TSTP Solution File: KRS076+1 by Leo-III-SAT---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : KRS076+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 10:38:13 EDT 2024
% Result : Unsatisfiable 13.82s 3.48s
% Output : Refutation 13.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 73 ( 16 unt; 11 typ; 0 def)
% Number of atoms : 186 ( 33 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 466 ( 50 ~; 40 |; 33 &; 320 @)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 105 ( 0 ^ 90 !; 15 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
thf(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
thf(cowlThing_type,type,
cowlThing: $i > $o ).
thf(cp_type,type,
cp: $i > $o ).
thf(rf_type,type,
rf: $i > $i > $o ).
thf(rf1_type,type,
rf1: $i > $i > $o ).
thf(rinvF1_type,type,
rinvF1: $i > $i > $o ).
thf(rs_type,type,
rs: $i > $i > $o ).
thf(i2003_11_14_17_19_06193_type,type,
i2003_11_14_17_19_06193: $i ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: $i > $i > $i ).
thf(28,axiom,
cUnsatisfiable @ i2003_11_14_17_19_06193,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(149,plain,
cUnsatisfiable @ i2003_11_14_17_19_06193,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(21,axiom,
! [A: $i] :
( ( cUnsatisfiable @ A )
<=> ( ? [B: $i] :
( ( rf @ A @ B )
& ( cp @ B ) )
& ? [B: $i] :
( ( rf1 @ A @ B )
& ~ ( cp @ B )
& ! [C: $i] :
( ( rinvF1 @ B @ C )
=> ? [D: $i] :
( ( rs @ C @ D )
& ( cowlThing @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(113,plain,
! [A: $i] :
( ( ( cUnsatisfiable @ A )
=> ( ? [B: $i] :
( ( rf @ A @ B )
& ( cp @ B ) )
& ? [B: $i] :
( ( rf1 @ A @ B )
& ~ ( cp @ B )
& ! [C: $i] :
( ( rinvF1 @ B @ C )
=> ? [D: $i] :
( ( rs @ C @ D )
& ( cowlThing @ D ) ) ) ) ) )
& ( ( ? [B: $i] :
( ( rf @ A @ B )
& ( cp @ B ) )
& ? [B: $i] :
( ( rf1 @ A @ B )
& ~ ( cp @ B )
& ! [C: $i] :
( ( rinvF1 @ B @ C )
=> ? [D: $i] :
( ( rs @ C @ D )
& ( cowlThing @ D ) ) ) ) )
=> ( cUnsatisfiable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(114,plain,
( ! [A: $i] :
( ( cUnsatisfiable @ A )
=> ( ? [B: $i] :
( ( rf @ A @ B )
& ( cp @ B ) )
& ? [B: $i] :
( ( rf1 @ A @ B )
& ~ ( cp @ B )
& ! [C: $i] :
( ( rinvF1 @ B @ C )
=> ? [D: $i] :
( ( rs @ C @ D )
& ( cowlThing @ D ) ) ) ) ) )
& ! [A: $i] :
( ( ? [B: $i] :
( ( rf @ A @ B )
& ( cp @ B ) )
& ? [B: $i] :
( ( rf1 @ A @ B )
& ~ ( cp @ B )
& ! [C: $i] :
( ( rinvF1 @ B @ C )
=> ? [D: $i] :
( ( rs @ C @ D )
& ( cowlThing @ D ) ) ) ) )
=> ( cUnsatisfiable @ A ) ) ),
inference(miniscope,[status(thm)],[113]) ).
thf(119,plain,
! [A: $i] :
( ~ ( cUnsatisfiable @ A )
| ( rf1 @ A @ ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(194,plain,
! [A: $i] :
( ( rf1 @ A @ ( sk2 @ A ) )
| ( ( cUnsatisfiable @ i2003_11_14_17_19_06193 )
!= ( cUnsatisfiable @ A ) ) ),
inference(paramod_ordered,[status(thm)],[149,119]) ).
