%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO295^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n015.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 08:45:33 AM UTC 2026
% Result : Theorem 7.49s 3.09s
% Output : Refutation 7.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO295^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n015.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:47:36 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.96 % [INFO] Parsing done (170ms).
% 1.16/0.97 % [INFO] Running in sequential loop mode.
% 1.70/1.36 % [INFO] eprover registered as external prover.
% 1.70/1.37 % [INFO] Scanning for conjecture ...
% 1.89/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.89/1.49 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.89/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 1.89/1.50 % [INFO] Type checking passed.
% 2.03/1.50 % [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 ...
% 2.75/2.00 % [INFO] GaveUp with current strategy, trying again with another strategy ...
% 7.49/3.09 % [INFO] Killing All external provers ...
% 7.49/3.09 % Time passed: 2740ms (effective reasoning time: 2107ms)
% 7.49/3.09 % 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)>
% 7.49/3.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2740 ms resp. 2107 ms w/o parsing
% 7.49/3.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.49/3.13 thf(b_decl, type, b: $i).
% 7.49/3.13 thf(y_decl, type, y: $i).
% 7.49/3.13 thf(a_decl, type, a: $i).
% 7.49/3.13 thf(x_decl, type, x: $i).
% 7.49/3.13 thf(18,axiom,((? [A:(($i > $o) > $i)]: ! [B:($i > $o)]: ((? [C:$i]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 7.49/3.13 thf(20,plain,(! [A:$i] : ((~ (((y = x) => (A = a)) & (A = b))) | (((y = x) => ((@+ [B:$i]: (((y = x) => (B = a)) & (B = b))) = a)) & ((@+ [B:$i]: (((y = x) => (B = a)) & (B = b))) = b)))),inference(choice,[status(esa)],[18])).
% 7.49/3.13 thf(35,plain,(! [A:$i] : ((((y = x) | ~ (A = b) | ~ (y = x) | ((@+ [B:$i]: (((y = x) => (B = a)) & (B = b))) = a)) & ((y = x) | ~ (A = b) | ((@+ [B:$i]: (((y = x) => (B = a)) & (B = b))) = b)) & (~ (A = a) | ~ (A = b) | ~ (y = x) | ((@+ [B:$i]: (((y = x) => (B = a)) & (B = b))) = a)) & (~ (A = a) | ~ (A = b) | ((@+ [B:$i]: (((y = x) => (B = a)) & (B = b))) = b))))),inference(cnf,[status(esa)],[20])).
% 7.49/3.13 thf(37,plain,(! [A:$i] : ((y = x) | (~ (A = b)) | ((@+ [B:$i]: (((y = x) => (B = a)) & (B = b))) = b))),inference(cnfConj,[status(thm)],[35])).
% 7.49/3.13 thf(42,plain,(! [A:$i] : ((y = x) | (A != b) | ((@+ [B:$i]: (((y = x) => (B = a)) & (B = b))) = b))),inference(lifteq,[status(thm)],[37])).
% 7.49/3.13 thf(43,plain,((y = x) | ((@+ [A:$i]: (((y = x) => (A = a)) & (A = b))) = b)),inference(simp,[status(thm)],[42])).
% 7.49/3.13 thf(1,conjecture,(((x != y) => (? [A:($i > $i)]: (((A @ x) = a) & ((A @ y) = b))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5311)).
% 7.49/3.13 thf(2,negated_conjecture,((~ ((x != y) => (? [A:($i > $i)]: (((A @ x) = a) & ((A @ y) = b)))))),inference(neg_conjecture,[status(cth)],[1])).
% 7.49/3.13 thf(3,plain,((~ ((~ (x = y)) => (? [A:($i > $i)]: (((A @ x) = a) & ((A @ y) = b)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 7.49/3.13 thf(4,plain,(! [A:($i > $i)] : ((~ (x = y) & (~ ((A @ x) = a) | ~ ((A @ y) = b))))),inference(cnf,[status(esa)],[3])).
% 7.49/3.13 thf(5,plain,((~ (x = y))),inference(cnfConj,[status(thm)],[4])).
% 7.49/3.13 thf(10,plain,((x != y)),inference(lifteq,[status(thm)],[5])).
% 7.49/3.13 thf(14,plain,(((@+ [A:$i]: (((x = x) => (A = a)) & ((x = y) => (A = b)))) != a) | ((@+ [A:$i]: (((y = x) => (A = a)) & ((y = y) => (A = b)))) != b)),introduced(choice instance)).
% 7.49/3.13 thf(15,plain,(((@+ [A:$i]: ((A = a) & ((x = y) => (A = b)))) != a) | ((@+ [A:$i]: (((y = x) => (A = a)) & (A = b))) != b)),inference(simp,[status(thm)],[14])).
% 7.49/3.13 thf(19,plain,(! [A:$i] : ((~ ((A = a) & ((x = y) => (A = b)))) | (((@+ [B:$i]: ((B = a) & ((x = y) => (B = b)))) = a) & ((x = y) => ((@+ [B:$i]: ((B = a) & ((x = y) => (B = b)))) = b))))),inference(choice,[status(esa)],[18])).
% 7.49/3.13 thf(22,plain,(! [A:$i] : (((~ (A = a) | (x = y) | ((@+ [B:$i]: ((B = a) & ((x = y) => (B = b)))) = a)) & (~ (A = a) | (x = y) | ~ (x = y) | ((@+ [B:$i]: ((B = a) & ((x = y) => (B = b)))) = b)) & (~ (A = a) | ~ (A = b) | ((@+ [B:$i]: ((B = a) & ((x = y) => (B = b)))) = a)) & (~ (A = a) | ~ (A = b) | ~ (x = y) | ((@+ [B:$i]: ((B = a) & ((x = y) => (B = b)))) = b))))),inference(cnf,[status(esa)],[19])).
% 7.49/3.13 thf(23,plain,(! [A:$i] : ((~ (A = a)) | (x = y) | ((@+ [B:$i]: ((B = a) & ((x = y) => (B = b)))) = a))),inference(cnfConj,[status(thm)],[22])).
% 7.49/3.13 thf(27,plain,(! [A:$i] : ((A != a) | (x = y) | ((@+ [B:$i]: ((B = a) & ((x = y) => (B = b)))) = a))),inference(lifteq,[status(thm)],[23])).
% 7.49/3.13 thf(28,plain,((x = y) | ((@+ [A:$i]: ((A = a) & ((x = y) => (A = b)))) = a)),inference(simp,[status(thm)],[27])).
% 7.49/3.13 thf(56,plain,(((@+ [A:$i]: ((A = a) & ((x = y) => (A = b)))) = a)),inference(simplifyReflect,[status(thm)],[28,10])).
% 7.49/3.13 thf(58,plain,(((@+ [A:$i]: (((y = x) => (A = a)) & (A = b))) != b)),inference(simplifyReflect,[status(thm)],[15,56])).
% 7.49/3.13 thf(452,plain,(($false)),inference(simplifyReflect,[status(thm)],[43,10,58])).
% 7.49/3.13 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.49/3.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------