%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO068^4.010 : 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 : n015.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 08:45:09 AM UTC 2026
% Result : Theorem 4.73s 2.52s
% Output : Refutation 4.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO068^4.010 : 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
% 0.09/0.22 % Computer : n015.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 16:32:48 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 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
% 1.02/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.53/1.06 % [INFO] Parsing done (245ms).
% 1.53/1.07 % [INFO] Running in sequential loop mode.
% 2.17/1.48 % [INFO] eprover registered as external prover.
% 2.17/1.48 % [INFO] Scanning for conjecture ...
% 2.58/1.63 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.58/1.66 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.58/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 2.58/1.68 % [INFO] Type checking passed.
% 2.58/1.69 % [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 ...
% 4.73/2.51 % External prover 'e' found a proof!
% 4.73/2.52 % [INFO] Killing All external provers ...
% 4.73/2.52 % Time passed: 2145ms (effective reasoning time: 1439ms)
% 4.73/2.52 % 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)>
% 4.73/2.52 % Axioms used in derivation (13): axiom6, axiom10, axiom2, axiom11, axiom5, axiom9, trans_axiom, axiom1, axiom8, axiom4, refl_axiom, axiom7, axiom3
% 4.73/2.52 % No. of inferences in proof: 30
% 4.73/2.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2145 ms resp. 1439 ms w/o parsing
% 4.96/2.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.96/2.60 thf(irel_decl, type, irel: ($i > ($i > $o))).
% 4.96/2.60 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.96/2.60 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.96/2.60 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.96/2.60 thf(mbox_s4_decl, type, mbox_s4: (($i > $o) > ($i > $o))).
% 4.96/2.60 thf(iatom_decl, type, iatom: (($i > $o) > ($i > $o))).
% 4.96/2.60 thf(iimplies_decl, type, iimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.96/2.60 thf(ivalid_decl, type, ivalid: (($i > $o) > $o)).
% 4.96/2.60 thf(p0_decl, type, p0: ($i > $o)).
% 4.96/2.60 thf(p1_decl, type, p1: ($i > $o)).
% 4.96/2.60 thf(p10_decl, type, p10: ($i > $o)).
% 4.96/2.60 thf(p2_decl, type, p2: ($i > $o)).
% 4.96/2.60 thf(p3_decl, type, p3: ($i > $o)).
% 4.96/2.60 thf(p4_decl, type, p4: ($i > $o)).
% 4.96/2.60 thf(p5_decl, type, p5: ($i > $o)).
% 4.96/2.60 thf(p6_decl, type, p6: ($i > $o)).
% 4.96/2.60 thf(p7_decl, type, p7: ($i > $o)).
% 4.96/2.60 thf(p8_decl, type, p8: ($i > $o)).
% 4.96/2.60 thf(p9_decl, type, p9: ($i > $o)).
% 4.96/2.60 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.96/2.60 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.96/2.60 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.96/2.60 thf(mbox_s4_def, definition, mbox_s4 = (^ [A:($i > $o),B:$i]: ! [C:$i]: ((irel @ B @ C) => (A @ C))) ).
% 4.96/2.60 thf(iatom_def, definition, iatom = (^ [A:($i > $o)]: (A)) ).
% 4.96/2.60 thf(iimplies_def, definition, iimplies = (^ [A:($i > $o),B:($i > $o)]: (mimplies @ (mbox_s4 @ A) @ (mbox_s4 @ B))) ).
% 4.96/2.60 thf(ivalid_def, definition, ivalid = ((!) @ $i) ).
% 4.96/2.60 thf(12,axiom,((ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8)).
% 4.96/2.60 thf(60,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p7 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p7 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p6 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 4.96/2.60 thf(5,axiom,((ivalid @ (iatom @ p10))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1)).
% 4.96/2.60 thf(22,plain,((! [A:$i]: (p10 @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.96/2.60 thf(11,axiom,((ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7)).
% 4.96/2.60 thf(54,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p6 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p6 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p5 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 4.96/2.60 thf(13,axiom,((ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9)).
% 4.96/2.60 thf(66,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p8 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p8 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p7 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 4.96/2.60 thf(1,conjecture,((ivalid @ (iatom @ p0))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 4.96/2.60 thf(2,negated_conjecture,((~ (ivalid @ (iatom @ p0)))),inference(neg_conjecture,[status(cth)],[1])).
% 4.96/2.60 thf(16,plain,((~ (! [A:$i]: (p0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.96/2.60 thf(14,axiom,((ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10)).
% 4.96/2.60 thf(72,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p9 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p9 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p8 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 4.96/2.60 thf(9,axiom,((ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5)).
% 4.96/2.60 thf(42,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p4 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p4 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p3 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 4.96/2.60 thf(6,axiom,((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2)).
% 4.96/2.60 thf(24,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p1 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p1 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p0 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 4.96/2.60 thf(4,axiom,((! [A:$i,B:$i,C:$i]: (((irel @ A @ B) & (irel @ B @ C)) => (irel @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom)).
% 4.96/2.60 thf(20,plain,((! [A:$i,B:$i,C:$i]: (((irel @ A @ B) & (irel @ B @ C)) => (irel @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.96/2.60 thf(15,axiom,((ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom11)).
% 4.96/2.60 thf(78,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p10 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p10 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p9 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 4.96/2.60 thf(10,axiom,((ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6)).
% 4.96/2.60 thf(48,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p5 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p5 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p4 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 4.96/2.60 thf(3,axiom,((! [A:$i]: (irel @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom)).
% 4.96/2.60 thf(18,plain,((! [A:$i]: (irel @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.96/2.60 thf(8,axiom,((ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4)).
% 4.96/2.60 thf(36,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p3 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p3 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p2 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 4.96/2.60 thf(7,axiom,((ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3)).
% 4.96/2.60 thf(30,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p2 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p2 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p1 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 4.96/2.60 thf(84,plain,(($false)),inference(e,[status(thm)],[60,22,54,66,16,72,42,24,20,78,48,18,36,30])).
% 4.96/2.60 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.96/2.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------