%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL121-2 : 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 : n009.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 11.08s 4.67s
% Output : Refutation 11.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 464 ( 26 ~; 24 |; 0 &; 414 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Comb_Odiamond_decl,type,
c_Comb_Odiamond: $i > $i > $o ).
thf(v_r_decl,type,
v_r: $i ).
thf(t_a_decl,type,
t_a: $i ).
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_ya_decl,type,
v_ya: $i ).
thf(v_z_decl,type,
v_z: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(v_y_decl,type,
v_y: $i ).
thf(v_xaa_decl,type,
v_xaa: $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(v_x_decl,type,
v_x: $i > $i ).
thf(c_Comb_Odiamond__strip__lemmaE__1_decl,type,
c_Comb_Odiamond__strip__lemmaE__1: $i > $i > $i > $i > $i ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(24,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)],[9]) ).
thf(2,negated_conjecture,
t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_z @ ( v_ya @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(14,plain,
t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_z @ ( v_ya @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ ( D @ ( E @ ( A @ c_Comb_Odiamond__strip__lemmaE__1 ) ) ) @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Comb_Odiamond ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_0) ).
thf(20,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ ( D @ ( E @ ( A @ c_Comb_Odiamond__strip__lemmaE__1 ) ) ) @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Comb_Odiamond ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( A @ ( v_z @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( A @ ( v_xaa @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(13,plain,
! [A: $i] :
( ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( A @ ( v_z @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( A @ ( v_xaa @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( D @ ( E @ ( A @ c_Comb_Odiamond__strip__lemmaE__1 ) ) ) @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Comb_Odiamond ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Odiamond__strip__lemmaE_1) ).
thf(22,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( D @ ( E @ ( A @ c_Comb_Odiamond__strip__lemmaE__1 ) ) ) @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Comb_Odiamond ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
t_a @ ( v_r @ c_Comb_Odiamond ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(12,plain,
t_a @ ( v_r @ c_Comb_Odiamond ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,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 @ ( v_ya @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(16,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 @ ( v_ya @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,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 @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(11,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 @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__trans_0) ).
thf(26,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)],[10]) ).
thf(3,negated_conjecture,
t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( v_xaa @ ( v_y @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(15,plain,
t_a @ ( t_a @ tc_prod ) @ ( t_a @ ( v_r @ c_Transitive__Closure_Ortrancl ) @ ( t_a @ ( t_a @ ( v_xaa @ ( v_y @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(405,plain,
$false,
inference(e,[status(thm)],[24,14,20,13,22,12,16,11,26,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL121-2 : 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
% 0.22/0.47 % Computer : n009.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Sat Sep 26 23:17:30 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 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
% 1.43/1.31 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.78/1.59 % [INFO] Parsing done (274ms).
% 2.00/1.61 % [INFO] Running in sequential loop mode.
% 2.96/2.17 % [INFO] eprover registered as external prover.
% 2.96/2.19 % [INFO] Scanning for conjecture ...
% 3.22/2.34 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 3.42/2.41 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 3.42/2.43 % [INFO] Problem is propositional (TPTP CNF).
% 3.42/2.44 % [INFO] Type checking passed.
% 3.42/2.44 % [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 ...
% 11.08/4.67 % External prover 'e' found a proof!
% 11.08/4.67 % [INFO] Killing All external provers ...
% 11.08/4.67 % Time passed: 3988ms (effective reasoning time: 3053ms)
% 11.08/4.67 % Axioms used in derivation (4): cls_Transitive__Closure_Or__into__rtrancl_0, cls_Comb_Odiamond__strip__lemmaE_0, cls_Comb_Odiamond__strip__lemmaE_1, cls_Transitive__Closure_Ortrancl__trans_0
% 11.08/4.67 % No. of inferences in proof: 21
% 11.08/4.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3988 ms resp. 3053 ms w/o parsing
% 11.54/4.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.54/4.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------