TSTP Solution File: SET825-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET825-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:54:28 EDT 2023
% Result : Unsatisfiable 2.61s 1.60s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 25 ( 7 unt; 12 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 : 13 ( 13 >; 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_type,type,
v_Q: $i > $o ).
thf(v_n_type,type,
v_n: $i ).
thf(v_m_type,type,
v_m: $i ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(v_x_type,type,
v_x: $i > $i ).
thf(v_xa_type,type,
v_xa: $i > $i ).
thf(c_0_type,type,
c_0: $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i ).
thf(4,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ ( c_Suc @ ( v_x @ A ) ) @ ( c_Suc @ ( v_xa @ A ) ) @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(10,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ ( c_Suc @ ( v_x @ A ) ) @ ( c_Suc @ ( v_xa @ A ) ) @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(14,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ c_Relation_OId @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_in @ ( c_Pair @ ( v_x @ A ) @ ( v_xa @ A ) @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_n @ v_m @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) )
| ( c_in @ ( c_Pair @ ( v_x @ A ) @ ( v_xa @ A ) @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) )
| ~ ( c_in @ ( c_Pair @ c_0 @ c_0 @ tc_nat @ tc_nat ) @ A @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
v_Q @ v_n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
v_Q @ v_n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
~ ( v_Q @ v_m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,plain,
~ ( v_Q @ v_m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ c_Relation_OId @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[10,14,9,7,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET825-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n004.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Thu May 18 18:53:25 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.98/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.97 % [INFO] Parsing done (115ms).
% 1.21/0.98 % [INFO] Running in sequential loop mode.
% 1.71/1.19 % [INFO] eprover registered as external prover.
% 1.71/1.20 % [INFO] cvc4 registered as external prover.
% 1.71/1.20 % [INFO] Scanning for conjecture ...
% 1.86/1.26 % [INFO] Found a conjecture and 2 axioms. Running axiom selection ...
% 1.86/1.29 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.86/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.86/1.30 % [INFO] Type checking passed.
% 1.86/1.30 % [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 ...
% 2.61/1.60 % External prover 'e' found a proof!
% 2.61/1.60 % [INFO] Killing All external provers ...
% 2.61/1.60 % Time passed: 1068ms (effective reasoning time: 617ms)
% 2.61/1.60 % Solved by 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)>
% 2.61/1.60 % Axioms used in derivation (2): cls_Relation_OIdI_0, cls_Relation_Opair__in__Id__conv__iff1_0
% 2.61/1.60 % No. of inferences in proof: 13
% 2.61/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1068 ms resp. 617 ms w/o parsing
% 2.82/1.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.82/1.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------