%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS086+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 07:44:37 AM UTC 2026
% Result : Unsatisfiable 3.32s 1.96s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 22
% Syntax : Number of formulae : 45 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 141 ( 30 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 277 ( 8 ~; 0 |; 50 &; 173 @)
% ( 4 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 107 ( 0 ^; 98 !; 9 ?; 107 :)
% 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(rf_decl,type,
rf: $i > $i > $o ).
thf(rinvF_decl,type,
rinvF: $i > $i > $o ).
thf(rinvR_decl,type,
rinvR: $i > $i > $o ).
thf(rr_decl,type,
rr: $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_19_42328_decl,type,
i2003_11_14_17_19_42328: $i ).
thf(18,axiom,
! [A: $i] :
( ( A @ cowlThing )
=> ! [B: $i,C: $i] :
( ( ( C @ ( A @ rf ) )
& ( B @ ( A @ rf ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(101,plain,
! [A: $i] :
( ( A @ cowlThing )
=> ! [B: $i,C: $i] :
( ( ( C @ ( A @ rf ) )
& ( B @ ( A @ rf ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvR ) )
<=> ( A @ ( B @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ rr ) )
=> ( B @ ( A @ rinvR ) ) )
& ( ( B @ ( A @ rinvR ) )
=> ( A @ ( B @ rr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ rr ) )
& ( B @ ( A @ rr ) ) )
=> ( C @ ( A @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(116,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ rr ) )
& ( B @ ( A @ rr ) ) )
=> ( C @ ( A @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(85,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xsd_integer_substitution_1) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf ) )
& ( A = B ) )
=> ( C @ ( B @ rf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rf_substitution_1) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf ) )
& ( A = B ) )
=> ( C @ ( B @ rf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ cUnsatisfiable )
<=> ? [B: $i] :
( ( B @ cp1 )
& ? [C: $i] :
( ? [D: $i] :
( ~ ( D @ cp1 )
& ( D @ ( C @ rf ) ) )
& ( C @ ( B @ rinvF ) ) )
& ( B @ ( A @ rf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(91,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cp1 )
& ? [C: $i] :
( ? [D: $i] :
( ~ ( D @ cp1 )
& ( D @ ( C @ rf ) ) )
& ( C @ ( B @ rinvF ) ) )
& ( B @ ( A @ rf ) ) )
=> ( A @ cUnsatisfiable ) )
& ( ( A @ cUnsatisfiable )
=> ? [B: $i] :
( ( B @ cp1 )
& ? [C: $i] :
( ? [D: $i] :
( ~ ( D @ cp1 )
& ( D @ ( C @ rf ) ) )
& ( C @ ( B @ rinvF ) ) )
& ( B @ ( A @ rf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp1 )
& ( A = B ) )
=> ( B @ cp1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1_substitution_1) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( ( A @ cp1 )
& ( A = B ) )
=> ( B @ cp1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( A = B ) )
=> ( C @ ( B @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_substitution_1) ).
thf(63,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( A = B ) )
=> ( C @ ( B @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf ) )
& ( A = B ) )
=> ( B @ ( C @ rf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rf_substitution_2) ).
thf(43,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf ) )
& ( A = B ) )
=> ( B @ ( C @ rf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvF ) )
<=> ( A @ ( B @ rf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(104,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ rf ) )
=> ( B @ ( A @ rinvF ) ) )
& ( ( B @ ( A @ rinvF ) )
=> ( A @ ( B @ rf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xsd_string_substitution_1) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvF ) )
& ( A = B ) )
=> ( B @ ( C @ rinvF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvF_substitution_2) ).
thf(51,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvF ) )
& ( A = B ) )
=> ( B @ ( C @ rinvF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(79,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvF ) )
& ( A = B ) )
=> ( C @ ( B @ rinvF ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvF_substitution_1) ).
thf(47,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvF ) )
& ( A = B ) )
=> ( C @ ( B @ rinvF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(27,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 @ rinvR ) )
& ( A = B ) )
=> ( B @ ( C @ rinvR ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvR_substitution_2) ).
thf(59,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvR ) )
& ( A = B ) )
=> ( B @ ( C @ rinvR ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
i2003_11_14_17_19_42328 @ cUnsatisfiable,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(118,plain,
i2003_11_14_17_19_42328 @ cUnsatisfiable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rr ) )
& ( A = B ) )
=> ( B @ ( C @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_substitution_2) ).
thf(67,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rr ) )
& ( A = B ) )
=> ( B @ ( C @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvR ) )
& ( A = B ) )
=> ( C @ ( B @ rinvR ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvR_substitution_1) ).
thf(55,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvR ) )
& ( A = B ) )
=> ( C @ ( B @ rinvR ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(119,plain,
$false,
inference(e,[status(thm)],[101,110,116,85,71,39,91,35,63,43,104,75,51,79,47,27,59,118,67,31,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS086+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.41 % Computer : n002.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Fri Sep 25 19:41:35 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.69/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.91/0.83 % [INFO] Parsing done (106ms).
% 0.91/0.84 % [INFO] Running in sequential loop mode.
% 1.44/1.04 % [INFO] eprover registered as external prover.
% 1.44/1.05 % [INFO] Scanning for conjecture ...
% 1.44/1.09 % [INFO] 22 axioms and no conjecture found.
% 1.63/1.18 % [INFO] Problem is first-order (TPTP FOF).
% 1.63/1.19 % [INFO] Type checking passed.
% 1.63/1.20 % [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 ...
% 3.32/1.96 % External prover 'e' found a proof!
% 3.32/1.96 % [INFO] Killing All external provers ...
% 3.32/1.96 % Time passed: 1451ms (effective reasoning time: 1115ms)
% 3.32/1.96 % 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
% 3.32/1.96 % No. of inferences in proof: 45
% 3.32/1.96 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1451 ms resp. 1115 ms w/o parsing
% 3.32/2.03 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.32/2.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------