%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO068^4.005 : 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 : n003.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 3.94s 2.01s
% Output : Refutation 4.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO068^4.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.08/0.21 % Computer : n003.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 16:31:14 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 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
% 0.64/0.50 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.06/0.66 % [INFO] Parsing done (161ms).
% 1.06/0.67 % [INFO] Running in sequential loop mode.
% 1.80/1.08 % [INFO] eprover registered as external prover.
% 1.80/1.09 % [INFO] Scanning for conjecture ...
% 2.18/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.18/1.26 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.18/1.27 % [INFO] Problem is higher-order (TPTP THF).
% 2.18/1.27 % [INFO] Type checking passed.
% 2.18/1.28 % [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 ...
% 3.94/2.00 % External prover 'e' found a proof!
% 3.94/2.00 % [INFO] Killing All external provers ...
% 3.94/2.00 % Time passed: 1713ms (effective reasoning time: 1325ms)
% 3.94/2.01 % 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)>
% 3.94/2.01 % Axioms used in derivation (8): axiom6, axiom2, axiom5, trans_axiom, axiom1, axiom4, refl_axiom, axiom3
% 3.94/2.01 % No. of inferences in proof: 20
% 3.94/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1713 ms resp. 1325 ms w/o parsing
% 4.29/2.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.29/2.08 thf(irel_decl, type, irel: ($i > ($i > $o))).
% 4.29/2.08 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))).
% 4.29/2.08 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.29/2.08 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.29/2.08 thf(mbox_s4_decl, type, mbox_s4: (($i > $o) > ($i > $o))).
% 4.29/2.08 thf(iatom_decl, type, iatom: (($i > $o) > ($i > $o))).
% 4.29/2.08 thf(iimplies_decl, type, iimplies: (($i > $o) > (($i > $o) > ($i > $o)))).
% 4.29/2.08 thf(ivalid_decl, type, ivalid: (($i > $o) > $o)).
% 4.29/2.08 thf(p0_decl, type, p0: ($i > $o)).
% 4.29/2.08 thf(p1_decl, type, p1: ($i > $o)).
% 4.29/2.08 thf(p2_decl, type, p2: ($i > $o)).
% 4.29/2.08 thf(p3_decl, type, p3: ($i > $o)).
% 4.29/2.08 thf(p4_decl, type, p4: ($i > $o)).
% 4.29/2.08 thf(p5_decl, type, p5: ($i > $o)).
% 4.29/2.08 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ).
% 4.29/2.08 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ).
% 4.29/2.08 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ).
% 4.29/2.08 thf(mbox_s4_def, definition, mbox_s4 = (^ [A:($i > $o),B:$i]: ! [C:$i]: ((irel @ B @ C) => (A @ C))) ).
% 4.29/2.08 thf(iatom_def, definition, iatom = (^ [A:($i > $o)]: (A)) ).
% 4.29/2.08 thf(iimplies_def, definition, iimplies = (^ [A:($i > $o),B:($i > $o)]: (mimplies @ (mbox_s4 @ A) @ (mbox_s4 @ B))) ).
% 4.29/2.08 thf(ivalid_def, definition, ivalid = ((!) @ $i) ).
% 4.29/2.08 thf(3,axiom,((! [A:$i]: (irel @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom)).
% 4.29/2.08 thf(13,plain,((! [A:$i]: (irel @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.29/2.08 thf(5,axiom,((ivalid @ (iatom @ p5))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1)).
% 4.29/2.08 thf(17,plain,((! [A:$i]: (p5 @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.29/2.08 thf(8,axiom,((ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4)).
% 4.29/2.08 thf(31,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p3 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p3 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p2 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 4.29/2.08 thf(6,axiom,((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2)).
% 4.29/2.08 thf(19,plain,((! [A:$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])).
% 4.29/2.08 thf(4,axiom,((! [A:$i,B:$i,C:$i]: (((irel @ A @ B) & (irel @ B @ C)) => (irel @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom)).
% 4.29/2.08 thf(15,plain,((! [A:$i,B:$i,C:$i]: (((irel @ A @ B) & (irel @ B @ C)) => (irel @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.29/2.08 thf(9,axiom,((ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5)).
% 4.29/2.08 thf(37,plain,((! [A:$i]: (~ (! [B:$i]: ((irel @ A @ B) => (p4 @ B))) | ! [B:$i]: ((irel @ A @ B) => (~ (! [C:$i]: ((irel @ B @ C) => (p4 @ C))) | ! [C:$i]: ((irel @ B @ C) => (p3 @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 4.29/2.08 thf(7,axiom,((ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3)).
% 4.29/2.08 thf(25,plain,((! [A:$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])).
% 4.29/2.08 thf(1,conjecture,((ivalid @ (iatom @ p0))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 4.29/2.08 thf(2,negated_conjecture,((~ (ivalid @ (iatom @ p0)))),inference(neg_conjecture,[status(cth)],[1])).
% 4.29/2.08 thf(11,plain,((~ (! [A:$i]: (p0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.29/2.08 thf(10,axiom,((ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6)).
% 4.29/2.08 thf(43,plain,((! [A:$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])).
% 4.29/2.08 thf(49,plain,(($false)),inference(e,[status(thm)],[13,17,31,19,15,37,25,11,43])).
% 4.29/2.08 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.29/2.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------