TSTP Solution File: KRS162+1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : KRS162+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 07:52:02 EDT 2024
% Result : Theorem 3.56s 1.89s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 29
% Syntax : Number of formulae : 51 ( 1 unt; 9 typ; 0 def)
% Number of atoms : 189 ( 66 equ; 0 cnn)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 393 ( 58 ~; 0 |; 105 &; 188 @)
% ( 3 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 121 ( 0 ^ 91 !; 30 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(cowlThing_type,type,
cowlThing: $i > $o ).
thf(cowlNothing_type,type,
cowlNothing: $i > $o ).
thf(xsd_string_type,type,
xsd_string: $i > $o ).
thf(xsd_integer_type,type,
xsd_integer: $i > $o ).
thf(rp_type,type,
rp: $i > $i > $o ).
thf(rq_type,type,
rq: $i > $i > $o ).
thf(rr_type,type,
rr: $i > $i > $o ).
thf(cA_type,type,
cA: $i > $o ).
thf(cB_type,type,
cB: $i > $o ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rq @ A @ C ) )
=> ( rq @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rq_substitution_1) ).
thf(93,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rq @ A @ C ) )
=> ( rq @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( rp @ A @ B )
=> ( rr @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( rp @ A @ B )
=> ( rr @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(16,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(89,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_integer @ A ) )
=> ( xsd_integer @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(97,plain,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rp @ A @ C ) )
=> ( rp @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rp_substitution_1) ).
thf(77,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rp @ A @ C ) )
=> ( rp @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( rq @ A @ B )
=> ( rr @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( rq @ A @ B )
=> ( rr @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,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(67,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ A @ C ) )
=> ( rr @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cA @ A ) )
=> ( cA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cA_substitution_1) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cA @ A ) )
=> ( cA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( rp @ A @ B )
=> ( cA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( rp @ A @ B )
=> ( cA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i] :
~ ( ( cB @ A )
& ( cA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(51,plain,
! [A: $i] :
~ ( ( cB @ A )
& ( cA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cB @ A ) )
=> ( cB @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cB_substitution_1) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cB @ A ) )
=> ( cB @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( rq @ A @ B )
=> ( cB @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( rq @ A @ B )
=> ( cB @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rp @ C @ A ) )
=> ( rp @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rp_substitution_2) ).
thf(85,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rp @ C @ A ) )
=> ( rp @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rq @ C @ A ) )
=> ( rq @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rq_substitution_2) ).
thf(102,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rq @ C @ A ) )
=> ( rq @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
( ! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) )
& ! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) )
& ! [A: $i] :
( ( ? [B: $i,C: $i] :
( ( rp @ A @ B )
& ( rp @ A @ C )
& ( B != C ) )
& ? [B: $i,C: $i,D: $i] :
( ( rq @ A @ B )
& ( rq @ A @ C )
& ( rq @ A @ D )
& ( B != C )
& ( B != D )
& ( C != D ) ) )
=> ? [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( rr @ A @ B )
& ( rr @ A @ C )
& ( rr @ A @ D )
& ( rr @ A @ E )
& ( rr @ A @ F )
& ( B != C )
& ( B != D )
& ( B != E )
& ( B != F )
& ( C != D )
& ( C != E )
& ( C != F )
& ( D != E )
& ( D != F )
& ( E != F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) )
& ! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) )
& ! [A: $i] :
( ( ? [B: $i,C: $i] :
( ( rp @ A @ B )
& ( rp @ A @ C )
& ( B != C ) )
& ? [B: $i,C: $i,D: $i] :
( ( rq @ A @ B )
& ( rq @ A @ C )
& ( rq @ A @ D )
& ( B != C )
& ( B != D )
& ( C != D ) ) )
=> ? [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( rr @ A @ B )
& ( rr @ A @ C )
& ( rr @ A @ D )
& ( rr @ A @ E )
& ( rr @ A @ F )
& ( B != C )
& ( B != D )
& ( B != E )
& ( B != F )
& ( C != D )
& ( C != E )
& ( C != F )
& ( D != E )
& ( D != F )
& ( E != F ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ( ! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) )
& ! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) )
& ! [A: $i] :
( ( ? [B: $i,C: $i] :
( ( rp @ A @ B )
& ( rp @ A @ C )
& ( B != C ) )
& ? [B: $i,C: $i,D: $i] :
( ( rq @ A @ B )
& ( rq @ A @ C )
& ( rq @ A @ D )
& ( B != C )
& ( B != D )
& ( C != D ) ) )
=> ? [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( rr @ A @ B )
& ( rr @ A @ C )
& ( rr @ A @ D )
& ( rr @ A @ E )
& ( rr @ A @ F )
& ( B != C )
& ( B != D )
& ( B != E )
& ( B != F )
& ( C != D )
& ( C != E )
& ( C != F )
& ( D != E )
& ( D != F )
& ( E != F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,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(59,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_string @ A ) )
=> ( xsd_string @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,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(71,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rr @ C @ A ) )
=> ( rr @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(54,plain,
! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(112,plain,
$false,
inference(e,[status(thm)],[93,106,89,97,77,81,108,63,67,43,75,51,47,83,85,102,22,59,71,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS162+1 : TPTP v8.1.2. Released v3.1.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 6 15:20:39 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.82/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.96 % [INFO] Parsing done (122ms).
% 1.22/0.97 % [INFO] Running in sequential loop mode.
% 1.71/1.19 % [INFO] eprover registered as external prover.
% 1.71/1.20 % [INFO] cvc4 registered as external prover.
% 1.71/1.20 % [INFO] Scanning for conjecture ...
% 1.88/1.28 % [INFO] Found a conjecture and 19 axioms. Running axiom selection ...
% 1.88/1.32 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.19/1.34 % [INFO] Problem is first-order (TPTP FOF).
% 2.19/1.35 % [INFO] Type checking passed.
% 2.19/1.35 % [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 ...
% 3.56/1.88 % External prover 'e' found a proof!
% 3.56/1.88 % [INFO] Killing All external provers ...
% 3.56/1.89 % Time passed: 1372ms (effective reasoning time: 908ms)
% 3.56/1.89 % Solved by 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)>
% 3.56/1.89 % Axioms used in derivation (19): cA_substitution_1, rr_substitution_1, axiom_6, cowlThing_substitution_1, axiom_3, axiom_5, axiom_0, rp_substitution_1, rr_substitution_2, axiom_4, cowlNothing_substitution_1, cB_substitution_1, axiom_2, rp_substitution_2, xsd_string_substitution_1, rq_substitution_1, axiom_1, xsd_integer_substitution_1, rq_substitution_2
% 3.56/1.89 % No. of inferences in proof: 42
% 3.56/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1372 ms resp. 908 ms w/o parsing
% 3.96/1.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.96/1.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------