%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO068^4.020 : 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 : n008.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 6.42s 2.95s
% Output : Refutation 6.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO068^4.020 : 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
% 0.11/0.22 % Computer : n008.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 16:30:09 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 1.03/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.49/1.09 % [INFO] Parsing done (260ms).
% 1.49/1.10 % [INFO] Running in sequential loop mode.
% 2.18/1.49 % [INFO] eprover registered as external prover.
% 2.40/1.50 % [INFO] Scanning for conjecture ...
% 2.61/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 23 axioms. Running axiom selection ...
% 2.83/1.72 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 2.83/1.75 % [INFO] Problem is higher-order (TPTP THF).
% 2.83/1.75 % [INFO] Type checking passed.
% 2.83/1.76 % [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 ...
% 6.42/2.95 % External prover 'e' found a proof!
% 6.42/2.95 % [INFO] Killing All external provers ...
% 6.42/2.95 % Time passed: 2576ms (effective reasoning time: 1843ms)
% 6.42/2.95 % 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)>
% 6.42/2.95 % Axioms used in derivation (23): axiom6, axiom14, axiom10, axiom17, axiom2, axiom11, axiom5, axiom13, trans_axiom, axiom1, axiom12, axiom18, refl_axiom, axiom7, axiom20, axiom3, axiom21, axiom16, axiom9, axiom19, axiom8, axiom15, axiom4
% 6.42/2.95 % No. of inferences in proof: 50
% 6.42/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2576 ms resp. 1843 ms w/o parsing
% 6.89/3.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.89/3.05 thf(irel_decl, type, irel: ($i > ($i > $o))).
% 6.89/3.05 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 6.89/3.05 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 6.89/3.05 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 6.89/3.05 thf(mbox_s4_decl, type, mbox_s4: (($i > $o) > ($i > $o))).
% 6.89/3.05 thf(iatom_decl, type, iatom: (($i > $o) > ($i > $o))).
% 6.89/3.05 thf(iimplies_decl, type, iimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 6.89/3.05 thf(ivalid_decl, type, ivalid: (($i > $o) > $o)).
% 6.89/3.05 thf(p0_decl, type, p0: ($i > $o)).
% 6.89/3.05 thf(p1_decl, type, p1: ($i > $o)).
% 6.89/3.05 thf(p10_decl, type, p10: ($i > $o)).
% 6.89/3.05 thf(p11_decl, type, p11: ($i > $o)).
% 6.89/3.05 thf(p12_decl, type, p12: ($i > $o)).
% 6.89/3.05 thf(p13_decl, type, p13: ($i > $o)).
% 6.89/3.05 thf(p14_decl, type, p14: ($i > $o)).
% 6.89/3.05 thf(p15_decl, type, p15: ($i > $o)).
% 6.89/3.05 thf(p16_decl, type, p16: ($i > $o)).
% 6.89/3.05 thf(p17_decl, type, p17: ($i > $o)).
% 6.89/3.05 thf(p18_decl, type, p18: ($i > $o)).
% 6.89/3.05 thf(p19_decl, type, p19: ($i > $o)).
% 6.89/3.05 thf(p2_decl, type, p2: ($i > $o)).
% 6.89/3.05 thf(p20_decl, type, p20: ($i > $o)).
% 6.89/3.05 thf(p3_decl, type, p3: ($i > $o)).
% 6.89/3.05 thf(p4_decl, type, p4: ($i > $o)).
% 6.89/3.05 thf(p5_decl, type, p5: ($i > $o)).
% 6.89/3.05 thf(p6_decl, type, p6: ($i > $o)).
% 6.89/3.05 thf(p7_decl, type, p7: ($i > $o)).
% 6.89/3.05 thf(p8_decl, type, p8: ($i > $o)).
% 6.89/3.05 thf(p9_decl, type, p9: ($i > $o)).
% 6.89/3.05 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 6.89/3.05 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 6.89/3.05 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 6.89/3.05 thf(mbox_s4_def, definition, mbox_s4 = (^ [A:($i > $o),B:$i]: ! [C:$i]: ((irel @ B @ C) => (A @ C))) ).
% 6.89/3.05 thf(iatom_def, definition, iatom = (^ [A:($i > $o)]: (A)) ).
% 6.89/3.05 thf(iimplies_def, definition, iimplies = (^ [A:($i > $o),B:($i > $o)]: (mimplies @ (mbox_s4 @ A) @ (mbox_s4 @ B))) ).
% 6.89/3.05 thf(ivalid_def, definition, ivalid = ((!) @ $i) ).
% 6.89/3.05 thf(18,axiom,((ivalid @ (iimplies @ (iatom @ p13) @ (iimplies @ (iatom @ p13) @ (iatom @ p12))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom14)).
% 6.89/3.05 thf(110,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p13 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p13 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p12 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 6.89/3.05 thf(15,axiom,((ivalid @ (iimplies @ (iatom @ p14) @ (iimplies @ (iatom @ p14) @ (iatom @ p13))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15)).
% 6.89/3.05 thf(92,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p14 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p14 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p13 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 6.89/3.05 thf(21,axiom,((ivalid @ (iatom @ p20))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1)).
