TSTP Solution File: KRS075+1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : KRS075+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 : Mon May 20 23:18:18 EDT 2024
% Result : Unsatisfiable 3.86s 1.95s
% Output : Refutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 43
% Syntax : Number of formulae : 74 ( 3 unt; 13 typ; 0 def)
% Number of atoms : 186 ( 42 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 371 ( 8 ~; 0 |; 64 &; 238 @)
% ( 5 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 149 ( 0 ^ 140 !; 9 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
thf(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
thf(cowlNothing_type,type,
cowlNothing: $i > $o ).
thf(cowlThing_type,type,
cowlThing: $i > $o ).
thf(cp_type,type,
cp: $i > $o ).
thf(rf_type,type,
rf: $i > $i > $o ).
thf(rf1_type,type,
rf1: $i > $i > $o ).
thf(rinvF_type,type,
rinvF: $i > $i > $o ).
thf(rinvF1_type,type,
rinvF1: $i > $i > $o ).
thf(rinvS_type,type,
rinvS: $i > $i > $o ).
thf(rs_type,type,
rs: $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_02584_type,type,
i2003_11_14_17_19_02584: $i ).
thf(28,axiom,
cUnsatisfiable @ i2003_11_14_17_19_02584,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(147,plain,
cUnsatisfiable @ i2003_11_14_17_19_02584,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( rinvF @ A @ B )
<=> ( rf @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(129,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)],[24]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( rinvF1 @ A @ B )
<=> ( rf1 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( ( rinvF1 @ A @ B )
=> ( rf1 @ B @ A ) )
& ( ( rf1 @ B @ A )
=> ( rinvF1 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( rs @ A @ B )
=> ( rf1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( rs @ A @ B )
=> ( rf1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(8,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(59,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf1 @ C @ A ) )
=> ( rf1 @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlNothing @ A ) )
=> ( cowlNothing @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rf @ A @ B )
& ( rf @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(123,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rf @ A @ B )
& ( rf @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp @ A ) )
=> ( cp @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp_substitution_1) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cp @ A ) )
=> ( cp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF1 @ C @ A ) )
=> ( rinvF1 @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF1_substitution_2) ).
thf(75,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF1 @ C @ A ) )
=> ( rinvF1 @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf @ C @ A ) )
=> ( rf @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf_substitution_2) ).
thf(51,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(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf @ A @ C ) )
=> ( rf @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf_substitution_1) ).
thf(47,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(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvS @ C @ A ) )
=> ( rinvS @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvS_substitution_2) ).
thf(83,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvS @ C @ A ) )
=> ( rinvS @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF1 @ A @ C ) )
=> ( rinvF1 @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF1_substitution_1) ).
thf(71,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF1 @ A @ C ) )
=> ( rinvF1 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rs @ A @ B )
& ( rs @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(144,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rs @ A @ B )
& ( rs @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(21,axiom,
! [A: $i] :
( ( cUnsatisfiable @ A )
<=> ( ? [B: $i] :
( ( rf1 @ A @ B )
& ~ ( cp @ B ) )
& ? [B: $i] :
( ( rs @ A @ B )
& ( cowlThing @ B ) )
& ? [B: $i] :
( ( rf @ A @ B )
& ( cp @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(113,plain,
! [A: $i] :
( ( ( cUnsatisfiable @ A )
=> ( ? [B: $i] :
( ( rf1 @ A @ B )
& ~ ( cp @ B ) )
& ? [B: $i] :
( ( rs @ A @ B )
& ( cowlThing @ B ) )
& ? [B: $i] :
( ( rf @ A @ B )
& ( cp @ B ) ) ) )
& ( ( ? [B: $i] :
( ( rf1 @ A @ B )
& ~ ( cp @ B ) )
& ? [B: $i] :
( ( rs @ A @ B )
& ( cowlThing @ B ) )
& ? [B: $i] :
( ( rf @ A @ B )
& ( cp @ B ) ) )
=> ( cUnsatisfiable @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cowlThing @ A ) )
=> ( cowlThing @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,axiom,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(103,plain,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rs @ C @ A ) )
=> ( rs @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rs_substitution_2) ).
thf(91,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rs @ C @ A ) )
=> ( rs @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(108,plain,
! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ A @ C ) )
=> ( rinvF @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF_substitution_1) ).
thf(63,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ A @ C ) )
=> ( rinvF @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( rs @ A @ B )
=> ( rf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( rs @ A @ B )
=> ( rf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(17,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(95,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_integer @ A ) )
=> ( xsd_integer @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ C @ A ) )
=> ( rinvF @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvF_substitution_2) ).
thf(67,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvF @ C @ A ) )
=> ( rinvF @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cUnsatisfiable @ A ) )
=> ( cUnsatisfiable @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( cUnsatisfiable @ A ) )
=> ( cUnsatisfiable @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(18,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(99,plain,
! [A: $i,B: $i] :
( ( ( A = B )
& ( xsd_string @ A ) )
=> ( xsd_string @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rs @ A @ C ) )
=> ( rs @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rs_substitution_1) ).
thf(87,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rs @ A @ C ) )
=> ( rs @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,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(55,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rf1 @ A @ C ) )
=> ( rf1 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( rinvS @ A @ B )
<=> ( rs @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( rinvS @ A @ B )
=> ( rs @ B @ A ) )
& ( ( rs @ B @ A )
=> ( rinvS @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rf1 @ A @ B )
& ( rf1 @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(126,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rf1 @ A @ B )
& ( rf1 @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvS @ A @ C ) )
=> ( rinvS @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvS_substitution_1) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = B )
& ( rinvS @ A @ C ) )
=> ( rinvS @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(152,plain,
$false,
inference(e,[status(thm)],[147,129,134,148,59,35,123,43,75,51,47,83,71,144,113,39,103,91,108,63,150,95,67,31,99,87,55,139,126,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KRS075+1 : TPTP v8.2.0. Released v3.1.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n003.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 : Sat May 18 22:28:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.07/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/1.06 % [INFO] Parsing done (133ms).
% 1.32/1.07 % [INFO] Running in sequential loop mode.
% 1.75/1.28 % [INFO] eprover registered as external prover.
% 1.75/1.29 % [INFO] cvc4 registered as external prover.
% 1.75/1.29 % [INFO] Scanning for conjecture ...
% 1.96/1.32 % [INFO] 30 axioms and no conjecture found.
% 2.13/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.13/1.39 % [INFO] Type checking passed.
% 2.13/1.39 % [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 ...
% 3.86/1.95 % External prover 'e' found a proof!
% 3.86/1.95 % [INFO] Killing All external provers ...
% 3.86/1.95 % Time passed: 1416ms (effective reasoning time: 875ms)
% 3.86/1.95 % Axioms used in derivation (30): rinvF1_substitution_1, axiom_2, axiom_6, rinvS_substitution_2, cowlThing_substitution_1, axiom_3, cUnsatisfiable_substitution_1, rinvS_substitution_1, axiom_5, axiom_11, rf_substitution_1, cp_substitution_1, axiom_4, axiom_7, cowlNothing_substitution_1, rinvF_substitution_2, axiom_10, xsd_string_substitution_1, rf1_substitution_2, axiom_1, xsd_integer_substitution_1, rf1_substitution_1, axiom_8, rs_substitution_2, rinvF1_substitution_2, rinvF_substitution_1, rf_substitution_2, axiom_0, axiom_9, rs_substitution_1
% 3.86/1.95 % No. of inferences in proof: 61
% 3.86/1.95 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1416 ms resp. 875 ms w/o parsing
% 4.01/2.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.01/2.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------