TSTP Solution File: SYN266-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYN266-1 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 : Fri May 19 12:28:08 EDT 2023
% Result : Unsatisfiable 66.38s 28.78s
% Output : Refutation 66.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 25
% Syntax : Number of formulae : 72 ( 19 unt; 13 typ; 0 def)
% Number of atoms : 129 ( 9 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 382 ( 57 ~; 52 |; 0 &; 273 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 99 ( 0 ^; 99 !; 0 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(p3_type,type,
p3: $i > $i > $i > $o ).
thf(b_type,type,
b: $i ).
thf(e_type,type,
e: $i ).
thf(m3_type,type,
m3: $i > $i > $i > $o ).
thf(d_type,type,
d: $i ).
thf(p0_type,type,
p0: $i > $i > $o ).
thf(p2_type,type,
p2: $i > $i > $i > $o ).
thf(n2_type,type,
n2: $i > $o ).
thf(p1_type,type,
p1: $i > $i > $i > $o ).
thf(s0_type,type,
s0: $i > $o ).
thf(m1_type,type,
m1: $i > $i > $i > $o ).
thf(n0_type,type,
n0: $i > $i > $o ).
thf(k1_type,type,
k1: $i > $o ).
thf(14,axiom,
! [A: $i] :
( ( m3 @ A @ A @ A )
| ~ ( n2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_236) ).
thf(396,plain,
! [A: $i] :
( ( m3 @ A @ A @ A )
| ~ ( n2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(397,plain,
! [A: $i] :
( ( m3 @ A @ A @ A )
| ~ ( n2 @ A ) ),
inference(cnf,[status(esa)],[396]) ).
thf(264,axiom,
! [A: $i] : ( p0 @ b @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(877,plain,
! [A: $i] : ( p0 @ b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( p1 @ A @ A @ A )
| ~ ( p0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_085) ).
thf(609,plain,
! [B: $i,A: $i] :
( ( p1 @ A @ A @ A )
| ~ ( p0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(610,plain,
! [B: $i,A: $i] :
( ( p1 @ A @ A @ A )
| ~ ( p0 @ B @ A ) ),
inference(cnf,[status(esa)],[609]) ).
thf(10065,plain,
! [C: $i,B: $i,A: $i] :
( ( p1 @ B @ B @ B )
| ( ( p0 @ b @ A )
!= ( p0 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[877,610]) ).
thf(10066,plain,
! [A: $i] : ( p1 @ A @ A @ A ),
inference(pattern_uni,[status(thm)],[10065:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( b ))]]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( n2 @ A )
| ~ ( p1 @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_137) ).
thf(547,plain,
! [C: $i,B: $i,A: $i] :
( ( n2 @ A )
| ~ ( p1 @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(548,plain,
! [C: $i,B: $i,A: $i] :
( ( n2 @ A )
| ~ ( p1 @ B @ C @ A ) ),
inference(cnf,[status(esa)],[547]) ).
thf(10093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( n2 @ B )
| ( ( p1 @ A @ A @ A )
!= ( p1 @ C @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10066,548]) ).
thf(10094,plain,
! [A: $i] : ( n2 @ A ),
inference(pattern_uni,[status(thm)],[10093:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(10106,plain,
! [A: $i] :
( ( m3 @ A @ A @ A )
| ~ $true ),
inference(rewrite,[status(thm)],[397,10094]) ).
thf(10107,plain,
! [A: $i] : ( m3 @ A @ A @ A ),
inference(simp,[status(thm)],[10106]) ).
thf(324,axiom,
n0 @ d @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(985,plain,
n0 @ d @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( k1 @ A )
| ~ ( n0 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_001) ).
thf(599,plain,
! [B: $i,A: $i] :
( ( k1 @ A )
| ~ ( n0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(600,plain,
! [B: $i,A: $i] :
( ( k1 @ A )
| ~ ( n0 @ B @ A ) ),
inference(cnf,[status(esa)],[599]) ).
