TSTP Solution File: KRS122+1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : KRS122+1 : TPTP v8.1.2. 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 : Tue May 7 07:51:55 EDT 2024
% Result : Unsatisfiable 3.62s 1.90s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 46
% Syntax : Number of formulae : 78 ( 3 unt; 15 typ; 0 def)
% Number of atoms : 193 ( 40 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 367 ( 8 ~; 0 |; 61 &; 229 @)
% ( 8 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 2 con; 0-2 aty)
% Number of variables : 145 ( 0 ^ 133 !; 12 ?; 145 :)
% 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(cowlNothing_type,type,
cowlNothing: $i > $o ).
thf(cowlThing_type,type,
cowlThing: $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(rinvR_type,type,
rinvR: $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_55116_type,type,
i2003_11_14_17_21_55116: $i ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvR @ C @ A ) )
=> ( rinvR @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvR_substitution_2) ).
thf(88,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvR @ C @ A ) )
=> ( rinvR @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp1 @ A ) )
=> ( cp1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1_substitution_1) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp1 @ A ) )
=> ( cp1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvR @ A @ C ) )
=> ( rinvR @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvR_substitution_1) ).
thf(84,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvR @ A @ C ) )
=> ( rinvR @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( ra_Px1 @ A @ C ) )
=> ( ra_Px1 @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ra_Px1_substitution_1) ).
thf(60,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)],[8]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ A @ C ) )
=> ( rr @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_substitution_1) ).
thf(92,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ A @ C ) )
=> ( rr @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( rinvR @ A @ B )
<=> ( rr @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
thf(156,plain,
! [A: $i,B: $i] :
( ( ( rinvR @ A @ B )
=> ( rr @ B @ A ) )
& ( ( rr @ B @ A )
=> ( rinvR @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
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(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(20,axiom,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(108,plain,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ C @ A ) )
=> ( rinvF @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvF_substitution_2) ).
thf(80,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ C @ A ) )
=> ( rinvF @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf @ C @ A ) )
=> ( rf @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rf_substitution_2) ).
thf(72,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf @ C @ A ) )
=> ( rf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_string @ A ) )
=> ( xsd_string @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xsd_string_substitution_1) ).
thf(104,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_string @ A ) )
=> ( xsd_string @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( ca_Vx3 @ A ) )
=> ( ca_Vx3 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ca_Vx3_substitution_1) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( ca_Vx3 @ A ) )
=> ( ca_Vx3 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_integer @ A ) )
=> ( xsd_integer @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xsd_integer_substitution_1) ).
thf(100,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_integer @ A ) )
=> ( xsd_integer @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp1xcomp @ A ) )
=> ( cp1xcomp @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1xcomp_substitution_1) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp1xcomp @ A ) )
=> ( cp1xcomp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
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(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(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ C @ A ) )
=> ( rr @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_substitution_2) ).
thf(96,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ C @ A ) )
=> ( rr @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cUnsatisfiable @ A ) )
=> ( cUnsatisfiable @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cUnsatisfiable @ A ) )
=> ( cUnsatisfiable @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
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(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rr @ A @ B )
& ( rr @ B @ C ) )
=> ( rr @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(161,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rr @ A @ B )
& ( rr @ B @ C ) )
=> ( rr @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( ra_Px1 @ C @ A ) )
=> ( ra_Px1 @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ra_Px1_substitution_2) ).
thf(64,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)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(21,axiom,
! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(113,plain,
! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ A @ C ) )
=> ( rinvF @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvF_substitution_1) ).
thf(76,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ A @ C ) )
=> ( rinvF @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(2,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( ca_Ax2 @ A ) )
=> ( ca_Ax2 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ca_Ax2_substitution_1) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( ca_Ax2 @ A ) )
=> ( ca_Ax2 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf @ A @ C ) )
=> ( rf @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rf_substitution_1) ).
thf(68,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf @ A @ C ) )
=> ( rf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(164,plain,
$false,
inference(e,[status(thm)],[88,52,84,60,92,156,129,134,108,80,48,72,104,40,100,56,142,124,96,32,148,161,64,44,118,113,76,151,36,163,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KRS122+1 : TPTP v8.1.2. Released v3.1.0.
% 0.11/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 6 15:18:09 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.80/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.99/0.93 % [INFO] Parsing done (136ms).
% 0.99/0.93 % [INFO] Running in sequential loop mode.
% 1.60/1.16 % [INFO] eprover registered as external prover.
% 1.60/1.17 % [INFO] cvc4 registered as external prover.
% 1.60/1.17 % [INFO] Scanning for conjecture ...
% 1.74/1.20 % [INFO] 31 axioms and no conjecture found.
% 1.74/1.27 % [INFO] Problem is first-order (TPTP FOF).
% 1.93/1.28 % [INFO] Type checking passed.
% 1.93/1.28 % [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 ...
% 3.62/1.90 % External prover 'e' found a proof!
% 3.62/1.90 % [INFO] Killing All external provers ...
% 3.62/1.90 % Time passed: 1411ms (effective reasoning time: 958ms)
% 3.62/1.90 % Axioms used in derivation (31): rr_substitution_1, ca_Ax2_substitution_1, axiom_2, xsd_string_substitution_1, cp1xcomp_substitution_1, cowlThing_substitution_1, axiom_3, axiom_8, rinvR_substitution_1, axiom_5, rinvF_substitution_1, rf_substitution_1, rinvR_substitution_2, axiom_7, cowlNothing_substitution_1, rinvF_substitution_2, axiom_10, axiom_6, ra_Px1_substitution_1, ra_Px1_substitution_2, cUnsatisfiable_substitution_1, axiom_1, xsd_integer_substitution_1, rf_substitution_2, axiom_0, cp1_substitution_1, axiom_11, axiom_9, rr_substitution_2, ca_Vx3_substitution_1, axiom_4
% 3.62/1.90 % No. of inferences in proof: 63
% 3.62/1.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1411 ms resp. 958 ms w/o parsing
% 3.62/1.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.62/1.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------