%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU709_8 : TPTP v9.3.1. Released v8.0.0.
% 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 : n006.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 08:40:02 AM UTC 2026
% Result : Theorem 2.71s 1.58s
% Output : Refutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 18 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 151 ( 4 ~; 0 |; 1 &; 106 @)
% ( 1 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 44 ( 0 ^; 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(setadjoinIL_decl,type,
setadjoinIL: $o ).
thf(in__Cong_decl,type,
in__Cong: $o ).
thf(secondinupair_decl,type,
secondinupair: $o ).
thf(if_decl,type,
if: $i > $o > $i > $i > $i ).
thf(iftrue_decl,type,
iftrue: $o ).
thf(iffalse_decl,type,
iffalse: $o ).
thf(6,axiom,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( A @ ( C @ in ) )
<=> ( B @ ( D @ in ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(24,plain,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( ( B @ ( D @ in ) )
=> ( A @ ( C @ in ) ) )
& ( ( A @ ( C @ in ) )
=> ( B @ ( D @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
( iftrue
= ( ! [A: $i,B: $o,C: $i] :
( ( A @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( B
=> ( ( D @ ( C @ ( B @ ( A @ if ) ) ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(20,plain,
( iftrue
= ( ! [A: $i,B: $o,C: $i] :
( ( A @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( B
=> ( ( D @ ( C @ ( B @ ( A @ if ) ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
( secondinupair
= ( ! [A: $i,B: $i] : ( emptyset @ ( B @ setadjoin ) @ ( A @ setadjoin ) @ ( B @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(22,plain,
( secondinupair
= ( ! [A: $i,B: $i] : ( emptyset @ ( B @ setadjoin ) @ ( A @ setadjoin ) @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
( iffalse
= ( ! [A: $i,B: $o,C: $i] :
( ( A @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( ~ B
=> ( ( D @ ( C @ ( B @ ( A @ if ) ) ) )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(18,plain,
( iffalse
= ( ! [A: $i,B: $o,C: $i] :
( ( A @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( ~ B
=> ( ( D @ ( C @ ( B @ ( A @ if ) ) ) )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
( setadjoinIL
= ( ! [A: $i,B: $i] : ( B @ ( A @ setadjoin ) @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(26,plain,
( setadjoinIL
= ( ! [A: $i,B: $i] : ( B @ ( A @ setadjoin ) @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [A: $i,B: $o,C: $i] :
( ( A @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( emptyset @ ( D @ setadjoin ) @ ( C @ setadjoin ) @ ( D @ ( C @ ( B @ ( A @ if ) ) ) @ in ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(2,negated_conjecture,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [A: $i,B: $o,C: $i] :
( ( A @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( emptyset @ ( D @ setadjoin ) @ ( C @ setadjoin ) @ ( D @ ( C @ ( B @ ( A @ if ) ) ) @ in ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [A: $i,B: $o,C: $i] :
( ( A @ ( C @ in ) )
=> ! [D: $i] :
( ( A @ ( D @ in ) )
=> ( emptyset @ ( D @ setadjoin ) @ ( C @ setadjoin ) @ ( D @ ( C @ ( B @ ( A @ if ) ) ) @ in ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,plain,
$false,
inference(e,[status(thm)],[24,20,22,18,26,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU709_8 : TPTP v9.3.1. Released v8.0.0.
% 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
% 0.13/0.39 % Computer : n006.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 10:20:40 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.71/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.94/0.82 % [INFO] Parsing done (105ms).
% 0.94/0.83 % [INFO] Running in sequential loop mode.
% 1.49/1.06 % [INFO] eprover registered as external prover.
% 1.49/1.06 % [INFO] Scanning for conjecture ...
% 1.49/1.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.49/1.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.49/1.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.49/1.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.49/1.12 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.49/1.14 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.75/1.16 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.75/1.16 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.75/1.16 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.75/1.16 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.75/1.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.75/1.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.75/1.17 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.75/1.17 % [INFO] Type checking passed.
% 1.75/1.17 % [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 ...
% 2.71/1.57 % External prover 'e' found a proof!
% 2.71/1.57 % [INFO] Killing All external provers ...
% 2.71/1.57 % Time passed: 1078ms (effective reasoning time: 738ms)
% 2.71/1.57 % 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)>
% 2.71/1.57 % Axioms used in derivation (5): secondinupair, setadjoinIL, iffalse, in__Cong, iftrue
% 2.71/1.57 % No. of inferences in proof: 14
% 2.71/1.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1078 ms resp. 738 ms w/o parsing
% 2.99/1.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.99/1.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------