thf(1814,plain,
! [B: $i,A: $i] :
( ( k1 @ A )
| ( ( n0 @ d @ b )
!= ( n0 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[985,600]) ).
thf(1815,plain,
k1 @ b,
inference(pattern_uni,[status(thm)],[1814:[bind(A,$thf( b )),bind(B,$thf( d ))]]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( m1 @ A @ B @ A )
| ~ ( p0 @ A @ B )
| ~ ( s0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_029) ).
thf(455,plain,
! [B: $i,A: $i] :
( ( m1 @ A @ B @ A )
| ~ ( p0 @ A @ B )
| ~ ( s0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(456,plain,
! [B: $i,A: $i] :
( ( m1 @ A @ B @ A )
| ~ ( p0 @ A @ B )
| ~ ( s0 @ A ) ),
inference(cnf,[status(esa)],[455]) ).
thf(4457,plain,
! [C: $i,B: $i,A: $i] :
( ( m1 @ B @ C @ B )
| ~ ( s0 @ B )
| ( ( p0 @ b @ A )
!= ( p0 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[877,456]) ).
thf(4458,plain,
! [A: $i] :
( ( m1 @ b @ A @ b )
| ~ ( s0 @ b ) ),
inference(pattern_uni,[status(thm)],[4457:[bind(A,$thf( A )),bind(B,$thf( b )),bind(C,$thf( A ))]]) ).
thf(258,axiom,
s0 @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(866,plain,
s0 @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(5012,plain,
! [A: $i] :
( ( m1 @ b @ A @ b )
| ~ $true ),
inference(rewrite,[status(thm)],[4458,866]) ).
thf(5013,plain,
! [A: $i] : ( m1 @ b @ A @ b ),
inference(simp,[status(thm)],[5012]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ( p2 @ A @ B @ A )
| ~ ( m1 @ B @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_176) ).
thf(641,plain,
! [B: $i,A: $i] :
( ( p2 @ A @ B @ A )
| ~ ( m1 @ B @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(642,plain,
! [B: $i,A: $i] :
( ( p2 @ A @ B @ A )
| ~ ( m1 @ B @ A @ B ) ),
inference(cnf,[status(esa)],[641]) ).
thf(13063,plain,
! [C: $i,B: $i,A: $i] :
( ( p2 @ B @ C @ B )
| ( ( m1 @ b @ A @ b )
!= ( m1 @ C @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5013,642]) ).
thf(13064,plain,
! [A: $i] : ( p2 @ A @ b @ A ),
inference(pattern_uni,[status(thm)],[13063:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( b ))]]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( p2 @ A @ B @ B )
| ~ ( k1 @ C )
| ~ ( p2 @ e @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_155) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] :
( ( p2 @ A @ B @ B )
| ~ ( k1 @ C )
| ~ ( p2 @ e @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(952,plain,
! [C: $i,B: $i,A: $i] :
( ( p2 @ A @ B @ B )
| ~ ( k1 @ C )
| ~ ( p2 @ e @ A @ B ) ),
inference(cnf,[status(esa)],[951]) ).
thf(31114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( p2 @ B @ C @ C )
| ~ ( k1 @ D )
| ( ( p2 @ A @ b @ A )
!= ( p2 @ e @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[13064,952]) ).
thf(31115,plain,
! [A: $i] :
( ( p2 @ b @ e @ e )
| ~ ( k1 @ A ) ),
inference(pattern_uni,[status(thm)],[31114:[bind(A,$thf( e )),bind(B,$thf( b )),bind(C,$thf( e ))]]) ).
thf(31192,plain,
! [A: $i] :
( ( p2 @ b @ e @ e )
| ~ ( k1 @ A ) ),
inference(simp,[status(thm)],[31115]) ).