% 6.89/3.05 thf(128,plain,((! [A:$i]: (p20 @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
% 6.89/3.05 thf(7,axiom,((ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5)).
% 6.89/3.05 thf(44,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p4 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p4 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p3 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 6.89/3.05 thf(14,axiom,((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2)).
% 6.89/3.05 thf(86,plain,((! [A:$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)],[14])).
% 6.89/3.05 thf(16,axiom,((ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6)).
% 6.89/3.05 thf(98,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p5 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p5 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p4 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 6.89/3.05 thf(8,axiom,((ivalid @ (iimplies @ (iatom @ p11) @ (iimplies @ (iatom @ p11) @ (iatom @ p10))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12)).
% 6.89/3.05 thf(50,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p11 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p11 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p10 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 6.89/3.05 thf(17,axiom,((ivalid @ (iimplies @ (iatom @ p19) @ (iimplies @ (iatom @ p19) @ (iatom @ p18))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20)).
% 6.89/3.05 thf(104,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p19 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p19 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p18 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 6.89/3.05 thf(1,conjecture,((ivalid @ (iatom @ p0))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 6.89/3.05 thf(2,negated_conjecture,((~ (ivalid @ (iatom @ p0)))),inference(neg_conjecture,[status(cth)],[1])).
% 6.89/3.05 thf(26,plain,((~ (! [A:$i]: (p0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 6.89/3.05 thf(4,axiom,((! [A:$i,B:$i,C:$i]: (((irel @ A @ B) & (irel @ B @ C)) => (irel @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom)).
% 6.89/3.05 thf(30,plain,((! [A:$i,B:$i,C:$i]: (((irel @ A @ B) & (irel @ B @ C)) => (irel @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 6.89/3.05 thf(23,axiom,((ivalid @ (iimplies @ (iatom @ p16) @ (iimplies @ (iatom @ p16) @ (iatom @ p15))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17)).
% 6.89/3.05 thf(136,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p16 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p16 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p15 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 6.89/3.05 thf(20,axiom,((ivalid @ (iimplies @ (iatom @ p8) @ (iimplies @ (iatom @ p8) @ (iatom @ p7))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9)).
% 6.89/3.05 thf(122,plain,((! [A:$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)],[20])).
% 6.89/3.05 thf(9,axiom,((ivalid @ (iimplies @ (iatom @ p10) @ (iimplies @ (iatom @ p10) @ (iatom @ p9))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom11)).
% 6.89/3.05 thf(56,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p10 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p10 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p9 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 6.89/3.05 thf(24,axiom,((ivalid @ (iimplies @ (iatom @ p18) @ (iimplies @ (iatom @ p18) @ (iatom @ p17))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19)).
% 6.89/3.05 thf(142,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p18 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p18 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p17 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
% 6.89/3.05 thf(19,axiom,((ivalid @ (iimplies @ (iatom @ p15) @ (iimplies @ (iatom @ p15) @ (iatom @ p14))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16)).
% 6.89/3.05 thf(116,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p15 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p15 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p14 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 6.89/3.05 thf(12,axiom,((ivalid @ (iimplies @ (iatom @ p12) @ (iimplies @ (iatom @ p12) @ (iatom @ p11))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13)).
% 6.89/3.05 thf(74,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p12 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p12 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p11 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 6.89/3.05 thf(3,axiom,((! [A:$i]: (irel @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom)).
% 6.89/3.05 thf(28,plain,((! [A:$i]: (irel @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 6.89/3.05 thf(6,axiom,((ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3)).
% 6.89/3.05 thf(38,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p2 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p2 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p1 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 6.89/3.05 thf(5,axiom,((ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4)).
% 6.89/3.05 thf(32,plain,((! [A:$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)],[5])).
% 6.89/3.05 thf(25,axiom,((ivalid @ (iimplies @ (iatom @ p20) @ (iimplies @ (iatom @ p20) @ (iatom @ p19))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21)).
% 6.89/3.05 thf(148,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p20 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p20 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p19 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 6.89/3.05 thf(22,axiom,((ivalid @ (iimplies @ (iatom @ p9) @ (iimplies @ (iatom @ p9) @ (iatom @ p8))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10)).
% 6.89/3.05 thf(130,plain,((! [A:$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)],[22])).
% 6.89/3.05 thf(13,axiom,((ivalid @ (iimplies @ (iatom @ p7) @ (iimplies @ (iatom @ p7) @ (iatom @ p6))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8)).
% 6.89/3.05 thf(80,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p7 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p7 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p6 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 6.89/3.05 thf(11,axiom,((ivalid @ (iimplies @ (iatom @ p17) @ (iimplies @ (iatom @ p17) @ (iatom @ p16))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18)).
% 6.89/3.05 thf(68,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p17 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p17 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p16 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 6.89/3.05 thf(10,axiom,((ivalid @ (iimplies @ (iatom @ p6) @ (iimplies @ (iatom @ p6) @ (iatom @ p5))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7)).
% 6.89/3.05 thf(62,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p6 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p6 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p5 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 6.89/3.05 thf(170,plain,(($false)),inference(e,[status(thm)],[110,92,128,44,86,98,50,104,26,30,136,122,56,142,116,74,28,38,32,148,130,80,68,62])).
% 6.89/3.05 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.89/3.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------