%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL102-2 : 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 : n013.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 06:56:29 AM UTC 2026
% Result : Unsatisfiable 3.41s 2.63s
% Output : Refutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 230 ( 10 ~; 8 |; 0 &; 212 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% 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_za_decl,type,
v_za: $i ).
thf(tc_Comb_Ocomb_decl,type,
tc_Comb_Ocomb: $i ).
thf(c_Comb_Ocontract_decl,type,
c_Comb_Ocontract: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_Comb_Ocomb_Oop_A_D_D_decl,type,
c_Comb_Ocomb_Oop_A_D_D: $i > $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(v_z_decl,type,
v_z: $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(3,negated_conjecture,
~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( tc_Comb_Ocomb @ ( c_Comb_Ocontract @ c_Transitive__Closure_Ortrancl ) @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_z @ ( v_za @ c_Comb_Ocomb_Oop_A_D_D ) @ ( v_z @ ( v_x @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(9,plain,
~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( tc_Comb_Ocomb @ ( c_Comb_Ocontract @ c_Transitive__Closure_Ortrancl ) @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_z @ ( v_za @ c_Comb_Ocomb_Oop_A_D_D ) @ ( v_z @ ( v_x @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,negated_conjecture,
tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Ocontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_za @ ( v_y @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(7,plain,
tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Ocontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_za @ ( v_y @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Ocontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ c_Comb_Ocomb_Oop_A_D_D ) @ ( C @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Ocontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocontract_OAp1_0) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Ocontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ c_Comb_Ocomb_Oop_A_D_D ) @ ( C @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Ocontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( tc_Comb_Ocomb @ ( c_Comb_Ocontract @ c_Transitive__Closure_Ortrancl ) @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_z @ ( v_y @ c_Comb_Ocomb_Oop_A_D_D ) @ ( v_z @ ( v_x @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(8,plain,
tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( tc_Comb_Ocomb @ ( c_Comb_Ocontract @ c_Transitive__Closure_Ortrancl ) @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_z @ ( v_y @ c_Comb_Ocomb_Oop_A_D_D ) @ ( v_z @ ( v_x @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__trans_0) ).
thf(15,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[9,13,7,11,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL102-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.13/0.40 % Computer : n013.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 23:14:51 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.82/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.23 % [INFO] Parsing done (215ms).
% 1.22/1.24 % [INFO] Running in sequential loop mode.
% 1.88/1.74 % [INFO] eprover registered as external prover.
% 1.88/1.74 % [INFO] Scanning for conjecture ...
% 2.06/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.06/1.88 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.20/1.90 % [INFO] Problem is propositional (TPTP CNF).
% 2.20/1.91 % [INFO] Type checking passed.
% 2.20/1.91 % [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 ...
% 3.41/2.63 % External prover 'e' found a proof!
% 3.41/2.63 % [INFO] Killing All external provers ...
% 3.41/2.63 % Time passed: 2082ms (effective reasoning time: 1387ms)
% 3.41/2.63 % Axioms used in derivation (3): cls_Transitive__Closure_Or__into__rtrancl_0, cls_Comb_Ocontract_OAp1_0, cls_Transitive__Closure_Ortrancl__trans_0
% 3.41/2.63 % No. of inferences in proof: 13
% 3.41/2.63 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2082 ms resp. 1387 ms w/o parsing
% 3.41/2.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.41/2.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------