TSTP Solution File: KRS122+1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : KRS122+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 May 20 23:19:17 EDT 2024
% Result : Unsatisfiable 7.79s 2.65s
% Output : Refutation 7.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 20
% Syntax : Number of formulae : 77 ( 15 unt; 12 typ; 0 def)
% Number of atoms : 192 ( 22 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 453 ( 58 ~; 37 |; 29 &; 292 @)
% ( 6 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 0 ^ 86 !; 20 ?; 106 :)
% Comments :
%------------------------------------------------------------------------------
thf(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
thf(ca_Ax2_type,type,
ca_Ax2: $i > $o ).
thf(ca_Vx3_type,type,
ca_Vx3: $i > $o ).
thf(cp1_type,type,
cp1: $i > $o ).
thf(cp1xcomp_type,type,
cp1xcomp: $i > $o ).
thf(ra_Px1_type,type,
ra_Px1: $i > $i > $o ).
thf(rf_type,type,
rf: $i > $i > $o ).
thf(rinvF_type,type,
rinvF: $i > $i > $o ).
thf(i2003_11_14_17_21_55116_type,type,
i2003_11_14_17_21_55116: $i ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(31,axiom,
cUnsatisfiable @ i2003_11_14_17_21_55116,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
thf(163,plain,
cUnsatisfiable @ i2003_11_14_17_21_55116,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(22,axiom,
! [A: $i] :
( ( cUnsatisfiable @ A )
<=> ? [B: $i] :
( ( rf @ A @ B )
& ( ca_Ax2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(118,plain,
! [A: $i] :
( ( ( cUnsatisfiable @ A )
=> ? [B: $i] :
( ( rf @ A @ B )
& ( ca_Ax2 @ B ) ) )
& ( ? [B: $i] :
( ( rf @ A @ B )
& ( ca_Ax2 @ B ) )
=> ( cUnsatisfiable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(119,plain,
( ! [A: $i] :
( ( cUnsatisfiable @ A )
=> ? [B: $i] :
( ( rf @ A @ B )
& ( ca_Ax2 @ B ) ) )
& ! [A: $i] :
( ? [B: $i] :
( ( rf @ A @ B )
& ( ca_Ax2 @ B ) )
=> ( cUnsatisfiable @ A ) ) ),
inference(miniscope,[status(thm)],[118]) ).
thf(121,plain,
! [A: $i] :
( ~ ( cUnsatisfiable @ A )
| ( rf @ A @ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(176,plain,
! [A: $i] :
( ( rf @ A @ ( sk1 @ A ) )
| ( ( cUnsatisfiable @ i2003_11_14_17_21_55116 )
!= ( cUnsatisfiable @ A ) ) ),
inference(paramod_ordered,[status(thm)],[163,121]) ).
thf(177,plain,
rf @ i2003_11_14_17_21_55116 @ ( sk1 @ i2003_11_14_17_21_55116 ),
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( i2003_11_14_17_21_55116 ))]]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( rinvF @ A @ B )
<=> ( rf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(151,plain,
! [A: $i,B: $i] :
( ( ( rinvF @ A @ B )
=> ( rf @ B @ A ) )
& ( ( rf @ B @ A )
=> ( rinvF @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(152,plain,
( ! [A: $i,B: $i] :
( ( rinvF @ A @ B )
=> ( rf @ B @ A ) )
& ! [A: $i,B: $i] :
( ( rf @ B @ A )
=> ( rinvF @ A @ B ) ) ),
inference(miniscope,[status(thm)],[151]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ~ ( rf @ B @ A )
| ( rinvF @ A @ B ) ),
inference(cnf,[status(esa)],[152]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ~ ( rf @ B @ A )
| ( rinvF @ A @ B ) ),
inference(simp,[status(thm)],[153]) ).
thf(344,plain,
! [B: $i,A: $i] :
( ( rinvF @ A @ B )
| ( ( rf @ i2003_11_14_17_21_55116 @ ( sk1 @ i2003_11_14_17_21_55116 ) )
!= ( rf @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[177,155]) ).
thf(345,plain,
rinvF @ ( sk1 @ i2003_11_14_17_21_55116 ) @ i2003_11_14_17_21_55116,
inference(pattern_uni,[status(thm)],[344:[bind(A,$thf( sk1 @ i2003_11_14_17_21_55116 )),bind(B,$thf( i2003_11_14_17_21_55116 ))]]) ).
