TSTP Solution File: KRS115+1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : KRS115+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 07:51:54 EDT 2024
% Result : Unsatisfiable 3.81s 1.89s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 40
% Syntax : Number of formulae : 68 ( 3 unt; 13 typ; 0 def)
% Number of atoms : 170 ( 36 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 319 ( 8 ~; 0 |; 57 &; 196 @)
% ( 4 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 127 ( 0 ^ 112 !; 15 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
thf(cowlNothing_type,type,
cowlNothing: $i > $o ).
thf(cowlThing_type,type,
cowlThing: $i > $o ).
thf(cp1_type,type,
cp1: $i > $o ).
thf(cp2_type,type,
cp2: $i > $o ).
thf(cp2xcomp_type,type,
cp2xcomp: $i > $o ).
thf(ra_Px1_type,type,
ra_Px1: $i > $i > $o ).
thf(rf1_type,type,
rf1: $i > $i > $o ).
thf(rf2_type,type,
rf2: $i > $i > $o ).
thf(rr_type,type,
rr: $i > $i > $o ).
thf(xsd_integer_type,type,
xsd_integer: $i > $o ).
thf(xsd_string_type,type,
xsd_string: $i > $o ).
thf(i2003_11_14_17_21_30578_type,type,
i2003_11_14_17_21_30578: $i ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_string @ A ) )
=> ( xsd_string @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_string_substitution_1) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_string @ A ) )
=> ( xsd_string @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( ra_Px1 @ C @ A ) )
=> ( ra_Px1 @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px1_substitution_2) ).
thf(56,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( ra_Px1 @ C @ A ) )
=> ( ra_Px1 @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( ra_Px1 @ A @ C ) )
=> ( ra_Px1 @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px1_substitution_1) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( ra_Px1 @ A @ C ) )
=> ( ra_Px1 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_integer @ A ) )
=> ( xsd_integer @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_integer_substitution_1) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_integer @ A ) )
=> ( xsd_integer @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( rr @ A @ B )
=> ( rf1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(133,plain,
! [A: $i,B: $i] :
( ( rr @ A @ B )
=> ( rf1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cUnsatisfiable @ A ) )
=> ( cUnsatisfiable @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cUnsatisfiable @ A ) )
=> ( cUnsatisfiable @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,axiom,
! [A: $i] :
( ( cowlThing @ A )
=> ! [B: $i,C: $i] :
( ( ( rf1 @ A @ B )
& ( rf1 @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(124,plain,
! [A: $i] :
( ( cowlThing @ A )
=> ! [B: $i,C: $i] :
( ( ( rf1 @ A @ B )
& ( rf1 @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp2 @ A ) )
=> ( cp2 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2_substitution_1) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp2 @ A ) )
=> ( cp2 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ A @ C ) )
=> ( rr @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rr_substitution_1) ).
thf(76,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ A @ C ) )
=> ( rr @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [A: $i] :
( ( cp1 @ A )
=> ( cp2xcomp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(112,plain,
! [A: $i] :
( ( cp1 @ A )
=> ( cp2xcomp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp2xcomp @ A ) )
=> ( cp2xcomp @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2xcomp_substitution_1) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp2xcomp @ A ) )
=> ( cp2xcomp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,axiom,
! [A: $i] :
( ( cowlThing @ A )
=> ! [B: $i,C: $i] :
( ( ( rf2 @ A @ B )
& ( rf2 @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(127,plain,
! [A: $i] :
( ( cowlThing @ A )
=> ! [B: $i,C: $i] :
( ( ( rf2 @ A @ B )
& ( rf2 @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf2 @ C @ A ) )
=> ( rf2 @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf2_substitution_2) ).
thf(72,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf2 @ C @ A ) )
=> ( rf2 @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(22,axiom,
! [A: $i] :
( ( cp2xcomp @ A )
<=> ? [B: $i] : ( ra_Px1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(119,plain,
! [A: $i] :
( ( ( cp2xcomp @ A )
=> ? [B: $i] : ( ra_Px1 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px1 @ A @ B )
=> ( cp2xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf1 @ A @ C ) )
=> ( rf1 @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf1_substitution_1) ).
