%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT007-3 : TPTP v9.3.1. Released v1.0.0.
% 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 : n014.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 06:55:19 AM UTC 2026
% Result : Unsatisfiable 2.46s 1.49s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 160 ( 18 ~; 22 |; 0 &; 120 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(there_exists_decl,type,
there_exists: $i > $o ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(c2_decl,type,
c2: $i ).
thf(c1_decl,type,
c1: $i ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(domain_decl,type,
domain: $i > $i ).
thf(codomain_decl,type,
codomain: $i > $i ).
thf(f1_decl,type,
f1: $i > $i > $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ( B @ ( A @ f1 ) @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles1) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ( B @ ( A @ f1 ) @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ domain @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
thf(20,plain,
! [A: $i] :
( ( A @ there_exists )
| ~ ( A @ domain @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( B @ ( A @ f1 ) @ ( B @ equalish ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles3) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( B @ ( A @ f1 ) @ ( B @ equalish ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
~ ( c1 @ ( c2 @ compose ) @ there_exists ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c1_c2_is_defined) ).
thf(13,plain,
~ ( c1 @ ( c2 @ compose ) @ there_exists ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
c1 @ codomain @ ( c2 @ domain @ equalish ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_c2_equals_codomain_of_c1) ).
thf(32,plain,
c1 @ codomain @ ( c2 @ domain @ equalish ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ compose ) @ there_exists )
| ~ ( B @ codomain @ ( A @ domain @ equalish ) )
| ~ ( A @ domain @ there_exists ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ compose ) @ there_exists )
| ~ ( B @ codomain @ ( A @ domain @ equalish ) )
| ~ ( A @ domain @ there_exists ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ( B @ ( A @ f1 ) @ ( B @ equalish ) )
| ( B @ ( A @ f1 ) @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',indiscernibles2) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ( B @ ( A @ f1 ) @ ( B @ equalish ) )
| ( B @ ( A @ f1 ) @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
c2 @ domain @ there_exists,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_c2_exists) ).
thf(30,plain,
c2 @ domain @ there_exists,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(15,plain,
! [A: $i] : ( A @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
c1 @ domain @ there_exists,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_c1_exists) ).
thf(31,plain,
c1 @ domain @ there_exists,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[24,20,28,13,32,22,18,26,30,15,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT007-3 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.14/0.40 % Computer : n014.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 22:48:46 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
% 0.70/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.94/0.80 % [INFO] Parsing done (93ms).
% 0.94/0.81 % [INFO] Running in sequential loop mode.
% 1.13/1.00 % [INFO] eprover registered as external prover.
% 1.13/1.00 % [INFO] Scanning for conjecture ...
% 1.42/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.42/1.06 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.42/1.07 % [INFO] Problem is propositional (TPTP CNF).
% 1.42/1.07 % [INFO] Type checking passed.
% 1.42/1.08 % [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 ...
% 2.46/1.48 % External prover 'e' found a proof!
% 2.46/1.48 % [INFO] Killing All external provers ...
% 2.46/1.48 % Time passed: 988ms (effective reasoning time: 670ms)
% 2.46/1.49 % Axioms used in derivation (11): domain_has_elements, indiscernibles3, domain_codomain_composition2, reflexivity, indiscernibles1, domain_of_c2_equals_codomain_of_c1, domain_of_c1_exists, domain_of_c2_exists, symmetry, transitivity, indiscernibles2
% 2.46/1.49 % No. of inferences in proof: 25
% 2.46/1.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 988 ms resp. 670 ms w/o parsing
% 2.73/1.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.73/1.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------