%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET825-2 : 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 : n016.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 08:31:01 AM UTC 2026
% Result : Unsatisfiable 3.52s 2.51s
% Output : Refutation 3.52s
% 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 : 23 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 180 ( 10 ~; 10 |; 0 &; 160 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_Q_decl,type,
v_Q: $i > $o ).
thf(v_n_decl,type,
v_n: $i ).
thf(v_m_decl,type,
v_m: $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(tc_nat_decl,type,
tc_nat: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(v_x_decl,type,
v_x: $i > $i ).
thf(v_xa_decl,type,
v_xa: $i > $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_Relation_OId_decl,type,
c_Relation_OId: $i ).
thf(4,negated_conjecture,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ v_xa @ c_Suc @ ( A @ v_x @ c_Suc @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( v_m @ ( v_n @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(10,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ v_xa @ c_Suc @ ( A @ v_x @ c_Suc @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( v_m @ ( v_n @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(14,plain,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ v_xa @ ( A @ v_x @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( v_m @ ( v_n @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( A @ v_xa @ ( A @ v_x @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_nat @ ( tc_nat @ tc_prod ) @ ( A @ ( tc_nat @ ( tc_nat @ ( v_m @ ( v_n @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
v_n @ v_Q,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
v_n @ v_Q,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
~ ( v_m @ v_Q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,plain,
~ ( v_m @ v_Q ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[10,14,9,7,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET825-2 : 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
% 0.13/0.59 % Computer : n016.cluster.edu
% 0.13/0.59 % Model : x86_64 x86_64
% 0.13/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.59 % Memory : 8046.5625MB
% 0.13/0.59 % OS : Linux 6.8.0-71-generic
% 0.13/0.59 % CPULimit : 300
% 0.13/0.59 % WCLimit : 300
% 0.13/0.59 % DateTime : Sat Sep 26 08:23:47 UTC 2026
% 0.13/0.59 % CPUTime :
% 0.13/0.59 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
% 0.94/1.18 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.37 % [INFO] Parsing done (185ms).
% 1.24/1.39 % [INFO] Running in sequential loop mode.
% 2.01/1.80 % [INFO] eprover registered as external prover.
% 2.01/1.81 % [INFO] Scanning for conjecture ...
% 2.19/1.92 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.19/1.96 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.19/1.97 % [INFO] Problem is propositional (TPTP CNF).
% 2.19/1.98 % [INFO] Type checking passed.
% 2.19/1.98 % [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 ...
% 3.52/2.50 % External prover 'e' found a proof!
% 3.52/2.50 % [INFO] Killing All external provers ...
% 3.52/2.50 % Time passed: 1765ms (effective reasoning time: 1111ms)
% 3.52/2.51 % Axioms used in derivation (2): cls_Relation_OIdI_0, cls_Relation_Opair__in__Id__conv__iff1_0
% 3.52/2.51 % No. of inferences in proof: 13
% 3.52/2.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1765 ms resp. 1111 ms w/o parsing
% 3.52/2.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.52/2.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------