thf(60,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf1 @ A @ C ) )
=> ( rf1 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [A: $i] :
( ( cUnsatisfiable @ A )
<=> ( ? [B: $i] :
( ( rf2 @ A @ B )
& ( cp2 @ B ) )
& ? [B: $i] :
( ( rf1 @ A @ B )
& ( cp1 @ B ) )
& ? [B: $i] :
( ( rr @ A @ B )
& ( cowlThing @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(102,plain,
! [A: $i] :
( ( ( cUnsatisfiable @ A )
=> ( ? [B: $i] :
( ( rf2 @ A @ B )
& ( cp2 @ B ) )
& ? [B: $i] :
( ( rf1 @ A @ B )
& ( cp1 @ B ) )
& ? [B: $i] :
( ( rr @ A @ B )
& ( cowlThing @ B ) ) ) )
& ( ( ? [B: $i] :
( ( rf2 @ A @ B )
& ( cp2 @ B ) )
& ? [B: $i] :
( ( rf1 @ A @ B )
& ( cp1 @ B ) )
& ? [B: $i] :
( ( rr @ A @ B )
& ( cowlThing @ B ) ) )
=> ( cUnsatisfiable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(92,plain,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(18,axiom,
! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(97,plain,
! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf1 @ C @ A ) )
=> ( rf1 @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf1_substitution_2) ).
thf(64,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf1 @ C @ A ) )
=> ( rf1 @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(25,axiom,
cUnsatisfiable @ i2003_11_14_17_21_30578,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(130,plain,
cUnsatisfiable @ i2003_11_14_17_21_30578,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ C @ A ) )
=> ( rr @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rr_substitution_2) ).
thf(80,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ C @ A ) )
=> ( rr @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp1 @ A ) )
=> ( cp1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1_substitution_1) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp1 @ A ) )
=> ( cp1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,axiom,
! [A: $i] :
( ( cp2 @ A )
<=> ~ ? [B: $i] : ( ra_Px1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(114,plain,
! [A: $i] :
( ( ( cp2 @ A )
=> ~ ? [B: $i] : ( ra_Px1 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px1 @ A @ B )
=> ( cp2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( rr @ A @ B )
=> ( rf2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( rr @ A @ B )
=> ( rf2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf2 @ A @ C ) )
=> ( rf2 @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf2_substitution_1) ).
thf(68,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf2 @ A @ C ) )
=> ( rf2 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(135,plain,
$false,
inference(e,[status(thm)],[88,56,52,84,133,28,124,44,76,112,48,127,72,119,36,60,102,92,97,32,64,130,80,40,114,131,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KRS115+1 : TPTP v8.1.2. Released v3.1.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n015.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 15:19:24 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.00 % [INFO] Parsing done (124ms).
% 1.31/1.01 % [INFO] Running in sequential loop mode.
% 1.70/1.22 % [INFO] eprover registered as external prover.
% 1.70/1.23 % [INFO] cvc4 registered as external prover.
% 1.70/1.23 % [INFO] Scanning for conjecture ...
% 1.86/1.26 % [INFO] 27 axioms and no conjecture found.
% 1.93/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 1.93/1.33 % [INFO] Type checking passed.
% 2.15/1.33 % [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 ...
% 3.81/1.89 % External prover 'e' found a proof!
% 3.81/1.89 % [INFO] Killing All external provers ...
% 3.81/1.89 % Time passed: 1347ms (effective reasoning time: 877ms)
% 3.81/1.89 % Axioms used in derivation (27): axiom_10, cp2xcomp_substitution_1, rr_substitution_1, rf2_substitution_2, axiom_2, cowlThing_substitution_1, axiom_3, rf2_substitution_1, axiom_8, axiom_0, cp1_substitution_1, axiom_4, axiom_7, cowlNothing_substitution_1, xsd_string_substitution_1, rf1_substitution_2, axiom_6, ra_Px1_substitution_1, ra_Px1_substitution_2, cUnsatisfiable_substitution_1, axiom_1, xsd_integer_substitution_1, rf1_substitution_1, axiom_5, cp2_substitution_1, axiom_9, rr_substitution_2
% 3.81/1.89 % No. of inferences in proof: 55
% 3.81/1.89 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1347 ms resp. 877 ms w/o parsing
% 3.96/1.97 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.96/1.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------