%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU615_8 : TPTP v9.3.1. Released v8.0.0.
% 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 08:39:40 AM UTC 2026
% Result : Theorem 4.52s 2.64s
% Output : Refutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 101 ( 8 equ; 0 cnn)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 369 ( 60 ~; 43 |; 11 &; 212 @)
% ( 0 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 0 ^; 48 !; 0 ?; 51 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(symdiff_decl,type,
symdiff: $i > $i > $i ).
thf(symdiffE_decl,type,
symdiffE: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ~ ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ~ ( sk1 @ ( B @ in ) )
=> ( ~ ( A @ ( B @ in ) )
=> ~ ( A @ ( sk1 @ symdiff ) @ ( B @ in ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ~ ( sk1 @ ( A @ in ) )
=> ( ~ ( sk2 @ ( A @ in ) )
=> ~ ( sk2 @ ( sk1 @ symdiff ) @ ( A @ in ) ) ) ) ) ) ).
thf(1,conjecture,
( symdiffE
=> ! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(2,negated_conjecture,
~ ( symdiffE
=> ! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ( symdiffE
=> ! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( sk2 @ ( sk1 @ symdiff ) @ ( sk3 @ in ) )
& ~ ( sk2 @ ( sk3 @ in ) )
& ~ ( sk1 @ ( sk3 @ in ) )
& symdiffE ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
sk2 @ ( sk1 @ symdiff ) @ ( sk3 @ in ),
inference(cnfConj,[status(thm)],[5]) ).
thf(3,axiom,
( symdiffE
= ( ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ symdiff ) @ ( C @ in ) )
=> ! [D: $o] :
( ( ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> D ) )
=> ( ( ~ ( A @ ( C @ in ) )
=> ( ( B @ ( C @ in ) )
=> D ) )
=> D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(10,plain,
( symdiffE
= ( ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ symdiff ) @ ( C @ in ) )
=> ! [D: $o] :
( ( ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> D ) )
=> ( ( ~ ( A @ ( C @ in ) )
=> ( ( B @ ( C @ in ) )
=> D ) )
=> D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
( symdiffE
= ( ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ symdiff ) @ ( C @ in ) )
=> ! [D: $o] :
( ( ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> D ) )
=> ( ( ~ ( A @ ( C @ in ) )
=> ( ( B @ ( C @ in ) )
=> D ) )
=> D ) ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(6,plain,
symdiffE,
inference(cnfConj,[status(thm)],[5]) ).
thf(20,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ symdiff ) @ ( C @ in ) )
=> ! [D: $o] :
( ( ( A @ ( C @ in ) )
=> ( ~ ( B @ ( C @ in ) )
=> D ) )
=> ( ( ~ ( A @ ( C @ in ) )
=> ( ( B @ ( C @ in ) )
=> D ) )
=> D ) ) ),
inference(rewrite,[status(thm)],[11,6]) ).
thf(21,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( D
| ~ D
| ~ D
| ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) )
& ( D
| ( B @ ( C @ in ) )
| ~ D
| ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) )
& ( D
| ~ ( A @ ( C @ in ) )
| ~ D
| ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) )
& ( D
| ~ D
| ~ ( B @ ( C @ in ) )
| ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) )
& ( D
| ( B @ ( C @ in ) )
| ~ ( B @ ( C @ in ) )
| ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) )
& ( D
| ~ ( A @ ( C @ in ) )
| ~ ( B @ ( C @ in ) )
| ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) )
& ( D
| ~ D
| ( A @ ( C @ in ) )
| ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) )
& ( D
| ( B @ ( C @ in ) )
| ( A @ ( C @ in ) )
| ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) )
& ( D
| ~ ( A @ ( C @ in ) )
| ( A @ ( C @ in ) )
| ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( D
| ( B @ ( C @ in ) )
| ( A @ ( C @ in ) )
| ~ ( B @ ( A @ symdiff ) @ ( C @ in ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(32,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ symdiff ) @ ( sk3 @ in ) )
!= ( B @ ( A @ symdiff ) @ ( C @ in ) ) )
| D
| ( B @ ( C @ in ) )
| ( A @ ( C @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9,22]) ).
thf(33,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ symdiff ) @ ( sk3 @ in ) )
!= ( B @ ( A @ symdiff ) @ ( C @ in ) ) )
| D
| ( B @ ( C @ in ) )
| ( A @ ( C @ in ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(34,plain,
! [A: $o] :
( A
| ( sk2 @ ( sk3 @ in ) )
| ( sk1 @ ( sk3 @ in ) ) ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(57,plain,
! [A: $o] :
( A
| ( sk2 @ ( sk3 @ in ) )
| ( sk1 @ ( sk3 @ in ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(7,plain,
~ ( sk1 @ ( sk3 @ in ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
~ ( sk2 @ ( sk3 @ in ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(68,plain,
! [A: $o] :
( A
| $false
| $false ),
inference(rewrite,[status(thm)],[57,7,8]) ).
thf(69,plain,
! [A: $o] : A,
inference(simp,[status(thm)],[68]) ).
thf(81,plain,
$false,
inference(prim_subst,[status(thm)],[69:[bind(A,$thf( $false ))]]) ).
thf(84,plain,
$false,
inference(simp,[status(thm)],[81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU615_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % 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
% 0.14/0.40 % Computer : n004.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 10:13:21 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.17 % [INFO] Parsing done (184ms).
% 1.27/1.18 % [INFO] Running in sequential loop mode.
% 1.82/1.58 % [INFO] eprover registered as external prover.
% 1.82/1.59 % [INFO] Scanning for conjecture ...
% 2.01/1.68 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.21/1.75 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.21/1.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.21/1.76 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.21/1.76 % [INFO] Type checking passed.
% 2.21/1.76 % [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 ...
% 4.52/2.63 % [INFO] Killing All external provers ...
% 4.52/2.64 % Time passed: 2094ms (effective reasoning time: 1445ms)
% 4.52/2.64 % 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)>
% 4.52/2.64 % Axioms used in derivation (1): symdiffE
% 4.52/2.64 % No. of inferences in proof: 22
% 4.52/2.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2094 ms resp. 1445 ms w/o parsing
% 4.52/2.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.52/2.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------