%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT038^2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/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 07:46:07 AM UTC 2026
% Result : Theorem 13.39s 4.78s
% Output : Refutation 12.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : CAT038^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.10 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.25 % Computer : n008.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 17:46:09 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.21/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.68/1.18 % [INFO] Parsing done (190ms).
% 1.68/1.20 % [INFO] Running in sequential loop mode.
% 2.55/1.76 % [INFO] eprover registered as external prover.
% 2.55/1.77 % [INFO] Scanning for conjecture ...
% 2.66/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.86/1.92 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.86/1.92 % [INFO] Problem is higher-order (TPTP THF).
% 2.86/1.93 % [INFO] Type checking passed.
% 2.86/1.93 % [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 ...
% 4.53/2.70 % [INFO] GaveUp with current strategy, trying again with another strategy ...
% 13.39/4.77 % [INFO] Killing All external provers ...
% 13.39/4.77 % Time passed: 4298ms (effective reasoning time: 3566ms)
% 13.39/4.77 % Solved by strategy<name(funcspec),share(0.5),primSubst(2),sos(false),unifierCount(10),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(true), domConstr(0),specialInstances(-1),restrictUniAttempts(false),termOrdering(none)>
% 13.39/4.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4298 ms resp. 3566 ms w/o parsing
% 12.50/4.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.50/4.83 thf(sk1_decl, type, sk1: $i).
% 12.50/4.83 thf(sk2_decl, type, sk2: $i).
% 12.50/4.83 thf(sk1_def, definition, sk1 = (@+ [A:$i]: ~ (! [B:$i]: ? [C:($i > $i)]: (((C @ A) = B) & ((C @ B) = A)))) ).
% 12.50/4.83 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ (? [B:($i > $i)]: (((B @ sk1) = A) & ((B @ A) = sk1)))) ).
% 12.50/4.83 thf(17,axiom,((? [A:(($i > $o) > $i)]: ! [B:($i > $o)]: ((? [C:$i]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 12.50/4.83 thf(19,plain,(! [A:$i] : ((~ (((sk2 = sk1) => (A = sk2)) & (A = sk1))) | (((sk2 = sk1) => ((@+ [B:$i]: (((sk2 = sk1) => (B = sk2)) & (B = sk1))) = sk2)) & ((@+ [B:$i]: (((sk2 = sk1) => (B = sk2)) & (B = sk1))) = sk1)))),inference(choice,[status(esa)],[17])).
% 12.50/4.83 thf(34,plain,(! [A:$i] : ((((sk2 = sk1) | ~ (A = sk1) | ~ (sk2 = sk1) | ((@+ [B:$i]: (((sk2 = sk1) => (B = sk2)) & (B = sk1))) = sk2)) & ((sk2 = sk1) | ~ (A = sk1) | ((@+ [B:$i]: (((sk2 = sk1) => (B = sk2)) & (B = sk1))) = sk1)) & (~ (A = sk2) | ~ (A = sk1) | ~ (sk2 = sk1) | ((@+ [B:$i]: (((sk2 = sk1) => (B = sk2)) & (B = sk1))) = sk2)) & (~ (A = sk2) | ~ (A = sk1) | ((@+ [B:$i]: (((sk2 = sk1) => (B = sk2)) & (B = sk1))) = sk1))))),inference(cnf,[status(esa)],[19])).
% 12.50/4.83 thf(36,plain,(! [A:$i] : ((sk2 = sk1) | (~ (A = sk1)) | ((@+ [B:$i]: (((sk2 = sk1) => (B = sk2)) & (B = sk1))) = sk1))),inference(cnfConj,[status(thm)],[34])).
% 12.50/4.83 thf(41,plain,(! [A:$i] : ((sk2 = sk1) | (A != sk1) | ((@+ [B:$i]: (((sk2 = sk1) => (B = sk2)) & (B = sk1))) = sk1))),inference(lifteq,[status(thm)],[36])).
% 12.50/4.83 thf(42,plain,((sk2 = sk1) | ((@+ [A:$i]: (((sk2 = sk1) => (A = sk2)) & (A = sk1))) = sk1)),inference(simp,[status(thm)],[41])).
% 12.50/4.83 thf(1,conjecture,((! [A:$i,B:$i]: ? [C:($i > $i)]: (((C @ A) = B) & ((C @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifi)).
% 12.50/4.83 thf(2,negated_conjecture,((~ (! [A:$i,B:$i]: ? [C:($i > $i)]: (((C @ A) = B) & ((C @ B) = A))))),inference(neg_conjecture,[status(cth)],[1])).