thf(195,plain,
rf1 @ i2003_11_14_17_19_06193 @ ( sk2 @ i2003_11_14_17_19_06193 ),
inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( i2003_11_14_17_19_06193 ))]]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( rinvF1 @ A @ B )
<=> ( rf1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(136,plain,
! [A: $i,B: $i] :
( ( ( rinvF1 @ A @ B )
=> ( rf1 @ B @ A ) )
& ( ( rf1 @ B @ A )
=> ( rinvF1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(137,plain,
( ! [A: $i,B: $i] :
( ( rinvF1 @ A @ B )
=> ( rf1 @ B @ A ) )
& ! [A: $i,B: $i] :
( ( rf1 @ B @ A )
=> ( rinvF1 @ A @ B ) ) ),
inference(miniscope,[status(thm)],[136]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( rf1 @ B @ A )
| ( rinvF1 @ A @ B ) ),
inference(cnf,[status(esa)],[137]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ~ ( rf1 @ B @ A )
| ( rinvF1 @ A @ B ) ),
inference(simp,[status(thm)],[138]) ).
thf(266,plain,
! [B: $i,A: $i] :
( ( rinvF1 @ A @ B )
| ( ( rf1 @ i2003_11_14_17_19_06193 @ ( sk2 @ i2003_11_14_17_19_06193 ) )
!= ( rf1 @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[195,140]) ).
thf(267,plain,
rinvF1 @ ( sk2 @ i2003_11_14_17_19_06193 ) @ i2003_11_14_17_19_06193,
inference(pattern_uni,[status(thm)],[266:[bind(A,$thf( sk2 @ i2003_11_14_17_19_06193 )),bind(B,$thf( i2003_11_14_17_19_06193 ))]]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ~ ( cUnsatisfiable @ A )
| ~ ( rinvF1 @ ( sk2 @ A ) @ B )
| ( rs @ B @ ( sk3 @ B @ A ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ~ ( rinvF1 @ ( sk2 @ A ) @ B )
| ( rs @ B @ ( sk3 @ B @ A ) )
| ( ( cUnsatisfiable @ i2003_11_14_17_19_06193 )
!= ( cUnsatisfiable @ A ) ) ),
inference(paramod_ordered,[status(thm)],[149,118]) ).
thf(202,plain,
! [A: $i] :
( ~ ( rinvF1 @ ( sk2 @ i2003_11_14_17_19_06193 ) @ A )
| ( rs @ A @ ( sk3 @ A @ i2003_11_14_17_19_06193 ) ) ),
inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( i2003_11_14_17_19_06193 ))]]) ).
thf(204,plain,
! [A: $i] :
( ~ ( rinvF1 @ ( sk2 @ i2003_11_14_17_19_06193 ) @ A )
| ( rs @ A @ ( sk3 @ A @ i2003_11_14_17_19_06193 ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(279,plain,
! [A: $i] :
( ( rs @ A @ ( sk3 @ A @ i2003_11_14_17_19_06193 ) )
| ( ( rinvF1 @ ( sk2 @ i2003_11_14_17_19_06193 ) @ i2003_11_14_17_19_06193 )
!= ( rinvF1 @ ( sk2 @ i2003_11_14_17_19_06193 ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[267,204]) ).
thf(280,plain,
rs @ i2003_11_14_17_19_06193 @ ( sk3 @ i2003_11_14_17_19_06193 @ i2003_11_14_17_19_06193 ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( i2003_11_14_17_19_06193 ))]]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( rs @ A @ B )
=> ( rf1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( rs @ A @ B )
=> ( rf1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ~ ( rs @ A @ B )
| ( rf1 @ A @ B ) ),
inference(cnf,[status(esa)],[150]) ).
thf(403,plain,
! [B: $i,A: $i] :
( ( rf1 @ A @ B )
| ( ( rs @ i2003_11_14_17_19_06193 @ ( sk3 @ i2003_11_14_17_19_06193 @ i2003_11_14_17_19_06193 ) )
!= ( rs @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[280,151]) ).
thf(404,plain,
rf1 @ i2003_11_14_17_19_06193 @ ( sk3 @ i2003_11_14_17_19_06193 @ i2003_11_14_17_19_06193 ),
inference(pattern_uni,[status(thm)],[403:[bind(A,$thf( i2003_11_14_17_19_06193 )),bind(B,$thf( sk3 @ i2003_11_14_17_19_06193 @ i2003_11_14_17_19_06193 ))]]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( rs @ A @ B )
=> ( rf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(152,plain,
! [A: $i,B: $i] :
( ( rs @ A @ B )
=> ( rf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ~ ( rs @ A @ B )
| ( rf @ A @ B ) ),
inference(cnf,[status(esa)],[152]) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( rf @ A @ B )
| ( ( rs @ i2003_11_14_17_19_06193 @ ( sk3 @ i2003_11_14_17_19_06193 @ i2003_11_14_17_19_06193 ) )
!= ( rs @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[280,153]) ).