thf(31401,plain,
! [A: $i] :
( ( p2 @ b @ e @ e )
| ( ( k1 @ b )
!= ( k1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1815,31192]) ).
thf(31402,plain,
p2 @ b @ e @ e,
inference(pattern_uni,[status(thm)],[31401:[bind(A,$thf( b ))]]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( p3 @ A @ B @ B )
| ~ ( m3 @ B @ C @ D )
| ~ ( p2 @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_251) ).
thf(974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( p3 @ A @ B @ B )
| ~ ( m3 @ B @ C @ D )
| ~ ( p2 @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( p3 @ A @ B @ B )
| ~ ( m3 @ B @ C @ D )
| ~ ( p2 @ A @ B @ D ) ),
inference(cnf,[status(esa)],[974]) ).
thf(32539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( p3 @ A @ B @ B )
| ~ ( m3 @ B @ C @ D )
| ( ( p2 @ b @ e @ e )
!= ( p2 @ A @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[31402,975]) ).
thf(32540,plain,
! [A: $i] :
( ( p3 @ b @ e @ e )
| ~ ( m3 @ e @ A @ e ) ),
inference(pattern_uni,[status(thm)],[32539:[bind(A,$thf( b )),bind(B,$thf( e )),bind(C,$thf( C )),bind(D,$thf( e ))]]) ).
thf(32588,plain,
! [A: $i] :
( ( p3 @ b @ e @ e )
| ~ ( m3 @ e @ A @ e ) ),
inference(simp,[status(thm)],[32540]) ).
thf(1,negated_conjecture,
~ ( p3 @ b @ e @ e ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(370,plain,
~ ( p3 @ b @ e @ e ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(371,plain,
~ ( p3 @ b @ e @ e ),
inference(polarity_switch,[status(thm)],[370]) ).
thf(42216,plain,
! [A: $i] :
( $false
| ~ ( m3 @ e @ A @ e ) ),
inference(rewrite,[status(thm)],[32588,371]) ).
thf(42217,plain,
! [A: $i] :
~ ( m3 @ e @ A @ e ),
inference(simp,[status(thm)],[42216]) ).
thf(42225,plain,
! [B: $i,A: $i] :
( ( m3 @ A @ A @ A )
!= ( m3 @ e @ B @ e ) ),
inference(paramod_ordered,[status(thm)],[10107,42217]) ).
thf(42226,plain,
$false,
inference(pattern_uni,[status(thm)],[42225:[bind(A,$thf( e )),bind(B,$thf( e ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN266-1 : TPTP v8.1.2. Released v1.1.0.
% 0.07/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 19:59:14 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.84/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.03 % [INFO] Parsing done (202ms).
% 1.53/1.04 % [INFO] Running in sequential loop mode.
% 2.18/1.24 % [INFO] eprover registered as external prover.
% 2.26/1.24 % [INFO] cvc4 registered as external prover.
% 2.26/1.24 % [INFO] Scanning for conjecture ...
% 2.49/1.33 % [INFO] Found a conjecture and 368 axioms. Running axiom selection ...
% 2.73/1.42 % [INFO] Axiom selection finished. Selected 368 axioms (removed 0 axioms).
% 3.24/1.53 % [INFO] Problem is propositional (TPTP CNF).
% 3.24/1.53 % [INFO] Type checking passed.
% 3.24/1.54 % [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 ...
% 66.38/28.78 % [INFO] Killing All external provers ...
% 66.38/28.78 % Time passed: 28267ms (effective reasoning time: 27733ms)
% 66.38/28.78 % 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)>
% 66.38/28.78 % Axioms used in derivation (11): axiom_7, rule_085, rule_176, rule_137, rule_251, rule_155, axiom_5, axiom_14, rule_001, rule_029, rule_236
% 66.38/28.78 % No. of inferences in proof: 59
% 66.38/28.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 28267 ms resp. 27733 ms w/o parsing
% 66.50/28.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 66.50/28.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------