thf(122,plain,
! [A: $i] :
( ~ ( cUnsatisfiable @ A )
| ( ca_Ax2 @ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(173,plain,
! [A: $i] :
( ( ca_Ax2 @ ( sk1 @ A ) )
| ( ( cUnsatisfiable @ i2003_11_14_17_21_55116 )
!= ( cUnsatisfiable @ A ) ) ),
inference(paramod_ordered,[status(thm)],[163,122]) ).
thf(174,plain,
ca_Ax2 @ ( sk1 @ i2003_11_14_17_21_55116 ),
inference(pattern_uni,[status(thm)],[173:[bind(A,$thf( i2003_11_14_17_21_55116 ))]]) ).
thf(25,axiom,
! [A: $i] :
( ( ca_Ax2 @ A )
<=> ( ( cp1 @ A )
& ! [B: $i] :
( ( rinvF @ A @ B )
=> ( ca_Vx3 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(134,plain,
! [A: $i] :
( ( ( ca_Ax2 @ A )
=> ( ( cp1 @ A )
& ! [B: $i] :
( ( rinvF @ A @ B )
=> ( ca_Vx3 @ B ) ) ) )
& ( ( ( cp1 @ A )
& ! [B: $i] :
( ( rinvF @ A @ B )
=> ( ca_Vx3 @ B ) ) )
=> ( ca_Ax2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(135,plain,
( ! [A: $i] :
( ( ca_Ax2 @ A )
=> ( ( cp1 @ A )
& ! [B: $i] :
( ( rinvF @ A @ B )
=> ( ca_Vx3 @ B ) ) ) )
& ! [A: $i] :
( ( ( cp1 @ A )
& ! [B: $i] :
( ( rinvF @ A @ B )
=> ( ca_Vx3 @ B ) ) )
=> ( ca_Ax2 @ A ) ) ),
inference(miniscope,[status(thm)],[134]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ~ ( ca_Ax2 @ A )
| ~ ( rinvF @ A @ B )
| ( ca_Vx3 @ B ) ),
inference(cnf,[status(esa)],[135]) ).
thf(227,plain,
! [B: $i,A: $i] :
( ~ ( rinvF @ A @ B )
| ( ca_Vx3 @ B )
| ( ( ca_Ax2 @ ( sk1 @ i2003_11_14_17_21_55116 ) )
!= ( ca_Ax2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[174,139]) ).
thf(228,plain,
! [A: $i] :
( ~ ( rinvF @ ( sk1 @ i2003_11_14_17_21_55116 ) @ A )
| ( ca_Vx3 @ A ) ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( sk1 @ i2003_11_14_17_21_55116 )),bind(B,$thf( B ))]]) ).
thf(231,plain,
! [A: $i] :
( ~ ( rinvF @ ( sk1 @ i2003_11_14_17_21_55116 ) @ A )
| ( ca_Vx3 @ A ) ),
inference(simp,[status(thm)],[228]) ).
thf(363,plain,
! [A: $i] :
( ( ca_Vx3 @ A )
| ( ( rinvF @ ( sk1 @ i2003_11_14_17_21_55116 ) @ i2003_11_14_17_21_55116 )
!= ( rinvF @ ( sk1 @ i2003_11_14_17_21_55116 ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[345,231]) ).
thf(364,plain,
ca_Vx3 @ i2003_11_14_17_21_55116,
inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( i2003_11_14_17_21_55116 ))]]) ).
thf(26,axiom,
! [A: $i] :
( ( ca_Vx3 @ A )
<=> ? [B: $i] :
( ( rf @ A @ B )
& ( cp1xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(142,plain,
! [A: $i] :
( ( ( ca_Vx3 @ A )
=> ? [B: $i] :
( ( rf @ A @ B )
& ( cp1xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rf @ A @ B )
& ( cp1xcomp @ B ) )
=> ( ca_Vx3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(143,plain,
( ! [A: $i] :
( ( ca_Vx3 @ A )
=> ? [B: $i] :
( ( rf @ A @ B )
& ( cp1xcomp @ B ) ) )
& ! [A: $i] :
( ? [B: $i] :
( ( rf @ A @ B )
& ( cp1xcomp @ B ) )
=> ( ca_Vx3 @ A ) ) ),
inference(miniscope,[status(thm)],[142]) ).