thf(485,plain,
rf @ i2003_11_14_17_19_06193 @ ( sk3 @ i2003_11_14_17_19_06193 @ i2003_11_14_17_19_06193 ),
inference(pattern_uni,[status(thm)],[484:[bind(A,$thf( i2003_11_14_17_19_06193 )),bind(B,$thf( sk3 @ i2003_11_14_17_19_06193 @ i2003_11_14_17_19_06193 ))]]) ).
thf(117,plain,
! [A: $i] :
( ~ ( cUnsatisfiable @ A )
| ( rf @ A @ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(168,plain,
! [A: $i] :
( ( rf @ A @ ( sk1 @ A ) )
| ( ( cUnsatisfiable @ i2003_11_14_17_19_06193 )
!= ( cUnsatisfiable @ A ) ) ),
inference(paramod_ordered,[status(thm)],[149,117]) ).
thf(169,plain,
rf @ i2003_11_14_17_19_06193 @ ( sk1 @ i2003_11_14_17_19_06193 ),
inference(pattern_uni,[status(thm)],[168:[bind(A,$thf( i2003_11_14_17_19_06193 ))]]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rf @ A @ B )
& ( rf @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(125,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rf @ A @ B )
& ( rf @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rf @ A @ B )
| ~ ( rf @ A @ C )
| ( B = C ) ),
inference(cnf,[status(esa)],[125]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( rf @ A @ B )
| ~ ( rf @ A @ C ) ),
inference(lifteq,[status(thm)],[126]) ).
thf(601,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( rf @ A @ C )
| ( ( rf @ i2003_11_14_17_19_06193 @ ( sk1 @ i2003_11_14_17_19_06193 ) )
!= ( rf @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[169,127]) ).
thf(602,plain,
! [A: $i] :
( ( ( sk1 @ i2003_11_14_17_19_06193 )
= A )
| ~ ( rf @ i2003_11_14_17_19_06193 @ A ) ),
inference(pattern_uni,[status(thm)],[601:[bind(A,$thf( i2003_11_14_17_19_06193 )),bind(B,$thf( sk1 @ i2003_11_14_17_19_06193 )),bind(C,$thf( C ))]]) ).
thf(902,plain,
! [A: $i] :
( ( ( sk1 @ i2003_11_14_17_19_06193 )
= A )
| ~ ( rf @ i2003_11_14_17_19_06193 @ A ) ),
inference(simp,[status(thm)],[602]) ).
thf(1088,plain,
! [A: $i] :
( ( ( sk1 @ i2003_11_14_17_19_06193 )
= A )
| ( ( rf @ i2003_11_14_17_19_06193 @ ( sk3 @ i2003_11_14_17_19_06193 @ i2003_11_14_17_19_06193 ) )
!= ( rf @ i2003_11_14_17_19_06193 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[485,902]) ).
thf(1089,plain,
( ( sk3 @ i2003_11_14_17_19_06193 @ i2003_11_14_17_19_06193 )
= ( sk1 @ i2003_11_14_17_19_06193 ) ),
inference(pattern_uni,[status(thm)],[1088:[bind(A,$thf( sk3 @ i2003_11_14_17_19_06193 @ i2003_11_14_17_19_06193 ))]]) ).
thf(1255,plain,
rf1 @ i2003_11_14_17_19_06193 @ ( sk1 @ i2003_11_14_17_19_06193 ),
inference(rewrite,[status(thm)],[404,1089]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rf1 @ A @ B )
& ( rf1 @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(128,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rf1 @ A @ B )
& ( rf1 @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rf1 @ A @ B )
| ~ ( rf1 @ A @ C )
| ( B = C ) ),
inference(cnf,[status(esa)],[128]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( rf1 @ A @ B )
| ~ ( rf1 @ A @ C ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(1655,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( rf1 @ A @ C )
| ( ( rf1 @ i2003_11_14_17_19_06193 @ ( sk2 @ i2003_11_14_17_19_06193 ) )
!= ( rf1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[195,130]) ).
