%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM007+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 : n010.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 06:57:51 AM UTC 2026
% Result : Theorem 4.93s 3.18s
% Output : Refutation 5.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 22 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 112 ( 2 ~; 2 |; 10 &; 84 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 32 !; 2 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(goal_decl,type,
goal: $o ).
thf(reflexive_rewrite_decl,type,
reflexive_rewrite: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(rewrite_decl,type,
rewrite: $i > $i > $o ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ reflexive_rewrite ) )
& ( B @ ( A @ equalish ) ) )
=> ( C @ ( A @ reflexive_rewrite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution) ).
thf(24,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ reflexive_rewrite ) )
& ( B @ ( A @ equalish ) ) )
=> ( C @ ( A @ reflexive_rewrite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] : ( A @ ( A @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(20,plain,
! [A: $i] : ( A @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rewrite ) )
=> ( B @ ( A @ reflexive_rewrite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_in_reflexive_rewrite) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rewrite ) )
=> ( B @ ( A @ reflexive_rewrite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
( ( c @ ( a @ reflexive_rewrite ) )
& ( b @ ( a @ reflexive_rewrite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
thf(13,plain,
( ( c @ ( a @ reflexive_rewrite ) )
& ( b @ ( a @ reflexive_rewrite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equalish ) )
=> ( A @ ( B @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmtery) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ equalish ) )
=> ( A @ ( B @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
thf(2,negated_conjecture,
~ goal,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ goal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equalish ) )
=> ( B @ ( A @ reflexive_rewrite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_in_reflexive_rewrite) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ equalish ) )
=> ( B @ ( A @ reflexive_rewrite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ reflexive_rewrite ) )
=> ( ( B @ ( A @ rewrite ) )
| ( B @ ( A @ equalish ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_or_rewrite) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ reflexive_rewrite ) )
=> ( ( B @ ( A @ rewrite ) )
| ( B @ ( A @ equalish ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rewrite ) )
& ( B @ ( A @ rewrite ) ) )
=> ? [D: $i] :
( ( D @ ( C @ rewrite ) )
& ( D @ ( B @ rewrite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_diamond) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rewrite ) )
& ( B @ ( A @ rewrite ) ) )
=> ? [D: $i] :
( ( D @ ( C @ rewrite ) )
& ( D @ ( B @ rewrite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i] :
( ( ( A @ ( c @ reflexive_rewrite ) )
& ( A @ ( b @ reflexive_rewrite ) ) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_ax) ).
thf(17,plain,
! [A: $i] :
( ( ( A @ ( c @ reflexive_rewrite ) )
& ( A @ ( b @ reflexive_rewrite ) ) )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,plain,
$false,
inference(e,[status(thm)],[24,20,28,13,22,12,26,30,32,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM007+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.21/0.47 % Computer : n010.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sat Sep 26 23:20:45 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.47 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
% 1.26/1.23 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.77/1.51 % [INFO] Parsing done (278ms).
% 1.77/1.53 % [INFO] Running in sequential loop mode.
% 2.57/2.14 % [INFO] eprover registered as external prover.
% 2.57/2.15 % [INFO] Scanning for conjecture ...
% 2.86/2.27 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 3.01/2.31 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 3.01/2.36 % [INFO] Problem is first-order (TPTP FOF).
% 3.01/2.37 % [INFO] Type checking passed.
% 3.01/2.38 % [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 ...
% 4.93/3.18 % External prover 'e' found a proof!
% 4.93/3.18 % [INFO] Killing All external provers ...
% 4.93/3.18 % Time passed: 2484ms (effective reasoning time: 1633ms)
% 4.93/3.18 % 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)>
% 4.93/3.18 % Axioms used in derivation (9): rewrite_in_reflexive_rewrite, rewrite_diamond, assumption, reflexivity, symmtery, equalish_or_rewrite, equalish_in_reflexive_rewrite, substitution, goal_ax
% 4.93/3.18 % No. of inferences in proof: 22
% 4.93/3.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2484 ms resp. 1633 ms w/o parsing
% 5.02/3.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.02/3.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------