2.04/1.36 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/1.36 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.36 % [INFO] Type checking passed.
% 2.19/1.37 % [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 ...
% 3.26/1.80 % [INFO] Killing All external provers ...
% 3.26/1.81 % Time passed: 1273ms (effective reasoning time: 752ms)
% 3.26/1.81 % 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)>
% 3.26/1.81 % Axioms used in derivation (0):
% 3.26/1.81 % No. of inferences in proof: 21
% 3.26/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1273 ms resp. 752 ms w/o parsing
% 3.33/1.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.33/1.84 % [INFO] Killing All external provers ...
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