TSTP Solution File: KRS158+1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : KRS158+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 23:18:35 EDT 2024
% Result : Theorem 3.78s 2.08s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 56
% Syntax : Number of formulae : 89 ( 23 unt; 25 typ; 0 def)
% Number of atoms : 199 ( 0 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 394 ( 23 ~; 0 |; 79 &; 236 @)
% ( 18 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 25 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 0 ^ 44 !; 30 ?; 74 :)
% 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(cC18_type,type,
cC18: $i > $o ).
thf(iV16560_type,type,
iV16560: $i ).
thf(cC14_type,type,
cC14: $i > $o ).
thf(cC8_type,type,
cC8: $i > $o ).
thf(cC16_type,type,
cC16: $i > $o ).
thf(cC6_type,type,
cC6: $i > $o ).
thf(iV16561_type,type,
iV16561: $i ).
thf(cC12_type,type,
cC12: $i > $o ).
thf(iV16562_type,type,
iV16562: $i ).
thf(cC4_type,type,
cC4: $i > $o ).
thf(ra_Px6_type,type,
ra_Px6: $i > $i > $o ).
thf(cC10_type,type,
cC10: $i > $o ).
thf(ra_Px3_type,type,
ra_Px3: $i > $i > $o ).
thf(cC10xcomp_type,type,
cC10xcomp: $i > $o ).
thf(rR1_type,type,
rR1: $i > $i > $o ).
thf(cC2xcomp_type,type,
cC2xcomp: $i > $o ).
thf(ra_Px1_type,type,
ra_Px1: $i > $i > $o ).
thf(cC2_type,type,
cC2: $i > $o ).
thf(cC4xcomp_type,type,
cC4xcomp: $i > $o ).
thf(cTEST_type,type,
cTEST: $i > $o ).
thf(cTOP_type,type,
cTOP: $i > $o ).
thf(13,axiom,
! [A: $i] :
( ( cTEST @ A )
<=> ( ( cTOP @ A )
& ( cC18 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(88,plain,
! [A: $i] :
( ( ( cTEST @ A )
=> ( ( cTOP @ A )
& ( cC18 @ A ) ) )
& ( ( ( cTOP @ A )
& ( cC18 @ A ) )
=> ( cTEST @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,axiom,
! [A: $i] :
( ( cC12 @ A )
<=> ( ( cC10xcomp @ A )
& ( cC2xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(120,plain,
! [A: $i] :
( ( ( cC12 @ A )
=> ( ( cC10xcomp @ A )
& ( cC2xcomp @ A ) ) )
& ( ( ( cC10xcomp @ A )
& ( cC2xcomp @ A ) )
=> ( cC12 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(32,axiom,
! [A: $i] :
( ( cC16 @ A )
<=> ( ( cC14 @ A )
& ( cC8 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(142,plain,
! [A: $i] :
( ( ( cC16 @ A )
=> ( ( cC14 @ A )
& ( cC8 @ A ) ) )
& ( ( ( cC14 @ A )
& ( cC8 @ A ) )
=> ( cC16 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(19,axiom,
! [A: $i] :
( ( cC8 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC6 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
thf(110,plain,
! [A: $i] :
( ( ( cC8 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC6 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC6 @ B ) )
=> ( cC8 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(20,axiom,
rR1 @ iV16560 @ iV16562,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(116,plain,
rR1 @ iV16560 @ iV16562,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
! [A: $i] :
( ( cC2 @ A )
<=> ~ ? [B: $i] : ( ra_Px1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
thf(65,plain,
! [A: $i] :
( ( ( cC2 @ A )
=> ~ ? [B: $i] : ( ra_Px1 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px1 @ A @ B )
=> ( cC2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,axiom,
cTOP @ iV16560,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(141,plain,
cTOP @ iV16560,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(27,axiom,
cowlThing @ iV16560,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(129,plain,
cowlThing @ iV16560,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(26,axiom,
cC4xcomp @ iV16561,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(128,plain,
cC4xcomp @ iV16561,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(17,axiom,
cC2xcomp @ iV16561,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(108,plain,
cC2xcomp @ iV16561,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(16,axiom,
! [A: $i] :
( ( cC18 @ A )
<=> ( ( cTOP @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(102,plain,
! [A: $i] :
( ( ( cC18 @ A )
=> ( ( cTOP @ A )
& ( cC16 @ A ) ) )
& ( ( ( cTOP @ A )
& ( cC16 @ A ) )
=> ( cC18 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: $i] :
( ( cC2xcomp @ A )
<=> ? [B: $i] : ( ra_Px1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(60,plain,
! [A: $i] :
( ( ( cC2xcomp @ A )
=> ? [B: $i] : ( ra_Px1 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px1 @ A @ B )
=> ( cC2xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
rR1 @ iV16560 @ iV16561,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(117,plain,
rR1 @ iV16560 @ iV16561,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [A: $i] :
( ( cC4xcomp @ A )
<=> ~ ? [B: $i] : ( ra_Px6 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(70,plain,
! [A: $i] :
( ( ( cC4xcomp @ A )
=> ~ ? [B: $i] : ( ra_Px6 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px6 @ A @ B )
=> ( cC4xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
( ! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) )
& ! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) )
& ( cC18 @ iV16560 )
& ( cC14 @ iV16560 )
& ( cC8 @ iV16560 )
& ( cC16 @ iV16560 )
& ( cowlThing @ iV16560 )
& ( cC6 @ iV16561 )
& ( cowlThing @ iV16561 )
& ( cC12 @ iV16562 )
& ( cowlThing @ iV16562 ) ),
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 ) )
& ( cC18 @ iV16560 )
& ( cC14 @ iV16560 )
& ( cC8 @ iV16560 )
& ( cC16 @ iV16560 )
& ( cowlThing @ iV16560 )
& ( cC6 @ iV16561 )
& ( cowlThing @ iV16561 )
& ( cC12 @ iV16562 )
& ( cowlThing @ iV16562 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(33,plain,
~ ( ! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) )
& ! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) )
& ( cC18 @ iV16560 )
& ( cC14 @ iV16560 )
& ( cC8 @ iV16560 )
& ( cC16 @ iV16560 )
& ( cowlThing @ iV16560 )
& ( cC6 @ iV16561 )
