%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO064^4.002 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 08:45:08 AM UTC 2026
% Result : Theorem 4.58s 2.20s
% Output : Refutation 4.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO064^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.21 % Computer : n002.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 16:29:07 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.77/0.62 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.86 % [INFO] Parsing done (233ms).
% 1.21/0.87 % [INFO] Running in sequential loop mode.
% 1.94/1.27 % [INFO] eprover registered as external prover.
% 1.94/1.28 % [INFO] Scanning for conjecture ...
% 2.37/1.42 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.37/1.46 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.37/1.47 % [INFO] Problem is higher-order (TPTP THF).
% 2.37/1.47 % [INFO] Type checking passed.
% 2.37/1.48 % [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 ...
% 4.16/2.20 % External prover 'e' found a proof!
% 4.16/2.20 % [INFO] Killing All external provers ...
% 4.16/2.20 % Time passed: 1885ms (effective reasoning time: 1321ms)
% 4.16/2.20 % 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)>
% 4.58/2.20 % Axioms used in derivation (5): axiom2, trans_axiom, axiom1, refl_axiom, axiom3
% 4.58/2.20 % No. of inferences in proof: 14
% 4.58/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1885 ms resp. 1321 ms w/o parsing
% 4.58/2.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.58/2.27 thf(irel_decl, type, irel: ($i > ($i > $o))).
% 4.58/2.27 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.58/2.27 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.58/2.27 thf(mand_decl, type, mand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.58/2.27 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.58/2.27 thf(mbox_s4_decl, type, mbox_s4: (($i > $o) > ($i > $o))).
% 4.58/2.27 thf(iatom_decl, type, iatom: (($i > $o) > ($i > $o))).
% 4.58/2.27 thf(iand_decl, type, iand: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.58/2.27 thf(ior_decl, type, ior: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.58/2.27 thf(iimplies_decl, type, iimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.58/2.27 thf(ivalid_decl, type, ivalid: (($i > $o) > $o)).
% 4.58/2.27 thf(a_decl, type, a: ($i > $o)).
% 4.58/2.27 thf(a1_decl, type, a1: ($i > $o)).
% 4.58/2.27 thf(a2_decl, type, a2: ($i > $o)).
% 4.58/2.27 thf(b_decl, type, b: ($i > $o)).
% 4.58/2.27 thf(b1_decl, type, b1: ($i > $o)).
% 4.58/2.27 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.58/2.27 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.58/2.27 thf(mand_def, definition, mand = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) & (B @ C))) ).
% 4.58/2.27 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.58/2.27 thf(mbox_s4_def, definition, mbox_s4 = (^ [A:($i > $o),B:$i]: ! [C:$i]: ((irel @ B @ C) => (A @ C))) ).
% 4.58/2.27 thf(iatom_def, definition, iatom = (^ [A:($i > $o)]: (A)) ).
% 4.58/2.27 thf(iand_def, definition, iand = (mand) ).
% 4.58/2.27 thf(ior_def, definition, ior = (^ [A:($i > $o),B:($i > $o)]: (mor @ (mbox_s4 @ A) @ (mbox_s4 @ B))) ).
% 4.58/2.27 thf(iimplies_def, definition, iimplies = (^ [A:($i > $o),B:($i > $o)]: (mimplies @ (mbox_s4 @ A) @ (mbox_s4 @ B))) ).
% 4.58/2.27 thf(ivalid_def, definition, ivalid = ((!) @ $i) ).
% 4.58/2.27 thf(5,axiom,((ivalid @ (iatom @ a2))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1)).
% 4.58/2.27 thf(21,plain,((! [A:$i]: (a2 @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.58/2.27 thf(3,axiom,((! [A:$i]: (irel @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom)).
% 4.58/2.27 thf(17,plain,((! [A:$i]: (irel @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.58/2.27 thf(7,axiom,((ivalid @ (ior @ (ior @ (iatom @ b) @ (iatom @ a)) @ (iatom @ b)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3)).
% 4.58/2.27 thf(27,plain,((! [A:$i]: (! [B:$i]: ((irel @ A @ B) => (! [C:$i]: ((irel @ B @ C) => (b @ C)) | ! [C:$i]: ((irel @ B @ C) => (a @ C)))) | ! [B:$i]: ((irel @ A @ B) => (b @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 4.58/2.27 thf(6,axiom,((ivalid @ (iimplies @ (iatom @ b) @ (ior @ (ior @ (iatom @ b1) @ (iatom @ a1)) @ (iatom @ b1))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2)).
% 4.58/2.27 thf(23,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (b @ B))) | ! [B:$i]: ((irel @ A @ B) => (! [C:$i]: ((irel @ B @ C) => (! [D:$i]: ((irel @ C @ D) => (b1 @ D)) | ! [D:$i]: ((irel @ C @ D) => (a1 @ D)))) | ! [C:$i]: ((irel @ B @ C) => (b1 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 4.58/2.27 thf(1,conjecture,((ivalid @ (ior @ (iatom @ a) @ (ior @ (iand @ (iatom @ b) @ (iatom @ a1)) @ (iand @ (iatom @ b1) @ (iatom @ a2)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 4.58/2.27 thf(2,negated_conjecture,((~ (ivalid @ (ior @ (iatom @ a) @ (ior @ (iand @ (iatom @ b) @ (iatom @ a1)) @ (iand @ (iatom @ b1) @ (iatom @ a2))))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.58/2.27 thf(8,plain,((~ (! [A:$i]: (! [B:$i]: ((irel @ A @ B) => (a @ B)) | ! [B:$i]: ((irel @ A @ B) => (! [C:$i]: ((irel @ B @ C) => ((b @ C) & (a1 @ C))) | ! [C:$i]: ((irel @ B @ C) => ((b1 @ C) & (a2 @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.58/2.27 thf(4,axiom,((! [A:$i,B:$i,C:$i]: (((irel @ A @ B) & (irel @ B @ C)) => (irel @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom)).
% 4.58/2.27 thf(19,plain,((! [A:$i,B:$i,C:$i]: (((irel @ A @ B) & (irel @ B @ C)) => (irel @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.58/2.27 thf(31,plain,(($false)),inference(e,[status(thm)],[21,17,27,23,8,19])).
% 4.58/2.27 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.58/2.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------