%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS084+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 : n018.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 07:44:36 AM UTC 2026
% Result : Unsatisfiable 4.69s 2.61s
% Output : Refutation 4.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 25
% Syntax : Number of formulae : 51 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 164 ( 32 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 325 ( 11 ~; 0 |; 59 &; 201 @)
% ( 5 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 120 ( 0 ^; 111 !; 9 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
thf(cUnsatisfiable_decl,type,
cUnsatisfiable: $i > $o ).
thf(cc_decl,type,
cc: $i > $o ).
thf(cd_decl,type,
cd: $i > $o ).
thf(cowlNothing_decl,type,
cowlNothing: $i > $o ).
thf(cowlThing_decl,type,
cowlThing: $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_35232_decl,type,
i2003_11_14_17_19_35232: $i ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ cd )
<=> ( ( A @ cc )
& ? [B: $i] :
( ~ ( B @ cc )
& ( B @ ( A @ rf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(110,plain,
! [A: $i] :
( ( ( ( A @ cc )
& ? [B: $i] :
( ~ ( B @ cc )
& ( B @ ( A @ rf ) ) ) )
=> ( A @ cd ) )
& ( ( A @ cd )
=> ( ( A @ cc )
& ? [B: $i] :
( ~ ( B @ cc )
& ( B @ ( A @ rf ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvF ) )
<=> ( A @ ( B @ rf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(121,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)],[21]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(92,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ cd )
& ( A = B ) )
=> ( B @ cd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cd_substitution_1) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( ( A @ cd )
& ( A = B ) )
=> ( B @ cd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf ) )
& ( B @ ( A @ rf ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(118,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf ) )
& ( B @ ( A @ rf ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ cUnsatisfiable )
<=> ( ~ ( A @ cc )
& ! [B: $i] :
( ( B @ ( A @ rinvR ) )
=> ? [C: $i] :
( ( C @ cd )
& ( C @ ( B @ rinvF ) ) ) )
& ? [B: $i] :
( ( B @ cd )
& ( B @ ( A @ rinvF ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(98,plain,
! [A: $i] :
( ( ( ~ ( A @ cc )
& ! [B: $i] :
( ( B @ ( A @ rinvR ) )
=> ? [C: $i] :
( ( C @ cd )
& ( C @ ( B @ rinvF ) ) ) )
& ? [B: $i] :
( ( B @ cd )
& ( B @ ( A @ rinvF ) ) ) )
=> ( A @ cUnsatisfiable ) )
& ( ( A @ cUnsatisfiable )
=> ( ~ ( A @ cc )
& ! [B: $i] :
( ( B @ ( A @ rinvR ) )
=> ? [C: $i] :
( ( C @ cd )
& ( C @ ( B @ rinvF ) ) ) )
& ? [B: $i] :
( ( B @ cd )
& ( B @ ( A @ rinvF ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,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(66,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvR ) )
& ( A = B ) )
=> ( B @ ( C @ rinvR ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(24,axiom,
i2003_11_14_17_19_35232 @ cUnsatisfiable,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(135,plain,
i2003_11_14_17_19_35232 @ cUnsatisfiable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ( A @ cc )
& ( A = B ) )
=> ( B @ cc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc_substitution_1) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( ( A @ cc )
& ( A = B ) )
=> ( B @ cc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rf ) )
=> ( B @ ( A @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
thf(136,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rf ) )
=> ( B @ ( A @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(10,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(62,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvR ) )
& ( A = B ) )
=> ( C @ ( B @ rinvR ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,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(46,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rf ) )
& ( A = B ) )
=> ( C @ ( B @ rf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,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(78,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ rr ) )
& ( B @ ( A @ rr ) ) )
=> ( C @ ( A @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ rr ) )
& ( B @ ( A @ rr ) ) )
=> ( C @ ( A @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(13,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(74,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rr ) )
& ( A = B ) )
=> ( B @ ( C @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,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(70,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( A = B ) )
=> ( C @ ( B @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,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(54,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvF ) )
& ( A = B ) )
=> ( C @ ( B @ rinvF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(86,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,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(50,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rf ) )
& ( A = B ) )
=> ( B @ ( C @ rf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvR ) )
<=> ( A @ ( B @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(127,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)],[22]) ).
thf(9,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(58,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvF ) )
& ( A = B ) )
=> ( B @ ( C @ rinvF ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,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(82,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(138,plain,
$false,
inference(e,[status(thm)],[42,110,121,92,34,118,98,66,135,26,30,136,62,46,78,133,74,38,70,54,86,50,127,58,82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS084+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % 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
% 0.14/0.39 % Computer : n018.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 19:41:06 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.20 % [INFO] Parsing done (207ms).
% 1.43/1.21 % [INFO] Running in sequential loop mode.
% 2.20/1.61 % [INFO] eprover registered as external prover.
% 2.20/1.62 % [INFO] Scanning for conjecture ...
% 2.20/1.67 % [INFO] 25 axioms and no conjecture found.
% 2.39/1.77 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.78 % [INFO] Type checking passed.
% 2.39/1.78 % [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 ...
% 4.69/2.61 % External prover 'e' found a proof!
% 4.69/2.61 % [INFO] Killing All external provers ...
% 4.69/2.61 % Time passed: 2069ms (effective reasoning time: 1390ms)
% 4.69/2.61 % Axioms used in derivation (25): rinvF_substitution_2, cc_substitution_1, rr_substitution_1, axiom_2, xsd_string_substitution_1, axiom_6, axiom_3, cUnsatisfiable_substitution_1, axiom_8, rinvR_substitution_1, axiom_5, rinvF_substitution_1, rf_substitution_1, rinvR_substitution_2, axiom_4, axiom_7, cowlNothing_substitution_1, cowlThing_substitution_1, cd_substitution_1, axiom_1, xsd_integer_substitution_1, rf_substitution_2, axiom_0, axiom_9, rr_substitution_2
% 4.69/2.61 % No. of inferences in proof: 51
% 4.69/2.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2069 ms resp. 1390 ms w/o parsing
% 4.69/2.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.69/2.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------