0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 180 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39 0.25/0.49 % Computer : n013.cluster.edu 0.25/0.49 % Model : x86_64 x86_64 0.25/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.25/0.49 % Memory : 8046.5625MB 0.25/0.49 % OS : Linux 6.8.0-71-generic 0.25/0.49 % CPULimit : 1440 0.25/0.49 % WCLimit : 180 0.25/0.49 % DateTime : Mon Jul 27 10:12:24 UTC 2026 0.25/0.50 % CPUTime : 0.25/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 180 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39 1.27/1.19 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 1.97/1.53 % [INFO] Parsing done (335ms). 1.97/1.54 % [INFO] Running in sequential loop mode. 3.14/2.06 % [INFO] eprover registered as external prover. 3.14/2.08 % [INFO] Scanning for conjecture ... 3.71/2.34 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 3.71/2.39 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms). 3.71/2.40 % [INFO] Problem is higher-order (TPTP THF). 3.92/2.40 % [INFO] Type checking passed. 3.92/2.41 % [CONFIG] Using configuration: timeout(180) with strategy. Searching for refutation ... 5.96/3.21 % External prover 'e' found a proof! 5.96/3.21 % [INFO] Killing All external provers ... 5.96/3.21 % Time passed: 2516ms (effective reasoning time: 1663ms) 5.96/3.21 % Solved by strategy 5.96/3.22 % Axioms used in derivation (3): a1, a2, a3 5.96/3.22 % No. of inferences in proof: 10 5.96/3.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2516 ms resp. 1663 ms w/o parsing 6.15/3.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 6.15/3.30 thf(mu_type, type, mu: $tType). 6.15/3.30 thf(mnot_decl, type, mnot: (($i > $o) > ($i > $o))). 6.15/3.30 thf(mor_decl, type, mor: (($i > $o) > (($i > $o) > ($i > $o)))). 6.15/3.30 thf(mimplies_decl, type, mimplies: (($i > $o) > (($i > $o) > ($i > $o)))). 6.15/3.30 thf(mreflexive_decl, type, mreflexive: (($i > ($i > $o)) > $o)). 6.15/3.30 thf(msymmetric_decl, type, msymmetric: (($i > ($i > $o)) > $o)). 6.15/3.30 thf(mtransitive_decl, type, mtransitive: (($i > ($i > $o)) > $o)). 6.15/3.30 thf(mvalid_decl, type, mvalid: (($i > $o) > $o)). 6.15/3.30 thf(rel_s5_decl, type, rel_s5: ($i > ($i > $o))). 6.15/3.30 thf(mbox_s5_decl, type, mbox_s5: (($i > $o) > ($i > $o))). 6.15/3.30 thf(p_decl, type, p: ($i > $o)). 6.15/3.30 thf(q_decl, type, q: ($i > $o)). 6.15/3.30 thf(mnot_def, definition, mnot = (^ [A:($i > $o),B:$i]: ~ (A @ B)) ). 6.15/3.30 thf(mor_def, definition, mor = (^ [A:($i > $o),B:($i > $o),C:$i]: ((A @ C) | (B @ C))) ). 6.15/3.30 thf(mimplies_def, definition, mimplies = (^ [A:($i > $o)]: (mor @ (mnot @ A))) ). 6.15/3.30 thf(mreflexive_def, definition, mreflexive = (^ [A:($i > ($i > $o))]: ! [B:$i]: (A @ B @ B)) ). 6.15/3.30 thf(msymmetric_def, definition, msymmetric = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i]: ((A @ B @ C) => (A @ C @ B))) ). 6.15/3.30 thf(mtransitive_def, definition, mtransitive = (^ [A:($i > ($i > $o))]: ! [B:$i,C:$i,D:$i]: (((A @ B @ C) & (A @ C @ D)) => (A @ B @ D))) ). 6.15/3.30 thf(mvalid_def, definition, mvalid = ((!) @ $i) ). 6.15/3.30 thf(mbox_s5_def, definition, mbox_s5 = (^ [A:($i > $o),B:$i]: ! [C:$i]: (~ (rel_s5 @ B @ C) | (A @ C))) ). 6.15/3.30 thf(1,conjecture,((mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ (mbox_s5 @ q))) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ (mbox_s5 @ p)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)). 6.15/3.30 thf(2,negated_conjecture,((~ (mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ (mbox_s5 @ q))) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ (mbox_s5 @ p))))))),inference(neg_conjecture,[status(cth)],[1])). 6.15/3.30 thf(6,plain,((~ (! [A:$i]: (! [B:$i]: (~ (rel_s5 @ A @ B) | ~ (! [C:$i]: (~ (rel_s5 @ B @ C) | (p @ C))) | ! [C:$i]: (~ (rel_s5 @ B @ C) | (q @ C))) | ! [B:$i]: (~ (rel_s5 @ A @ B) | ~ (! [C:$i]: (~ (rel_s5 @ B @ C) | (q @ C))) | ! [C:$i]: (~ (rel_s5 @ B @ C) | (p @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 6.15/3.30 thf(3,axiom,((mreflexive @ rel_s5)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)). 6.15/3.30 thf(17,plain,((! [A:$i]: (rel_s5 @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 6.15/3.30 thf(4,axiom,((mtransitive @ rel_s5)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)). 6.15/3.30 thf(19,plain,((! [A:$i,B:$i,C:$i]: (((rel_s5 @ A @ B) & (rel_s5 @ B @ C)) => (rel_s5 @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 6.15/3.30 thf(5,axiom,((msymmetric @ rel_s5)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3)). 6.15/3.30 thf(21,plain,((! [A:$i,B:$i]: ((rel_s5 @ A @ B) => (rel_s5 @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 6.15/3.30 thf(23,plain,(($false)),inference(e,[status(thm)],[6,17,19,21])). 6.15/3.30 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 6.15/3.30 % [INFO] Killing All external provers ... 6.15/3.34 EOF