%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL109-2 : 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 : n019.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 06:56:31 AM UTC 2026
% Result : Unsatisfiable 3.44s 2.30s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 232 ( 8 ~; 6 |; 0 &; 218 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 10 con; 0-4 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 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_z_decl,type,
v_z: $i ).
thf(v_w_decl,type,
v_w: $i ).
thf(tc_Comb_Ocomb_decl,type,
tc_Comb_Ocomb: $i ).
thf(c_Comb_Oparcontract_decl,type,
c_Comb_Oparcontract: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(v_xb_decl,type,
v_xb: $i ).
thf(v_x_H_decl,type,
v_x_H: $i ).
thf(v_yb_decl,type,
v_yb: $i ).
thf(v_y_Ha_decl,type,
v_y_Ha: $i ).
thf(c_Comb_Ocomb_Oop_A_D_D_decl,type,
c_Comb_Ocomb_Oop_A_D_D: $i > $i > $i ).
thf(c_Comb_Ocomb_OS_decl,type,
c_Comb_Ocomb_OS: $i ).
thf(4,negated_conjecture,
! [A: $i] :
( ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_w @ ( v_y_Ha @ ( v_x_H @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_z @ ( v_yb @ c_Comb_Ocomb_Oop_A_D_D ) @ ( v_z @ ( v_xb @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(10,plain,
! [A: $i] :
( ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_w @ ( v_y_Ha @ ( v_x_H @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_z @ ( v_yb @ c_Comb_Ocomb_Oop_A_D_D ) @ ( v_z @ ( v_xb @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,negated_conjecture,
tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_y_Ha @ ( v_yb @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,plain,
tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_y_Ha @ ( v_yb @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( D @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__4_0) ).
thf(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( D @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( 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_Comb_Ocomb_Oop_A_D_D ) @ ( C @ ( B @ ( A @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__3_0) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] : ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( 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_Comb_Ocomb_Oop_A_D_D ) @ ( C @ ( B @ ( A @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ 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_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_w @ ( v_z @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_w @ ( v_z @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x_H @ ( v_xb @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,plain,
tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x_H @ ( v_xb @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
$false,
inference(e,[status(thm)],[10,9,13,12,7,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL109-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.15/0.42 % Computer : n019.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 23:16:18 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 0.88/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.20 % [INFO] Parsing done (190ms).
% 1.40/1.21 % [INFO] Running in sequential loop mode.
% 2.04/1.62 % [INFO] eprover registered as external prover.
% 2.04/1.63 % [INFO] Scanning for conjecture ...
% 2.23/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.23/1.78 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.23/1.79 % [INFO] Problem is propositional (TPTP CNF).
% 2.23/1.79 % [INFO] Type checking passed.
% 2.41/1.80 % [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 ...
% 3.44/2.29 % External prover 'e' found a proof!
% 3.44/2.29 % [INFO] Killing All external provers ...
% 3.44/2.29 % Time passed: 1724ms (effective reasoning time: 1076ms)
% 3.44/2.30 % Axioms used in derivation (2): cls_Comb_Oparcontract_Ointros__4_0, cls_Comb_Oparcontract_Ointros__3_0
% 3.44/2.30 % No. of inferences in proof: 13
% 3.44/2.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1724 ms resp. 1076 ms w/o parsing
% 3.71/2.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.71/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------