%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS106+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:44:39 AM UTC 2026
% Result : Unsatisfiable 4.63s 2.60s
% Output : Refutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 27
% Syntax : Number of formulae : 55 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 38 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 317 ( 8 ~; 0 |; 59 &; 196 @)
% ( 4 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 131 ( 0 ^; 116 !; 15 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
thf(cUnsatisfiable_decl,type,
cUnsatisfiable: $i > $o ).
thf(cowlNothing_decl,type,
cowlNothing: $i > $o ).
thf(cowlThing_decl,type,
cowlThing: $i > $o ).
thf(cp1_decl,type,
cp1: $i > $o ).
thf(cp1xcomp_decl,type,
cp1xcomp: $i > $o ).
thf(cp2_decl,type,
cp2: $i > $o ).
thf(ra_Px1_decl,type,
ra_Px1: $i > $i > $o ).
thf(rf1_decl,type,
rf1: $i > $i > $o ).
thf(rf2_decl,type,
rf2: $i > $i > $o ).
thf(rf3_decl,type,
rf3: $i > $i > $o ).
thf(xsd_integer_decl,type,
xsd_integer: $i > $o ).
thf(xsd_string_decl,type,
xsd_string: $i > $o ).
thf(i2003_11_14_17_20_57644_decl,type,
i2003_11_14_17_20_57644: $i ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_string_substitution_1) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ cp1 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(115,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) )
=> ( A @ cp1 ) )
& ( ( A @ cp1 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px1 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px1_substitution_2) ).
thf(56,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px1 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px1 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px1_substitution_1) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px1 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf3 ) )
& ( B @ ( A @ rf3 ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf3 ) )
& ( B @ ( A @ rf3 ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf1 ) )
& ( A = B ) )
=> ( C @ ( B @ rf1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf1_substitution_1) ).
thf(60,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf1 ) )
& ( A = B ) )
=> ( C @ ( B @ rf1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(92,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp1xcomp )
& ( A = B ) )
=> ( B @ cp1xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1xcomp_substitution_1) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ( A @ cp1xcomp )
& ( A = B ) )
=> ( B @ cp1xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp2 )
& ( A = B ) )
=> ( B @ cp2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2_substitution_1) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( A @ cp2 )
& ( A = B ) )
=> ( B @ cp2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf1 ) )
& ( B @ ( A @ rf1 ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(127,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf1 ) )
& ( B @ ( A @ rf1 ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf2 ) )
& ( A = B ) )
=> ( B @ ( C @ rf2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf2_substitution_2) ).
thf(72,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf2 ) )
& ( A = B ) )
=> ( B @ ( C @ rf2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ cUnsatisfiable )
<=> ( ? [B: $i] :
( ( B @ cp1xcomp )
& ( B @ ( A @ rf2 ) ) )
& ? [B: $i] :
( ( B @ cp1 )
& ( B @ ( A @ rf1 ) ) )
& ? [B: $i] :
( ( B @ cp2 )
& ( B @ ( A @ rf3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(104,plain,
! [A: $i] :
( ( ( ? [B: $i] :
( ( B @ cp1xcomp )
& ( B @ ( A @ rf2 ) ) )
& ? [B: $i] :
( ( B @ cp1 )
& ( B @ ( A @ rf1 ) ) )
& ? [B: $i] :
( ( B @ cp2 )
& ( B @ ( A @ rf3 ) ) ) )
=> ( A @ cUnsatisfiable ) )
& ( ( A @ cUnsatisfiable )
=> ( ? [B: $i] :
( ( B @ cp1xcomp )
& ( B @ ( A @ rf2 ) ) )
& ? [B: $i] :
( ( B @ cp1 )
& ( B @ ( A @ rf1 ) ) )
& ? [B: $i] :
( ( B @ cp2 )
& ( B @ ( A @ rf3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,axiom,
i2003_11_14_17_20_57644 @ cUnsatisfiable,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(136,plain,
i2003_11_14_17_20_57644 @ cUnsatisfiable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf2 ) )
& ( A = B ) )
=> ( C @ ( B @ rf2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf2_substitution_1) ).
thf(68,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf2 ) )
& ( A = B ) )
=> ( C @ ( B @ rf2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ cp1xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(121,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px1 ) )
=> ( A @ cp1xcomp ) )
& ( ( A @ cp1xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_integer_substitution_1) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rf3 ) )
=> ( B @ ( A @ rf1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rf3 ) )
=> ( B @ ( A @ rf1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf1 ) )
& ( A = B ) )
=> ( B @ ( C @ rf1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf1_substitution_2) ).
thf(64,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf1 ) )
& ( A = B ) )
=> ( B @ ( C @ rf1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf3 ) )
& ( A = B ) )
=> ( C @ ( B @ rf3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf3_substitution_1) ).
thf(76,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf3 ) )
& ( A = B ) )
=> ( C @ ( B @ rf3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(98,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf2 ) )
& ( B @ ( A @ rf2 ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(130,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf2 ) )
& ( B @ ( A @ rf2 ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf3 ) )
& ( A = B ) )
=> ( B @ ( C @ rf3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rf3_substitution_2) ).
thf(80,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf3 ) )
& ( A = B ) )
=> ( B @ ( C @ rf3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp1 )
& ( A = B ) )
=> ( B @ cp1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1_substitution_1) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( ( A @ cp1 )
& ( A = B ) )
=> ( B @ cp1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rf3 ) )
=> ( B @ ( A @ rf2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rf3 ) )
=> ( B @ ( A @ rf2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(141,plain,
$false,
inference(e,[status(thm)],[88,115,56,52,133,60,92,44,48,127,72,104,36,136,68,121,84,28,137,32,64,76,98,130,80,40,139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS106+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.39 % Computer : n013.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Fri Sep 25 19:39:06 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.18 % [INFO] Parsing done (210ms).
% 1.31/1.19 % [INFO] Running in sequential loop mode.
% 1.99/1.59 % [INFO] eprover registered as external prover.
% 2.18/1.60 % [INFO] Scanning for conjecture ...
% 2.18/1.65 % [INFO] 27 axioms and no conjecture found.
% 2.35/1.75 % [INFO] Problem is first-order (TPTP FOF).
% 2.35/1.76 % [INFO] Type checking passed.
% 2.35/1.76 % [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 ...
% 4.63/2.60 % External prover 'e' found a proof!
% 4.63/2.60 % [INFO] Killing All external provers ...
% 4.63/2.60 % Time passed: 2072ms (effective reasoning time: 1396ms)
% 4.63/2.60 % Axioms used in derivation (27): axiom_10, rf2_substitution_2, axiom_2, cowlThing_substitution_1, axiom_3, rf2_substitution_1, axiom_8, axiom_0, cp1_substitution_1, axiom_9, axiom_4, axiom_7, cowlNothing_substitution_1, rf3_substitution_2, xsd_string_substitution_1, rf1_substitution_2, axiom_6, ra_Px1_substitution_1, rf3_substitution_1, cp1xcomp_substitution_1, ra_Px1_substitution_2, cUnsatisfiable_substitution_1, axiom_1, xsd_integer_substitution_1, rf1_substitution_1, axiom_5, cp2_substitution_1
% 4.63/2.60 % No. of inferences in proof: 55
% 4.63/2.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2072 ms resp. 1396 ms w/o parsing
% 4.63/2.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.63/2.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------