thf(1656,plain,
! [A: $i] :
( ( ( sk2 @ i2003_11_14_17_19_06193 )
= A )
| ~ ( rf1 @ i2003_11_14_17_19_06193 @ A ) ),
inference(pattern_uni,[status(thm)],[1655:[bind(A,$thf( i2003_11_14_17_19_06193 )),bind(B,$thf( sk2 @ i2003_11_14_17_19_06193 )),bind(C,$thf( C ))]]) ).
thf(1729,plain,
! [A: $i] :
( ( ( sk2 @ i2003_11_14_17_19_06193 )
= A )
| ~ ( rf1 @ i2003_11_14_17_19_06193 @ A ) ),
inference(simp,[status(thm)],[1656]) ).
thf(2987,plain,
! [A: $i] :
( ( ( sk2 @ i2003_11_14_17_19_06193 )
= A )
| ( ( rf1 @ i2003_11_14_17_19_06193 @ ( sk1 @ i2003_11_14_17_19_06193 ) )
!= ( rf1 @ i2003_11_14_17_19_06193 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1255,1729]) ).
thf(2988,plain,
( ( sk2 @ i2003_11_14_17_19_06193 )
= ( sk1 @ i2003_11_14_17_19_06193 ) ),
inference(pattern_uni,[status(thm)],[2987:[bind(A,$thf( sk1 @ i2003_11_14_17_19_06193 ))]]) ).
thf(121,plain,
! [A: $i] :
( ~ ( cUnsatisfiable @ A )
| ( cp @ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(159,plain,
! [A: $i] :
( ( cp @ ( sk1 @ A ) )
| ( ( cUnsatisfiable @ i2003_11_14_17_19_06193 )
!= ( cUnsatisfiable @ A ) ) ),
inference(paramod_ordered,[status(thm)],[149,121]) ).
thf(160,plain,
cp @ ( sk1 @ i2003_11_14_17_19_06193 ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( i2003_11_14_17_19_06193 ))]]) ).
thf(116,plain,
! [A: $i] :
( ~ ( cUnsatisfiable @ A )
| ~ ( cp @ ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(154,plain,
! [A: $i] :
( ~ ( cp @ ( sk2 @ A ) )
| ( ( cUnsatisfiable @ i2003_11_14_17_19_06193 )
!= ( cUnsatisfiable @ A ) ) ),
inference(paramod_ordered,[status(thm)],[149,116]) ).
thf(155,plain,
~ ( cp @ ( sk2 @ i2003_11_14_17_19_06193 ) ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( i2003_11_14_17_19_06193 ))]]) ).
thf(165,plain,
( ( cp @ ( sk2 @ i2003_11_14_17_19_06193 ) )
!= ( cp @ ( sk1 @ i2003_11_14_17_19_06193 ) ) ),
inference(paramod_ordered,[status(thm)],[160,155]) ).
thf(167,plain,
( ( sk2 @ i2003_11_14_17_19_06193 )
!= ( sk1 @ i2003_11_14_17_19_06193 ) ),
inference(simp,[status(thm)],[165]) ).
thf(3202,plain,
$false,
inference(simplifyReflect,[status(thm)],[2988,167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS076+1 : TPTP v8.1.2. Released v3.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n014.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 22:55:09 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.97/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/1.07 % [INFO] Parsing done (129ms).
% 1.17/1.08 % [INFO] Running in sequential loop mode.
% 1.62/1.28 % [INFO] nitpick registered as external prover.
% 1.62/1.28 % [INFO] Scanning for conjecture ...
% 1.81/1.31 % [INFO] 30 axioms and no conjecture found.
% 1.99/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 1.99/1.38 % [INFO] Type checking passed.
% 1.99/1.39 % [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 ...
% 13.82/3.47 % [INFO] Killing All external provers ...
% 13.82/3.48 % Time passed: 2856ms (effective reasoning time: 2395ms)
% 13.82/3.48 % Axioms used in derivation (7): axiom_10, axiom_2, axiom_6, axiom_3, axiom_11, axiom_9, axiom_4
% 13.82/3.48 % No. of inferences in proof: 62
% 13.82/3.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2856 ms resp. 2395 ms w/o parsing
% 13.82/3.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.82/3.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------