thf(145,plain,
! [A: $i] :
( ~ ( ca_Vx3 @ A )
| ( rf @ A @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(378,plain,
! [A: $i] :
( ( rf @ A @ ( sk5 @ A ) )
| ( ( ca_Vx3 @ i2003_11_14_17_21_55116 )
!= ( ca_Vx3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[364,145]) ).
thf(379,plain,
rf @ i2003_11_14_17_21_55116 @ ( sk5 @ i2003_11_14_17_21_55116 ),
inference(pattern_uni,[status(thm)],[378:[bind(A,$thf( i2003_11_14_17_21_55116 ))]]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rf @ A @ B )
& ( rf @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(148,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rf @ A @ B )
& ( rf @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(149,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rf @ A @ B )
| ~ ( rf @ A @ C )
| ( B = C ) ),
inference(cnf,[status(esa)],[148]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( rf @ A @ B )
| ~ ( rf @ A @ C ) ),
inference(lifteq,[status(thm)],[149]) ).
thf(146,plain,
! [A: $i] :
( ~ ( ca_Vx3 @ A )
| ( cp1xcomp @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(24,axiom,
! [A: $i] :
( ( cp1xcomp @ A )
<=> ? [B: $i] : ( ra_Px1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(129,plain,
! [A: $i] :
( ( ( cp1xcomp @ A )
=> ? [B: $i] : ( ra_Px1 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px1 @ A @ B )
=> ( cp1xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(130,plain,
( ! [A: $i] :
( ( cp1xcomp @ A )
=> ? [B: $i] : ( ra_Px1 @ A @ B ) )
& ! [A: $i] :
( ? [B: $i] : ( ra_Px1 @ A @ B )
=> ( cp1xcomp @ A ) ) ),
inference(miniscope,[status(thm)],[129]) ).
thf(132,plain,
! [A: $i] :
( ~ ( cp1xcomp @ A )
| ( ra_Px1 @ A @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[130]) ).
thf(138,plain,
! [A: $i] :
( ~ ( ca_Ax2 @ A )
| ( cp1 @ A ) ),
inference(cnf,[status(esa)],[135]) ).
thf(178,plain,
! [A: $i] :
( ( cp1 @ A )
| ( ( ca_Ax2 @ ( sk1 @ i2003_11_14_17_21_55116 ) )
!= ( ca_Ax2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[174,138]) ).
thf(179,plain,
cp1 @ ( sk1 @ i2003_11_14_17_21_55116 ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( sk1 @ i2003_11_14_17_21_55116 ))]]) ).
thf(23,axiom,
! [A: $i] :
( ( cp1 @ A )
<=> ~ ? [B: $i] : ( ra_Px1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(124,plain,
! [A: $i] :
( ( ( cp1 @ A )
=> ~ ? [B: $i] : ( ra_Px1 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px1 @ A @ B )
=> ( cp1 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(125,plain,
( ! [A: $i] :
( ( cp1 @ A )
=> ~ ? [B: $i] : ( ra_Px1 @ A @ B ) )
& ! [A: $i] :
( ~ ? [B: $i] : ( ra_Px1 @ A @ B )
=> ( cp1 @ A ) ) ),
inference(miniscope,[status(thm)],[124]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ~ ( cp1 @ A )
| ~ ( ra_Px1 @ A @ B ) ),
inference(cnf,[status(esa)],[125]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ~ ( ra_Px1 @ A @ B )
| ( ( cp1 @ ( sk1 @ i2003_11_14_17_21_55116 ) )
!= ( cp1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[179,127]) ).
thf(183,plain,
! [A: $i] :
~ ( ra_Px1 @ ( sk1 @ i2003_11_14_17_21_55116 ) @ A ),
inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( sk1 @ i2003_11_14_17_21_55116 )),bind(B,$thf( B ))]]) ).
thf(184,plain,
! [A: $i] :
~ ( ra_Px1 @ ( sk1 @ i2003_11_14_17_21_55116 ) @ A ),
inference(simp,[status(thm)],[183]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ~ ( cp1xcomp @ A )
| ( ( ra_Px1 @ A @ ( sk3 @ A ) )
!= ( ra_Px1 @ ( sk1 @ i2003_11_14_17_21_55116 ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[132,184]) ).
thf(248,plain,
~ ( cp1xcomp @ ( sk1 @ i2003_11_14_17_21_55116 ) ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( sk1 @ i2003_11_14_17_21_55116 )),bind(B,$thf( sk3 @ ( sk1 @ i2003_11_14_17_21_55116 ) ))]]) ).
