TSTP Solution File: KRS083+1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : KRS083+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 07:51:50 EDT 2024
% Result : Unsatisfiable 3.78s 2.05s
% Output : Refutation 4.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 37
% Syntax : Number of formulae : 63 ( 3 unt; 12 typ; 0 def)
% Number of atoms : 166 ( 32 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 329 ( 11 ~; 0 |; 59 &; 203 @)
% ( 5 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 120 ( 0 ^ 111 !; 9 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
thf(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
thf(cc_type,type,
cc: $i > $o ).
thf(cd_type,type,
cd: $i > $o ).
thf(cowlNothing_type,type,
cowlNothing: $i > $o ).
thf(cowlThing_type,type,
cowlThing: $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_19_32337_type,type,
i2003_11_14_17_19_32337: $i ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,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(74,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ C @ A ) )
=> ( rr @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( rinvF @ A @ B )
<=> ( rf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(117,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)],[21]) ).
thf(18,axiom,
! [A: $i] :
( ( cUnsatisfiable @ A )
<=> ( ! [B: $i] :
( ( rinvR @ A @ B )
=> ? [C: $i] :
( ( rinvF @ B @ C )
& ( cd @ C ) ) )
& ~ ( cc @ A )
& ? [B: $i] :
( ( rinvF @ A @ B )
& ( cd @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(96,plain,
! [A: $i] :
( ( ( cUnsatisfiable @ A )
=> ( ! [B: $i] :
( ( rinvR @ A @ B )
=> ? [C: $i] :
( ( rinvF @ B @ C )
& ( cd @ C ) ) )
& ~ ( cc @ A )
& ? [B: $i] :
( ( rinvF @ A @ B )
& ( cd @ B ) ) ) )
& ( ( ! [B: $i] :
( ( rinvR @ A @ B )
=> ? [C: $i] :
( ( rinvF @ B @ C )
& ( cd @ C ) ) )
& ~ ( cc @ A )
& ? [B: $i] :
( ( rinvF @ A @ B )
& ( cd @ B ) ) )
=> ( cUnsatisfiable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
cUnsatisfiable @ i2003_11_14_17_19_32337,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(129,plain,
cUnsatisfiable @ i2003_11_14_17_19_32337,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cd @ A ) )
=> ( cd @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cd_substitution_1) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cd @ A ) )
=> ( cd @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( rf @ A @ B )
=> ( rr @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
thf(130,plain,
! [A: $i,B: $i] :
( ( rf @ A @ B )
=> ( rr @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cc @ A ) )
=> ( cc @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc_substitution_1) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cc @ A ) )
=> ( cc @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,axiom,
! [A: $i] :
( ( cd @ A )
<=> ( ? [B: $i] :
( ( rf @ A @ B )
& ~ ( cc @ B ) )
& ( cc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(107,plain,
! [A: $i] :
( ( ( cd @ A )
=> ( ? [B: $i] :
( ( rf @ A @ B )
& ~ ( cc @ B ) )
& ( cc @ A ) ) )
& ( ( ? [B: $i] :
( ( rf @ A @ B )
& ~ ( cc @ B ) )
& ( cc @ A ) )
=> ( cd @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,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(62,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvR @ A @ C ) )
=> ( rinvR @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( rinvR @ A @ B )
<=> ( rr @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(122,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)],[22]) ).
thf(6,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(46,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf @ A @ C ) )
=> ( rf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,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(78,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_integer @ A ) )
=> ( xsd_integer @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,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(70,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ A @ C ) )
=> ( rr @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,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(54,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ A @ C ) )
=> ( rinvF @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(86,plain,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(91,plain,
! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,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(66,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvR @ C @ A ) )
=> ( rinvR @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,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(50,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf @ C @ A ) )
=> ( rf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rr @ A @ B )
& ( rr @ B @ C ) )
=> ( rr @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(127,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rr @ A @ B )
& ( rr @ B @ C ) )
=> ( rr @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cUnsatisfiable @ A ) )
=> ( cUnsatisfiable @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cUnsatisfiable @ A ) )
=> ( cUnsatisfiable @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(20,axiom,
! [A: $i] :
( ( cowlThing @ A )
=> ! [B: $i,C: $i] :
( ( ( rf @ A @ B )
& ( rf @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(114,plain,
! [A: $i] :
( ( cowlThing @ A )
=> ! [B: $i,C: $i] :
( ( ( rf @ A @ B )
& ( rf @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,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(58,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ C @ A ) )
=> ( rinvF @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,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(82,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_string @ A ) )
=> ( xsd_string @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(132,plain,
$false,
inference(e,[status(thm)],[42,74,117,96,129,34,130,30,107,62,122,46,78,38,70,54,86,91,66,50,127,26,114,58,82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : KRS083+1 : TPTP v8.1.2. Released v3.1.0.
% 0.09/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n022.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 :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.03 % [INFO] Parsing done (141ms).
% 1.35/1.04 % [INFO] Running in sequential loop mode.
% 1.75/1.28 % [INFO] eprover registered as external prover.
% 1.75/1.28 % [INFO] cvc4 registered as external prover.
% 1.75/1.29 % [INFO] Scanning for conjecture ...
% 1.93/1.33 % [INFO] 25 axioms and no conjecture found.
% 2.08/1.40 % [INFO] Problem is first-order (TPTP FOF).
% 2.08/1.40 % [INFO] Type checking passed.
% 2.08/1.41 % [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 ...
% 3.78/2.05 % External prover 'e' found a proof!
% 3.78/2.05 % [INFO] Killing All external provers ...
% 3.78/2.05 % Time passed: 1512ms (effective reasoning time: 1008ms)
% 3.78/2.05 % Axioms used in derivation (25): rinvF_substitution_2, cc_substitution_1, rr_substitution_1, axiom_2, xsd_string_substitution_1, axiom_6, axiom_3, cUnsatisfiable_substitution_1, axiom_8, rinvR_substitution_1, axiom_5, rinvF_substitution_1, rf_substitution_1, rinvR_substitution_2, axiom_4, axiom_7, cowlNothing_substitution_1, cowlThing_substitution_1, cd_substitution_1, axiom_1, xsd_integer_substitution_1, rf_substitution_2, axiom_0, axiom_9, rr_substitution_2
% 3.78/2.05 % No. of inferences in proof: 51
% 3.78/2.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1512 ms resp. 1008 ms w/o parsing
% 4.19/2.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.19/2.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------