%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL120-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n008.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 06:56:35 AM UTC 2026
% Result : Unsatisfiable 3.43s 6.91s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of formulae : 7 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 9 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 94 ( 4 ~; 2 |; 0 &; 88 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_y_decl,type,
v_y: $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(v_r_decl,type,
v_r: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(1,negated_conjecture,
t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( v_x @ ( v_y @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(4,plain,
t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( v_x @ ( v_y @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( A @ ( v_y @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(5,plain,
! [A: $i] :
( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( A @ ( v_y @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[4,5,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL120-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.24/5.50 % Computer : n008.cluster.edu
% 0.24/5.50 % Model : x86_64 x86_64
% 0.24/5.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/5.50 % Memory : 8046.5625MB
% 0.24/5.50 % OS : Linux 6.8.0-71-generic
% 0.24/5.50 % CPULimit : 300
% 0.24/5.50 % WCLimit : 300
% 0.24/5.50 % DateTime : Sat Sep 26 23:18:02 UTC 2026
% 0.24/5.51 % CPUTime :
% 0.24/5.51 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
% 1.06/6.11 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/6.21 % [INFO] Parsing done (99ms).
% 1.41/6.21 % [INFO] Running in sequential loop mode.
% 1.87/6.44 % [INFO] eprover registered as external prover.
% 1.87/6.44 % [INFO] Scanning for conjecture ...
% 2.07/6.50 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.07/6.52 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.07/6.52 % [INFO] Problem is propositional (TPTP CNF).
% 2.07/6.52 % [INFO] Type checking passed.
% 2.07/6.53 % [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 ...
% 3.43/6.91 % External prover 'e' found a proof!
% 3.43/6.91 % [INFO] Killing All external provers ...
% 3.43/6.91 % Time passed: 1208ms (effective reasoning time: 692ms)
% 3.43/6.91 % Axioms used in derivation (1): cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0
% 3.43/6.91 % No. of inferences in proof: 7
% 3.43/6.91 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1208 ms resp. 692 ms w/o parsing
% 3.43/6.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.43/6.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------