%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM008+2 : 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 7.85s 4.05s
% Output : Refutation 7.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 124 ( 2 ~; 2 |; 18 &; 88 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 32 !; 6 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(goal_decl,type,
goal: $o ).
thf(transitive_reflexive_rewrite_decl,type,
transitive_reflexive_rewrite: $i > $i > $o ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(a_decl,type,
a: $i ).
thf(rewrite_decl,type,
rewrite: $i > $i > $o ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ transitive_reflexive_rewrite ) )
& ( B @ ( A @ transitive_reflexive_rewrite ) ) )
=> ( C @ ( A @ transitive_reflexive_rewrite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_transitive_reflexive_rewrite) ).
thf(25,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ transitive_reflexive_rewrite ) )
& ( B @ ( A @ transitive_reflexive_rewrite ) ) )
=> ( C @ ( A @ transitive_reflexive_rewrite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rewrite ) )
& ( B @ ( A @ rewrite ) ) )
=> ? [D: $i] :
( ( D @ ( C @ transitive_reflexive_rewrite ) )
& ( D @ ( B @ transitive_reflexive_rewrite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lo_cfl) ).
thf(27,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rewrite ) )
& ( B @ ( A @ rewrite ) ) )
=> ? [D: $i] :
( ( D @ ( C @ transitive_reflexive_rewrite ) )
& ( D @ ( B @ transitive_reflexive_rewrite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i] :
( ( ( A @ ( c @ transitive_reflexive_rewrite ) )
& ( A @ ( b @ transitive_reflexive_rewrite ) ) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',found) ).
thf(12,plain,
! [A: $i] :
( ( ( A @ ( c @ transitive_reflexive_rewrite ) )
& ( A @ ( b @ transitive_reflexive_rewrite ) ) )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ transitive_reflexive_rewrite ) )
=> ( ? [C: $i] :
( ( B @ ( C @ transitive_reflexive_rewrite ) )
& ( C @ ( A @ rewrite ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_or_rewrite) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ transitive_reflexive_rewrite ) )
=> ( ? [C: $i] :
( ( B @ ( C @ transitive_reflexive_rewrite ) )
& ( C @ ( A @ rewrite ) ) )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ transitive_reflexive_rewrite ) )
& ( B @ ( A @ transitive_reflexive_rewrite ) )
& ( A @ ( a @ rewrite ) ) )
=> ? [D: $i] :
( ( D @ ( C @ transitive_reflexive_rewrite ) )
& ( D @ ( B @ transitive_reflexive_rewrite ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ih_cfl) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ transitive_reflexive_rewrite ) )
& ( B @ ( A @ transitive_reflexive_rewrite ) )
& ( A @ ( a @ rewrite ) ) )
=> ? [D: $i] :
( ( D @ ( C @ transitive_reflexive_rewrite ) )
& ( D @ ( B @ transitive_reflexive_rewrite ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(11,plain,
~ goal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rewrite ) )
=> ( B @ ( A @ transitive_reflexive_rewrite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_in_transitive_reflexive_rewrite) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rewrite ) )
=> ( B @ ( A @ transitive_reflexive_rewrite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ transitive_reflexive_rewrite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality_in_transitive_reflexive_rewrite) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ transitive_reflexive_rewrite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
( ( c @ ( a @ transitive_reflexive_rewrite ) )
& ( b @ ( a @ transitive_reflexive_rewrite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
thf(15,plain,
( ( c @ ( a @ transitive_reflexive_rewrite ) )
& ( b @ ( a @ transitive_reflexive_rewrite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(153,plain,
$false,
inference(e,[status(thm)],[25,27,12,35,31,11,23,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM008+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.23/0.49 % Computer : n010.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 23:20:30 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 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
% 1.43/1.37 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.92/1.66 % [INFO] Parsing done (284ms).
% 1.92/1.68 % [INFO] Running in sequential loop mode.
% 3.10/2.31 % [INFO] eprover registered as external prover.
% 3.10/2.32 % [INFO] Scanning for conjecture ...
% 3.29/2.44 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 3.29/2.48 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 3.44/2.54 % [INFO] Problem is first-order (TPTP FOF).
% 3.44/2.55 % [INFO] Type checking passed.
% 3.44/2.56 % [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 ...
% 7.42/4.05 % External prover 'e' found a proof!
% 7.85/4.05 % [INFO] Killing All external provers ...
% 7.85/4.05 % Time passed: 3341ms (effective reasoning time: 2359ms)
% 7.85/4.05 % 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)>
% 7.85/4.05 % Axioms used in derivation (8): transitivity_of_transitive_reflexive_rewrite, equal_or_rewrite, found, rewrite_in_transitive_reflexive_rewrite, lo_cfl, ih_cfl, assumption, equality_in_transitive_reflexive_rewrite
% 7.85/4.05 % No. of inferences in proof: 20
% 7.85/4.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3341 ms resp. 2359 ms w/o parsing
% 7.85/4.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.85/4.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------