%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU034+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n004.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 08:37:29 AM UTC 2026
% Result : Theorem 10.59s 14.73s
% Output : Refutation 11.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 33
% Syntax : Number of formulae : 68 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 190 ( 25 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 417 ( 18 ~; 0 |; 82 &; 277 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 73 ( 0 ^; 57 !; 16 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(function_inverse_decl,type,
function_inverse: $i > $i ).
thf(identity_relation_decl,type,
identity_relation: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(function_decl,type,
function: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(relation_composition_decl,type,
relation_composition: $i > $i > $i ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ relation_composition ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(115,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ relation_composition ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(42,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,axiom,
! [A: $i] : ( A @ identity_relation @ relation ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(121,plain,
! [A: $i] : ( A @ identity_relation @ relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(18,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(89,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(38,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(81,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ identity_relation @ function_inverse )
= ( A @ identity_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ identity_relation @ function_inverse )
= ( A @ identity_relation ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ! [A: $i] :
( ( A @ identity_relation @ function_inverse )
= ( A @ identity_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,axiom,
! [A: $i] : ( A @ identity_relation @ one_to_one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_1) ).
thf(123,plain,
! [A: $i] : ( A @ identity_relation @ one_to_one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(50,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(43,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(55,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(107,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(52,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( ( A @ ( A @ function_inverse @ relation_composition ) )
= ( A @ relation_rng @ identity_relation ) )
& ( ( A @ function_inverse @ ( A @ relation_composition ) )
= ( A @ relation_dom @ identity_relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_1) ).
thf(125,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( ( A @ ( A @ function_inverse @ relation_composition ) )
= ( A @ relation_rng @ identity_relation ) )
& ( ( A @ function_inverse @ ( A @ relation_composition ) )
= ( A @ relation_dom @ identity_relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(46,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( ( A @ relation_dom )
= ( A @ function_inverse @ relation_rng ) )
& ( ( A @ relation_rng )
= ( A @ function_inverse @ relation_dom ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(152,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( ( ( A @ relation_dom )
= ( A @ function_inverse @ relation_rng ) )
& ( ( A @ relation_rng )
= ( A @ function_inverse @ relation_dom ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( B @ ( A @ relation_composition ) @ relation )
& ( B @ ( A @ relation_composition ) @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( B @ ( A @ relation_composition ) @ relation )
& ( B @ ( A @ relation_composition ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(22,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(102,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(10,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(60,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(117,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation )
& ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_composition ) @ function )
& ( B @ ( A @ relation_composition ) @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation )
& ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_composition ) @ function )
& ( B @ ( A @ relation_composition ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(96,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(134,plain,
! [A: $i] :
( ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( A @ ( B @ relation_composition ) @ relation )
& ( A @ ( B @ relation_composition ) @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( A @ ( B @ relation_composition ) @ relation )
& ( A @ ( B @ relation_composition ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(33,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ function_inverse @ function )
& ( A @ function_inverse @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(148,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ function_inverse @ function )
& ( A @ function_inverse @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(64,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(32,axiom,
! [A: $i] :
( ( ( A @ identity_relation @ relation_rng )
= A )
& ( ( A @ identity_relation @ relation_dom )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
thf(140,plain,
! [A: $i] :
( ( ( A @ identity_relation @ relation_rng )
= A )
& ( ( A @ identity_relation @ relation_dom )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(19,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(91,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(30,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( ( B @ ( A @ relation_composition ) )
= A )
& ( ( A @ relation_rng )
= ( B @ relation_dom ) ) )
=> ( B
= ( B @ relation_dom @ identity_relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_funct_1) ).
thf(131,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( ( B @ ( A @ relation_composition ) )
= A )
& ( ( A @ relation_rng )
= ( B @ relation_dom ) ) )
=> ( B
= ( B @ relation_dom @ identity_relation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(12,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(68,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(111,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(16,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(83,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(100,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(451,plain,
$false,
inference(e,[status(thm)],[115,42,121,89,38,81,35,123,50,43,55,107,52,125,46,152,85,102,60,117,77,96,134,73,148,64,140,91,131,68,111,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU034+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.25/10.51 % Computer : n004.cluster.edu
% 0.25/10.51 % Model : x86_64 x86_64
% 0.25/10.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/10.51 % Memory : 8046.5625MB
% 0.25/10.51 % OS : Linux 6.8.0-71-generic
% 0.25/10.52 % CPULimit : 300
% 0.25/10.52 % WCLimit : 300
% 0.25/10.52 % DateTime : Sat Sep 26 08:32:18 UTC 2026
% 0.25/10.52 % CPUTime :
% 0.25/10.52 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
% 1.36/11.39 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.14/11.72 % [INFO] Parsing done (324ms).
% 2.14/11.74 % [INFO] Running in sequential loop mode.
% 3.22/12.36 % [INFO] eprover registered as external prover.
% 3.22/12.37 % [INFO] Scanning for conjecture ...
% 3.64/12.53 % [INFO] Found a conjecture (or negated_conjecture) and 44 axioms. Running axiom selection ...
% 3.82/12.65 % [INFO] Axiom selection finished. Selected 32 axioms (removed 12 axioms).
% 4.04/12.72 % [INFO] Problem is first-order (TPTP FOF).
% 4.04/12.74 % [INFO] Type checking passed.
% 4.04/12.74 % [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 ...
% 10.59/14.73 % External prover 'e' found a proof!
% 10.59/14.73 % [INFO] Killing All external provers ...
% 10.59/14.73 % Time passed: 3998ms (effective reasoning time: 2980ms)
% 10.59/14.73 % 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)>
% 10.59/14.73 % Axioms used in derivation (32): fc9_relat_1, rc1_funct_1, t52_funct_1, fc2_funct_1, dt_k2_funct_1, cc1_funct_1, fc5_relat_1, cc2_funct_1, t61_funct_1, rc2_relat_1, t44_funct_1, rc2_xboole_0, t71_relat_1, fc1_xboole_0, fc4_relat_1, rc3_funct_1, fc1_funct_1, cc1_relat_1, t55_funct_1, rc3_relat_1, t6_boole, rc2_funct_1, fc10_relat_1, rc1_relat_1, dt_k5_relat_1, dt_k6_relat_1, fc6_relat_1, t8_boole, rc1_xboole_0, fc7_relat_1, fc12_relat_1, fc8_relat_1
% 10.59/14.73 % No. of inferences in proof: 68
% 10.59/14.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3998 ms resp. 2980 ms w/o parsing
% 11.03/14.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.03/14.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------