%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET822-2 : TPTP v9.3.1. Released v3.2.0.
% 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 08:31:00 AM UTC 2026
% Result : Unsatisfiable 3.11s 2.60s
% Output : Refutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 10 ~; 8 |; 0 &; 72 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_P_decl,type,
v_P: $i > $o ).
thf(v_f_decl,type,
v_f: $i > $i ).
thf(v_b_decl,type,
v_b: $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(tc_IntDef_Oint_decl,type,
tc_IntDef_Oint: $i ).
thf(v_x_decl,type,
v_x: $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ v_x ) @ v_P )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ v_f @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ v_x ) @ v_P )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ v_f @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(12,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
v_b @ v_f @ v_P,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
v_b @ v_f @ v_P,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( B @ ( A @ v_x ) @ c_in ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ v_f @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( B @ ( A @ v_x ) @ c_in ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ v_f @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[14,9,12,7,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET822-2 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.16/0.41 % Computer : n018.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 08:20:52 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 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
% 0.88/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.23 % [INFO] Parsing done (210ms).
% 1.30/1.25 % [INFO] Running in sequential loop mode.
% 1.88/1.75 % [INFO] eprover registered as external prover.
% 1.88/1.76 % [INFO] Scanning for conjecture ...
% 2.04/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.16/1.95 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.16/1.96 % [INFO] Problem is propositional (TPTP CNF).
% 2.16/1.96 % [INFO] Type checking passed.
% 2.16/1.97 % [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 ...
% 3.11/2.59 % External prover 'e' found a proof!
% 3.11/2.59 % [INFO] Killing All external provers ...
% 3.11/2.59 % Time passed: 2034ms (effective reasoning time: 1333ms)
% 3.11/2.59 % Axioms used in derivation (3): cls_Set_OinsertCI_1, cls_Set_OemptyE_0, cls_Set_OinsertE_0
% 3.11/2.59 % No. of inferences in proof: 13
% 3.11/2.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2034 ms resp. 1333 ms w/o parsing
% 3.30/2.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.30/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------