% 12.50/4.83 thf(3,plain,((~ (! [A:$i,B:$i]: ? [C:($i > $i)]: (((C @ A) = B) & ((C @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 12.50/4.83 thf(4,plain,(! [A:($i > $i)] : ((~ ((A @ sk1) = sk2)) | (~ ((A @ sk2) = sk1)))),inference(cnf,[status(esa)],[3])).
% 12.50/4.83 thf(5,plain,(! [A:($i > $i)] : (((A @ sk1) != sk2) | ((A @ sk2) != sk1))),inference(lifteq,[status(thm)],[4])).
% 12.50/4.83 thf(6,plain,(! [A:($i > $i)] : (((A @ sk1) != sk2) | ((A @ sk2) != sk2) | ((A @ sk1) != sk1))),inference(eqfactor_ordered,[status(thm)],[5])).
% 12.50/4.83 thf(9,plain,((sk2 != sk1)),inference(pre_uni,[status(thm)],[6:[bind(A, $thf(^ [B:$i]: (B)))]])).
% 12.50/4.83 thf(12,plain,(((@+ [A:$i]: (((sk1 = sk1) => (A = sk2)) & ((sk1 = sk2) => (A = sk1)))) != sk2) | ((@+ [A:$i]: (((sk2 = sk1) => (A = sk2)) & ((sk2 = sk2) => (A = sk1)))) != sk1)),introduced(choice instance)).
% 12.50/4.83 thf(14,plain,(((@+ [A:$i]: ((A = sk2) & ((sk1 = sk2) => (A = sk1)))) != sk2) | ((@+ [A:$i]: (((sk2 = sk1) => (A = sk2)) & (A = sk1))) != sk1)),inference(simp,[status(thm)],[12])).
% 12.50/4.83 thf(18,plain,(! [A:$i] : ((~ ((A = sk2) & ((sk1 = sk2) => (A = sk1)))) | (((@+ [B:$i]: ((B = sk2) & ((sk1 = sk2) => (B = sk1)))) = sk2) & ((sk1 = sk2) => ((@+ [B:$i]: ((B = sk2) & ((sk1 = sk2) => (B = sk1)))) = sk1))))),inference(choice,[status(esa)],[17])).
% 12.50/4.83 thf(21,plain,(! [A:$i] : (((~ (A = sk2) | (sk1 = sk2) | ((@+ [B:$i]: ((B = sk2) & ((sk1 = sk2) => (B = sk1)))) = sk2)) & (~ (A = sk2) | (sk1 = sk2) | ~ (sk1 = sk2) | ((@+ [B:$i]: ((B = sk2) & ((sk1 = sk2) => (B = sk1)))) = sk1)) & (~ (A = sk2) | ~ (A = sk1) | ((@+ [B:$i]: ((B = sk2) & ((sk1 = sk2) => (B = sk1)))) = sk2)) & (~ (A = sk2) | ~ (A = sk1) | ~ (sk1 = sk2) | ((@+ [B:$i]: ((B = sk2) & ((sk1 = sk2) => (B = sk1)))) = sk1))))),inference(cnf,[status(esa)],[18])).
% 12.50/4.83 thf(22,plain,(! [A:$i] : ((~ (A = sk2)) | (sk1 = sk2) | ((@+ [B:$i]: ((B = sk2) & ((sk1 = sk2) => (B = sk1)))) = sk2))),inference(cnfConj,[status(thm)],[21])).
% 12.50/4.83 thf(26,plain,(! [A:$i] : ((A != sk2) | (sk1 = sk2) | ((@+ [B:$i]: ((B = sk2) & ((sk1 = sk2) => (B = sk1)))) = sk2))),inference(lifteq,[status(thm)],[22])).
% 12.50/4.83 thf(27,plain,((sk1 = sk2) | ((@+ [A:$i]: ((A = sk2) & ((sk1 = sk2) => (A = sk1)))) = sk2)),inference(simp,[status(thm)],[26])).
% 12.50/4.83 thf(55,plain,(((@+ [A:$i]: ((A = sk2) & ((sk1 = sk2) => (A = sk1)))) = sk2)),inference(simplifyReflect,[status(thm)],[27,9])).
% 12.50/4.83 thf(57,plain,(((@+ [A:$i]: (((sk2 = sk1) => (A = sk2)) & (A = sk1))) != sk1)),inference(simplifyReflect,[status(thm)],[14,55])).
% 12.50/4.83 thf(559,plain,(($false)),inference(simplifyReflect,[status(thm)],[42,9,57])).
% 12.50/4.83 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.50/4.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------