%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW345+1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n006.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 09:09:58 AM UTC 2026
% Result : Theorem 14.48s 15.31s
% Output : Refutation 14.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 2 ~; 0 |; 0 &; 58 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_R_decl,type,
v_R: $i > $i > $o ).
thf(v_Z_decl,type,
v_Z: $i ).
thf(v_s_H_decl,type,
v_s_H: $i ).
thf(c_Natural_Oevaln_decl,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(v_c_decl,type,
v_c: $i ).
thf(v_s_decl,type,
v_s: $i ).
thf(v_n_decl,type,
v_n: $i ).
thf(v_s1_decl,type,
v_s1: $i ).
thf(v_P_decl,type,
v_P: $i > $i > $o ).
thf(v_Q_decl,type,
v_Q: $i > $i > $o ).
thf(v_d_decl,type,
v_d: $i ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_c @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(10,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_c @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
v_s_H @ ( v_n @ ( v_s1 @ ( v_d @ c_Natural_Oevaln ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
thf(14,plain,
v_s_H @ ( v_n @ ( v_s1 @ ( v_d @ c_Natural_Oevaln ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
v_s1 @ ( v_n @ ( v_s @ ( v_c @ c_Natural_Oevaln ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(9,plain,
v_s1 @ ( v_n @ ( v_s @ ( v_c @ c_Natural_Oevaln ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ v_Q ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_d @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_R ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(12,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ v_Q ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_d @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_R ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
v_s_H @ ( v_Z @ v_R ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
thf(2,negated_conjecture,
~ ( v_s_H @ ( v_Z @ v_R ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( v_s_H @ ( v_Z @ v_R ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
v_s @ ( v_Z @ v_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(15,plain,
v_s @ ( v_Z @ v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(16,plain,
$false,
inference(e,[status(thm)],[10,14,9,12,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW345+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % 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
% 0.15/10.43 % Computer : n006.cluster.edu
% 0.15/10.43 % Model : x86_64 x86_64
% 0.15/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.43 % Memory : 8046.5625MB
% 0.15/10.43 % OS : Linux 6.8.0-71-generic
% 0.15/10.43 % CPULimit : 300
% 0.15/10.43 % WCLimit : 300
% 0.15/10.43 % DateTime : Sat Sep 26 15:42:21 UTC 2026
% 0.15/10.43 % CPUTime :
% 0.15/10.43 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
% 1.25/11.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 5.98/12.60 % [INFO] Parsing done (1329ms).
% 5.98/12.62 % [INFO] Running in sequential loop mode.
% 6.99/13.14 % [INFO] eprover registered as external prover.
% 6.99/13.15 % [INFO] Scanning for conjecture ...
% 11.97/14.41 % [INFO] Found a conjecture (or negated_conjecture) and 5210 axioms. Running axiom selection ...
% 12.19/14.59 % [INFO] Axiom selection finished. Selected 5 axioms (removed 5205 axioms).
% 12.61/14.62 % [INFO] Problem is first-order (TPTP FOF).
% 12.61/14.63 % [INFO] Type checking passed.
% 12.61/14.64 % [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 ...
% 14.48/15.30 % External prover 'e' found a proof!
% 14.48/15.30 % [INFO] Killing All external provers ...
% 14.48/15.31 % Time passed: 4671ms (effective reasoning time: 2680ms)
% 14.48/15.31 % 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)>
% 14.48/15.31 % Axioms used in derivation (5): conj_3, conj_2, conj_1, conj_4, conj_5
% 14.48/15.31 % No. of inferences in proof: 14
% 14.48/15.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4671 ms resp. 2680 ms w/o parsing
% 14.48/15.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.48/15.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------