& ( cowlThing @ iV16561 )
& ( cC12 @ iV16562 )
& ( cowlThing @ iV16562 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
cowlThing @ iV16561,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(109,plain,
cowlThing @ iV16561,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: $i] :
( ( cC14 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC12 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(96,plain,
! [A: $i] :
( ( ( cC14 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC12 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC12 @ B ) )
=> ( cC14 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i] :
( ( cC10 @ A )
<=> ? [B: $i] : ( ra_Px3 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(44,plain,
! [A: $i] :
( ( ( cC10 @ A )
=> ? [B: $i] : ( ra_Px3 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px3 @ A @ B )
=> ( cC10 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,axiom,
cC10xcomp @ iV16562,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
thf(118,plain,
cC10xcomp @ iV16562,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
! [A: $i] :
( ( cC10 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC2xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(54,plain,
! [A: $i] :
( ( ( cC10 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC2xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC2xcomp @ B ) )
=> ( cC10 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i] :
( ( cC10xcomp @ A )
<=> ~ ? [B: $i] : ( ra_Px3 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(49,plain,
! [A: $i] :
( ( ( cC10xcomp @ A )
=> ~ ? [B: $i] : ( ra_Px3 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px3 @ A @ B )
=> ( cC10xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
cowlThing @ iV16562,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
thf(81,plain,
cowlThing @ iV16562,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $i] :
( ( cC4 @ A )
<=> ? [B: $i] : ( ra_Px6 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
thf(39,plain,
! [A: $i] :
( ( ( cC4 @ A )
=> ? [B: $i] : ( ra_Px6 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px6 @ A @ B )
=> ( cC4 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,axiom,
! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(130,plain,
! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(29,axiom,
cTEST @ iV16560,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(135,plain,
cTEST @ iV16560,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [A: $i] :
( ( cC4 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC2xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
thf(75,plain,
! [A: $i] :
( ( ( cC4 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC2xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC2xcomp @ B ) )
=> ( cC4 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(23,axiom,
cC2xcomp @ iV16562,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(119,plain,
cC2xcomp @ iV16562,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(12,axiom,
! [A: $i] :
( ( cC6 @ A )
<=> ( ( cC4xcomp @ A )
& ( cC2xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(82,plain,
! [A: $i] :
( ( ( cC6 @ A )
=> ( ( cC4xcomp @ A )
& ( cC2xcomp @ A ) ) )
& ( ( ( cC4xcomp @ A )
& ( cC2xcomp @ A ) )
=> ( cC6 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( rR1 @ iV16561 @ A )
=> ( cC2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(94,plain,
! [A: $i] :
( ( rR1 @ iV16561 @ A )
=> ( cC2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(25,axiom,
! [A: $i] :
( ( rR1 @ iV16562 @ A )
=> ( cC2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
thf(126,plain,
! [A: $i] :
( ( rR1 @ iV16562 @ A )
=> ( cC2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(30,axiom,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(136,plain,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(148,plain,
$false,
inference(e,[status(thm)],[88,120,142,110,116,65,141,129,128,108,102,60,117,70,33,109,96,44,118,54,49,81,39,130,135,75,119,82,94,126,136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS158+1 : TPTP v8.2.0. Released v3.1.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n014.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat May 18 22:19:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.95/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/1.03 % [INFO] Parsing done (153ms).
% 1.32/1.04 % [INFO] Running in sequential loop mode.
% 1.69/1.27 % [INFO] eprover registered as external prover.
% 1.69/1.27 % [INFO] cvc4 registered as external prover.
% 1.69/1.27 % [INFO] Scanning for conjecture ...
% 1.87/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 30 axioms. Running axiom selection ...
% 1.98/1.41 % [INFO] Axiom selection finished. Selected 30 axioms (removed 0 axioms).
% 2.23/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.23/1.45 % [INFO] Type checking passed.
% 2.23/1.46 % [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 ...
% 3.78/2.08 % External prover 'e' found a proof!
% 3.78/2.08 % [INFO] Killing All external provers ...
% 3.78/2.08 % Time passed: 1545ms (effective reasoning time: 1042ms)
% 3.78/2.08 % 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)>
% 3.78/2.08 % Axioms used in derivation (30): axiom_10, axiom_22, axiom_15, axiom_2, axiom_27, axiom_6, axiom_16, axiom_3, axiom_20, axiom_24, axiom_1, axiom_28, axiom_8, axiom_17, axiom_25, axiom_0, axiom_23, axiom_9, axiom_14, axiom_4, axiom_7, axiom_26, axiom_21, axiom_19, axiom_5, axiom_13, axiom_29, axiom_11, axiom_18, axiom_12
% 3.78/2.08 % No. of inferences in proof: 64
% 3.78/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1545 ms resp. 1042 ms w/o parsing
% 3.86/2.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.86/2.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------