TSTP Solution File: KRS087+1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : KRS087+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 3.73s 1.98s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 33
% Syntax : Number of formulae : 56 ( 3 unt; 11 typ; 0 def)
% Number of atoms : 142 ( 30 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 279 ( 8 ~; 0 |; 50 &; 174 @)
% ( 4 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 107 ( 0 ^ 101 !; 6 ?; 107 :)
% 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(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_46763_type,type,
i2003_11_14_17_19_46763: $i ).
thf(22,axiom,
cUnsatisfiable @ i2003_11_14_17_19_46763,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(115,plain,
cUnsatisfiable @ i2003_11_14_17_19_46763,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(84,plain,
! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
! [A: $i] :
( ( cUnsatisfiable @ A )
<=> ( ( cp1 @ A )
& ? [B: $i] :
( ( rr @ A @ B )
& ? [C: $i] :
( ( rr @ B @ C )
& ! [D: $i] :
( ( rinvR @ C @ D )
=> ~ ( cp1 @ D ) )
& ( cp1 @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(89,plain,
! [A: $i] :
( ( ( cUnsatisfiable @ A )
=> ( ( cp1 @ A )
& ? [B: $i] :
( ( rr @ A @ B )
& ? [C: $i] :
( ( rr @ B @ C )
& ! [D: $i] :
( ( rinvR @ C @ D )
=> ~ ( cp1 @ D ) )
& ( cp1 @ C ) ) ) ) )
& ( ( ( cp1 @ A )
& ? [B: $i] :
( ( rr @ A @ B )
& ? [C: $i] :
( ( rr @ B @ C )
& ! [D: $i] :
( ( rinvR @ C @ D )
=> ~ ( cp1 @ D ) )
& ( cp1 @ C ) ) ) )
=> ( cUnsatisfiable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,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(71,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_integer @ A ) )
=> ( xsd_integer @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp1 @ A ) )
=> ( cp1 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1_substitution_1) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp1 @ A ) )
=> ( cp1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,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(63,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ A @ C ) )
=> ( rr @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,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(43,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf @ C @ A ) )
=> ( rf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,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(75,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_string @ A ) )
=> ( xsd_string @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,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(51,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ C @ A ) )
=> ( rinvF @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(79,plain,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,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(47,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ A @ C ) )
=> ( rinvF @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rf @ A @ B )
& ( rf @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(100,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rf @ A @ B )
& ( rf @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,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(59,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvR @ C @ A ) )
=> ( rinvR @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rr @ A @ B )
& ( rr @ B @ C ) )
=> ( rr @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(113,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rr @ A @ B )
& ( rr @ B @ C ) )
=> ( rr @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,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(39,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf @ A @ C ) )
=> ( rf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( rinvF @ A @ B )
<=> ( rf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(103,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)],[19]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( rinvR @ A @ B )
<=> ( rr @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(108,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)],[20]) ).
thf(12,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(67,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ C @ A ) )
=> ( rr @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(31,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 )
& ( rinvR @ A @ C ) )
=> ( rinvR @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvR_substitution_1) ).
thf(55,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvR @ A @ C ) )
=> ( rinvR @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cUnsatisfiable @ A ) )
=> ( cUnsatisfiable @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cUnsatisfiable @ A ) )
=> ( cUnsatisfiable @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(116,plain,
$false,
inference(e,[status(thm)],[115,84,89,71,35,63,43,75,51,79,47,100,59,27,113,39,103,108,67,31,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KRS087+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n027.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 : Mon May 6 15:16:24 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/1.01 % [INFO] Parsing done (132ms).
% 1.33/1.02 % [INFO] Running in sequential loop mode.
% 1.78/1.26 % [INFO] eprover registered as external prover.
% 1.78/1.27 % [INFO] cvc4 registered as external prover.
% 1.78/1.27 % [INFO] Scanning for conjecture ...
% 1.78/1.30 % [INFO] 22 axioms and no conjecture found.
% 2.00/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.00/1.37 % [INFO] Type checking passed.
% 2.00/1.38 % [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 ...
% 3.73/1.98 % External prover 'e' found a proof!
% 3.73/1.98 % [INFO] Killing All external provers ...
% 3.73/1.98 % Time passed: 1438ms (effective reasoning time: 950ms)
% 3.73/1.98 % Axioms used in derivation (22): rinvF_substitution_2, rr_substitution_1, axiom_2, xsd_string_substitution_1, axiom_6, cowlThing_substitution_1, axiom_3, cUnsatisfiable_substitution_1, rinvR_substitution_1, axiom_5, rinvF_substitution_1, cp1_substitution_1, rf_substitution_1, rr_substitution_2, rinvR_substitution_2, axiom_4, axiom_7, cowlNothing_substitution_1, axiom_1, xsd_integer_substitution_1, rf_substitution_2, axiom_0
% 3.73/1.98 % No. of inferences in proof: 45
% 3.73/1.98 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1438 ms resp. 950 ms w/o parsing
% 3.73/2.02 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.73/2.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------