%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : CAT038^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n001.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 12.45s 3.93s
% Output : Refutation 12.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT038^1 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.10/0.27 % Computer : n001.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 17:51:20 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 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
% 1.15/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.59/1.17 % [INFO] Parsing done (181ms).
% 1.59/1.19 % [INFO] Running in sequential loop mode.
% 2.37/1.65 % [INFO] eprover registered as external prover.
% 2.37/1.66 % [INFO] Scanning for conjecture ...
% 2.60/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.60/1.79 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.60/1.79 % [INFO] Problem is higher-order (TPTP THF).
% 2.76/1.80 % [INFO] Type checking passed.
% 2.76/1.81 % [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 ...
% 3.85/2.28 % [INFO] GaveUp with current strategy, trying again with another strategy ...
% 12.45/3.92 % [INFO] Killing All external provers ...
% 12.45/3.93 % Time passed: 3451ms (effective reasoning time: 2732ms)
% 12.45/3.93 % 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)>
% 12.45/3.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3451 ms resp. 2732 ms w/o parsing
% 12.45/4.00 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.45/4.00 thf(a_decl, type, a: $i).
% 12.45/4.00 thf(b_decl, type, b: $i).
% 12.45/4.00 thf(17,axiom,((? [A:(($i > $o) > $i)]: ! [B:($i > $o)]: ((? [C:$i]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 12.45/4.00 thf(19,plain,(! [A:$i] : ((~ (((b = a) => (A = b)) & (A = a))) | (((b = a) => ((@+ [B:$i]: (((b = a) => (B = b)) & (B = a))) = b)) & ((@+ [B:$i]: (((b = a) => (B = b)) & (B = a))) = a)))),inference(choice,[status(esa)],[17])).
% 12.45/4.00 thf(34,plain,(! [A:$i] : ((((b = a) | ~ (A = a) | ~ (b = a) | ((@+ [B:$i]: (((b = a) => (B = b)) & (B = a))) = b)) & ((b = a) | ~ (A = a) | ((@+ [B:$i]: (((b = a) => (B = b)) & (B = a))) = a)) & (~ (A = b) | ~ (A = a) | ~ (b = a) | ((@+ [B:$i]: (((b = a) => (B = b)) & (B = a))) = b)) & (~ (A = b) | ~ (A = a) | ((@+ [B:$i]: (((b = a) => (B = b)) & (B = a))) = a))))),inference(cnf,[status(esa)],[19])).
% 12.45/4.00 thf(36,plain,(! [A:$i] : ((b = a) | (~ (A = a)) | ((@+ [B:$i]: (((b = a) => (B = b)) & (B = a))) = a))),inference(cnfConj,[status(thm)],[34])).
% 12.45/4.00 thf(41,plain,(! [A:$i] : ((b = a) | (A != a) | ((@+ [B:$i]: (((b = a) => (B = b)) & (B = a))) = a))),inference(lifteq,[status(thm)],[36])).
% 12.45/4.00 thf(42,plain,((b = a) | ((@+ [A:$i]: (((b = a) => (A = b)) & (A = a))) = a)),inference(simp,[status(thm)],[41])).
% 12.45/4.00 thf(1,conjecture,((? [A:($i > $i)]: (((A @ a) = b) & ((A @ b) = a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',swap)).
% 12.45/4.00 thf(2,negated_conjecture,((~ (? [A:($i > $i)]: (((A @ a) = b) & ((A @ b) = a))))),inference(neg_conjecture,[status(cth)],[1])).
% 12.45/4.00 thf(3,plain,((~ (? [A:($i > $i)]: (((A @ a) = b) & ((A @ b) = a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 12.45/4.00 thf(4,plain,(! [A:($i > $i)] : ((~ ((A @ a) = b)) | (~ ((A @ b) = a)))),inference(cnf,[status(esa)],[3])).
% 12.45/4.00 thf(5,plain,(! [A:($i > $i)] : (((A @ a) != b) | ((A @ b) != a))),inference(lifteq,[status(thm)],[4])).
% 12.45/4.00 thf(6,plain,(! [A:($i > $i)] : (((A @ a) != b) | ((A @ b) != b) | ((A @ a) != a))),inference(eqfactor_ordered,[status(thm)],[5])).
% 12.45/4.00 thf(9,plain,((b != a)),inference(pre_uni,[status(thm)],[6:[bind(A, $thf(^ [B:$i]: (B)))]])).
% 12.45/4.00 thf(12,plain,(((@+ [A:$i]: (((a = a) => (A = b)) & ((a = b) => (A = a)))) != b) | ((@+ [A:$i]: (((b = a) => (A = b)) & ((b = b) => (A = a)))) != a)),introduced(choice instance)).
% 12.45/4.00 thf(14,plain,(((@+ [A:$i]: ((A = b) & ((a = b) => (A = a)))) != b) | ((@+ [A:$i]: (((b = a) => (A = b)) & (A = a))) != a)),inference(simp,[status(thm)],[12])).
% 12.45/4.00 thf(18,plain,(! [A:$i] : ((~ ((A = b) & ((a = b) => (A = a)))) | (((@+ [B:$i]: ((B = b) & ((a = b) => (B = a)))) = b) & ((a = b) => ((@+ [B:$i]: ((B = b) & ((a = b) => (B = a)))) = a))))),inference(choice,[status(esa)],[17])).
% 12.45/4.00 thf(21,plain,(! [A:$i] : (((~ (A = b) | (a = b) | ((@+ [B:$i]: ((B = b) & ((a = b) => (B = a)))) = b)) & (~ (A = b) | (a = b) | ~ (a = b) | ((@+ [B:$i]: ((B = b) & ((a = b) => (B = a)))) = a)) & (~ (A = b) | ~ (A = a) | ((@+ [B:$i]: ((B = b) & ((a = b) => (B = a)))) = b)) & (~ (A = b) | ~ (A = a) | ~ (a = b) | ((@+ [B:$i]: ((B = b) & ((a = b) => (B = a)))) = a))))),inference(cnf,[status(esa)],[18])).
% 12.45/4.00 thf(22,plain,(! [A:$i] : ((~ (A = b)) | (a = b) | ((@+ [B:$i]: ((B = b) & ((a = b) => (B = a)))) = b))),inference(cnfConj,[status(thm)],[21])).
% 12.45/4.00 thf(26,plain,(! [A:$i] : ((A != b) | (a = b) | ((@+ [B:$i]: ((B = b) & ((a = b) => (B = a)))) = b))),inference(lifteq,[status(thm)],[22])).
% 12.45/4.00 thf(27,plain,((a = b) | ((@+ [A:$i]: ((A = b) & ((a = b) => (A = a)))) = b)),inference(simp,[status(thm)],[26])).
% 12.45/4.00 thf(55,plain,(((@+ [A:$i]: ((A = b) & ((a = b) => (A = a)))) = b)),inference(simplifyReflect,[status(thm)],[27,9])).
% 12.45/4.00 thf(57,plain,(((@+ [A:$i]: (((b = a) => (A = b)) & (A = a))) != a)),inference(simplifyReflect,[status(thm)],[14,55])).
% 12.45/4.00 thf(559,plain,(($false)),inference(simplifyReflect,[status(thm)],[42,9,57])).
% 12.45/4.00 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.45/4.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------