thf(265,plain,
! [A: $i] :
( ~ ( ca_Vx3 @ A )
| ( ( cp1xcomp @ ( sk5 @ A ) )
!= ( cp1xcomp @ ( sk1 @ i2003_11_14_17_21_55116 ) ) ) ),
inference(paramod_ordered,[status(thm)],[146,248]) ).
thf(266,plain,
! [A: $i] :
( ~ ( ca_Vx3 @ A )
| ( ( sk5 @ A )
!= ( sk1 @ i2003_11_14_17_21_55116 ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(375,plain,
! [A: $i] :
( ( ( sk5 @ A )
!= ( sk1 @ i2003_11_14_17_21_55116 ) )
| ( ( ca_Vx3 @ i2003_11_14_17_21_55116 )
!= ( ca_Vx3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[364,266]) ).
thf(376,plain,
( ( sk5 @ i2003_11_14_17_21_55116 )
!= ( sk1 @ i2003_11_14_17_21_55116 ) ),
inference(pattern_uni,[status(thm)],[375:[bind(A,$thf( i2003_11_14_17_21_55116 ))]]) ).
thf(496,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rf @ A @ B )
| ~ ( rf @ A @ C )
| ( C
!= ( sk1 @ i2003_11_14_17_21_55116 ) )
| ( B
!= ( sk5 @ i2003_11_14_17_21_55116 ) ) ),
inference(paramod_ordered,[status(thm)],[150,376]) ).
thf(497,plain,
! [B: $i,A: $i] :
( ~ ( rf @ A @ ( sk5 @ i2003_11_14_17_21_55116 ) )
| ~ ( rf @ A @ B )
| ( B
!= ( sk1 @ i2003_11_14_17_21_55116 ) ) ),
inference(pattern_uni,[status(thm)],[496:[bind(A,$thf( A )),bind(B,$thf( sk5 @ i2003_11_14_17_21_55116 )),bind(C,$thf( C ))]]) ).
thf(700,plain,
! [A: $i] :
( ~ ( rf @ A @ ( sk5 @ i2003_11_14_17_21_55116 ) )
| ~ ( rf @ A @ ( sk1 @ i2003_11_14_17_21_55116 ) ) ),
inference(simp,[status(thm)],[497]) ).
thf(857,plain,
! [A: $i] :
( ~ ( rf @ A @ ( sk1 @ i2003_11_14_17_21_55116 ) )
| ( ( rf @ i2003_11_14_17_21_55116 @ ( sk5 @ i2003_11_14_17_21_55116 ) )
!= ( rf @ A @ ( sk5 @ i2003_11_14_17_21_55116 ) ) ) ),
inference(paramod_ordered,[status(thm)],[379,700]) ).
thf(858,plain,
~ ( rf @ i2003_11_14_17_21_55116 @ ( sk1 @ i2003_11_14_17_21_55116 ) ),
inference(pattern_uni,[status(thm)],[857:[bind(A,$thf( i2003_11_14_17_21_55116 ))]]) ).
thf(944,plain,
~ $true,
inference(rewrite,[status(thm)],[858,177]) ).
thf(945,plain,
$false,
inference(simp,[status(thm)],[944]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS122+1 : TPTP v8.2.0. Released v3.1.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n028.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 : Sat May 18 22:11:08 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.08/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.37/1.08 % [INFO] Parsing done (137ms).
% 1.46/1.09 % [INFO] Running in sequential loop mode.
% 1.84/1.30 % [INFO] nitpick registered as external prover.
% 1.84/1.30 % [INFO] Scanning for conjecture ...
% 1.84/1.33 % [INFO] 31 axioms and no conjecture found.
% 2.04/1.40 % [INFO] Problem is first-order (TPTP FOF).
% 2.04/1.40 % [INFO] Type checking passed.
% 2.04/1.41 % [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 ...
% 7.53/2.65 % [INFO] Killing All external provers ...
% 7.79/2.65 % Time passed: 2090ms (effective reasoning time: 1561ms)
% 7.79/2.65 % Axioms used in derivation (8): axiom_7, axiom_2, axiom_6, axiom_3, axiom_8, axiom_5, axiom_11, axiom_4
% 7.79/2.65 % No. of inferences in proof: 65
% 7.79/2.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2090 ms resp. 1561 ms w/o parsing
% 7.79/2.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.79/2.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------