%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO059^4 : TPTP v9.3.1. Released v4.0.0.
% 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 : n011.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 : Wed Sep 30 08:45:07 AM UTC 2026
% Result : Theorem 3.94s 2.15s
% Output : Refutation 4.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO059^4 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.09/0.21 % Computer : n011.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:26:16 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.55/1.03 % [INFO] Parsing done (242ms).
% 1.55/1.05 % [INFO] Running in sequential loop mode.
% 2.18/1.45 % [INFO] eprover registered as external prover.
% 2.18/1.46 % [INFO] Scanning for conjecture ...
% 2.40/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.62/1.63 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.62/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.62/1.64 % [INFO] Type checking passed.
% 2.62/1.64 % [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 ...
% 3.94/2.14 % External prover 'e' found a proof!
% 3.94/2.14 % [INFO] Killing All external provers ...
% 3.94/2.15 % Time passed: 1793ms (effective reasoning time: 1089ms)
% 3.94/2.15 % 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)>
% 3.94/2.15 % Axioms used in derivation (3): refl_axiom, trans_axiom, axiom1
% 3.94/2.15 % No. of inferences in proof: 10
% 3.94/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1793 ms resp. 1089 ms w/o parsing
% 4.11/2.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.11/2.20 thf(irel_decl, type, irel: ($i > ($i > $o))).
% 4.11/2.20 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.11/2.20 thf(mbox_s4_decl, type, mbox_s4: (($i > $o) > ($i > $o))).
% 4.11/2.20 thf(iatom_decl, type, iatom: (($i > $o) > ($i > $o))).
% 4.11/2.20 thf(inot_decl, type, inot: (($i > $o) > ($i > $o))).
% 4.11/2.20 thf(ivalid_decl, type, ivalid: (($i > $o) > $o)).
% 4.11/2.20 thf(a_decl, type, a: ($i > $o)).
% 4.11/2.20 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.11/2.20 thf(mbox_s4_def, definition, mbox_s4 = (^ [A:($i > $o),B:$i]: ! [C:$i]: ((irel @ B @ C) => (A @ C))) ).
% 4.11/2.20 thf(iatom_def, definition, iatom = (^ [A:($i > $o)]: (A)) ).
% 4.11/2.20 thf(inot_def, definition, inot = (^ [A:($i > $o)]: (mnot @ (mbox_s4 @ A))) ).
% 4.11/2.20 thf(ivalid_def, definition, ivalid = ((!) @ $i) ).
% 4.11/2.20 thf(1,conjecture,((ivalid @ (inot @ (inot @ (iatom @ a))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 4.11/2.20 thf(2,negated_conjecture,((~ (ivalid @ (inot @ (inot @ (iatom @ a)))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.11/2.20 thf(6,plain,((~ (! [A:$i]: ~ (! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (a @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.11/2.20 thf(3,axiom,((! [A:$i]: (irel @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom)).
% 4.11/2.20 thf(11,plain,((! [A:$i]: (irel @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.11/2.20 thf(4,axiom,((! [A:$i,B:$i,C:$i]: (((irel @ A @ B) & (irel @ B @ C)) => (irel @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_axiom)).
% 4.11/2.20 thf(13,plain,((! [A:$i,B:$i,C:$i]: (((irel @ A @ B) & (irel @ B @ C)) => (irel @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.11/2.20 thf(5,axiom,((ivalid @ (iatom @ a))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1)).
% 4.11/2.20 thf(15,plain,((! [A:$i]: (a @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.11/2.20 thf(17,plain,(($false)),inference(e,[status(thm)],[6,11,13,15])).
% 4.11/2.20 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.11/2.20 % [INFO] Killing All external provers ...
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