%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO607+1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n026.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 09:45:01 AM UTC 2026
% Result : Theorem 3.52s 2.46s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 0 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 231 ( 26 ~; 13 |; 39 &; 144 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 0 ^; 25 !; 36 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_false_only_decl,type,
g_false_only: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(g_true_only_decl,type,
g_true_only: $i > $i > $o ).
thf(g_both_decl,type,
g_both: $i > $i > $o ).
thf(g_true_decl,type,
g_true: $i > $i > $o ).
thf(g_false_decl,type,
g_false: $i > $i > $o ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ g_true_only ) )
<=> ( ~ ( B @ ( A @ g_false ) )
& ( B @ ( A @ g_true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_only_g) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( ( ~ ( B @ ( A @ g_false ) )
& ( B @ ( A @ g_true ) ) )
=> ( B @ ( A @ g_true_only ) ) )
& ( ( B @ ( A @ g_true_only ) )
=> ( ~ ( B @ ( A @ g_false ) )
& ( B @ ( A @ g_true ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ g_false_only ) )
| ( B @ ( A @ g_both ) )
| ( B @ ( A @ g_true_only ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exhaustion_g) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ g_false_only ) )
| ( B @ ( A @ g_both ) )
| ( B @ ( A @ g_true_only ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ g_false_only ) )
<=> ( ~ ( B @ ( A @ g_true ) )
& ( B @ ( A @ g_false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_only_g) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( ( ~ ( B @ ( A @ g_true ) )
& ( B @ ( A @ g_false ) ) )
=> ( B @ ( A @ g_false_only ) ) )
& ( ( B @ ( A @ g_false_only ) )
=> ( ~ ( B @ ( A @ g_true ) )
& ( B @ ( A @ g_false ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ g_both ) )
<=> ( ( B @ ( A @ g_false ) )
& ( B @ ( A @ g_true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both_g) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ g_false ) )
& ( B @ ( A @ g_true ) ) )
=> ( B @ ( A @ g_both ) ) )
& ( ( B @ ( A @ g_both ) )
=> ( ( B @ ( A @ g_false ) )
& ( B @ ( A @ g_true ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
( ( ~ ? [A: $i] :
! [B: $i] : ( B @ ( A @ g_true_only ) )
& ? [A: $i] :
( ~ ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ? [B: $i] : ( B @ ( A @ g_both ) ) )
& ~ ? [A: $i] :
( ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ( A @ ( a @ g_false_only ) ) )
& ? [A: $i] :
( ~ ! [B: $i] : ( B @ ( A @ g_true_only ) )
& ~ ( A @ ( a @ g_true_only ) )
& ( ( ~ ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ? [B: $i] : ( B @ ( A @ g_both ) ) )
| ( A @ ( a @ g_both ) ) ) ) )
| ? [A: $i] :
! [B: $i] : ( B @ ( A @ g_true_only ) )
| ? [A: $i] :
( ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ( A @ ( a @ g_false_only ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nc6) ).
thf(2,negated_conjecture,
~ ( ( ~ ? [A: $i] :
! [B: $i] : ( B @ ( A @ g_true_only ) )
& ? [A: $i] :
( ~ ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ? [B: $i] : ( B @ ( A @ g_both ) ) )
& ~ ? [A: $i] :
( ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ( A @ ( a @ g_false_only ) ) )
& ? [A: $i] :
( ~ ! [B: $i] : ( B @ ( A @ g_true_only ) )
& ~ ( A @ ( a @ g_true_only ) )
& ( ( ~ ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ? [B: $i] : ( B @ ( A @ g_both ) ) )
| ( A @ ( a @ g_both ) ) ) ) )
| ? [A: $i] :
! [B: $i] : ( B @ ( A @ g_true_only ) )
| ? [A: $i] :
( ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ( A @ ( a @ g_false_only ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ( ~ ? [A: $i] :
! [B: $i] : ( B @ ( A @ g_true_only ) )
& ? [A: $i] :
( ~ ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ? [B: $i] : ( B @ ( A @ g_both ) ) )
& ~ ? [A: $i] :
( ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ( A @ ( a @ g_false_only ) ) )
& ? [A: $i] :
( ~ ! [B: $i] : ( B @ ( A @ g_true_only ) )
& ~ ( A @ ( a @ g_true_only ) )
& ( ( ~ ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ? [B: $i] : ( B @ ( A @ g_both ) ) )
| ( A @ ( a @ g_both ) ) ) ) )
| ? [A: $i] :
! [B: $i] : ( B @ ( A @ g_true_only ) )
| ? [A: $i] :
( ? [B: $i] : ( B @ ( A @ g_false_only ) )
& ( A @ ( a @ g_false_only ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,plain,
$false,
inference(e,[status(thm)],[20,41,34,27,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO607+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % 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
% 0.13/0.38 % Computer : n026.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 19:39:55 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.86/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.15 % [INFO] Parsing done (182ms).
% 1.22/1.17 % [INFO] Running in sequential loop mode.
% 1.75/1.57 % [INFO] eprover registered as external prover.
% 1.75/1.58 % [INFO] Scanning for conjecture ...
% 1.95/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.11/1.73 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.11/1.74 % [INFO] Problem is first-order (TPTP FOF).
% 2.11/1.74 % [INFO] Type checking passed.
% 2.11/1.75 % [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 ...
% 3.52/2.45 % External prover 'e' found a proof!
% 3.52/2.45 % [INFO] Killing All external provers ...
% 3.52/2.45 % Time passed: 1920ms (effective reasoning time: 1278ms)
% 3.52/2.45 % 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)>
% 3.52/2.45 % Axioms used in derivation (4): true_only_g, exhaustion_g, false_only_g, both_g
% 3.52/2.45 % No. of inferences in proof: 12
% 3.52/2.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1920 ms resp. 1278 ms w/o parsing
% 4.00/2.50 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.00/2.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------