%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN023^1 : TPTP v9.3.1. Released v6.4.0.
% 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 : n017.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 08:19:48 AM UTC 2026
% Result : Theorem 49.28s 12.55s
% Output : Refutation 48.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN023^1 : TPTP v9.3.1. Released v6.4.0.
% 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
% 0.11/0.22 % Computer : n017.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 13:01:37 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.96 % [INFO] Parsing done (175ms).
% 1.25/0.98 % [INFO] Running in sequential loop mode.
% 1.86/1.37 % [INFO] eprover registered as external prover.
% 1.86/1.38 % [INFO] Scanning for conjecture ...
% 2.07/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.51 % [INFO] Type checking passed.
% 2.23/1.51 % [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 ...
% 4.55/2.47 % [INFO] GaveUp with current strategy, trying again with another strategy ...
% 49.28/12.54 % [INFO] Killing All external provers ...
% 49.28/12.55 % Time passed: 12186ms (effective reasoning time: 11564ms)
% 49.28/12.55 % 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)>
% 49.28/12.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12186 ms resp. 11564 ms w/o parsing
% 48.46/12.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.46/12.60 thf(zero_decl, type, zero: $i).
% 48.46/12.60 thf(s_decl, type, s: ($i > $i)).
% 48.46/12.60 thf(ite_decl, type, ite: ($o > ($i > ($i > $i)))).
% 48.46/12.60 thf(24957,axiom,((? [A:(($i > $o) > $i)]: ! [B:($i > $o)]: ((? [C:$i]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 48.46/12.60 thf(24958,plain,(! [A:$i] : ((~ ((A = (s @ zero)) & ((zero = (s @ zero)) => (A = zero)))) | (((@+ [B:$i]: ((B = (s @ zero)) & ((zero = (s @ zero)) => (B = zero)))) = (s @ zero)) & ((zero = (s @ zero)) => ((@+ [B:$i]: ((B = (s @ zero)) & ((zero = (s @ zero)) => (B = zero)))) = zero))))),inference(choice,[status(esa)],[24957])).
% 48.46/12.60 thf(25027,plain,(! [A:$i] : (((~ (A = (s @ zero)) | (zero = (s @ zero)) | ((@+ [B:$i]: ((B = (s @ zero)) & ((zero = (s @ zero)) => (B = zero)))) = (s @ zero))) & (~ (A = (s @ zero)) | (zero = (s @ zero)) | ~ (zero = (s @ zero)) | ((@+ [B:$i]: ((B = (s @ zero)) & ((zero = (s @ zero)) => (B = zero)))) = zero)) & (~ (A = (s @ zero)) | ~ (A = zero) | ((@+ [B:$i]: ((B = (s @ zero)) & ((zero = (s @ zero)) => (B = zero)))) = (s @ zero))) & (~ (A = (s @ zero)) | ~ (A = zero) | ~ (zero = (s @ zero)) | ((@+ [B:$i]: ((B = (s @ zero)) & ((zero = (s @ zero)) => (B = zero)))) = zero))))),inference(cnf,[status(esa)],[24958])).
% 48.46/12.60 thf(25028,plain,(! [A:$i] : ((~ (A = (s @ zero))) | (zero = (s @ zero)) | ((@+ [B:$i]: ((B = (s @ zero)) & ((zero = (s @ zero)) => (B = zero)))) = (s @ zero)))),inference(cnfConj,[status(thm)],[25027])).
% 48.46/12.60 thf(25032,plain,(! [A:$i] : ((A != (s @ zero)) | (zero = (s @ zero)) | ((@+ [B:$i]: ((B = (s @ zero)) & ((zero = (s @ zero)) => (B = zero)))) = (s @ zero)))),inference(lifteq,[status(thm)],[25028])).
% 48.46/12.60 thf(25033,plain,((zero = (s @ zero)) | ((@+ [A:$i]: ((A = (s @ zero)) & ((zero = (s @ zero)) => (A = zero)))) = (s @ zero))),inference(simp,[status(thm)],[25032])).
% 48.46/12.60 thf(127,plain,(((@+ [A:$i]: (((zero = zero) => (A = (s @ zero))) & ((zero = (s @ zero)) => (A = zero)))) != (s @ zero)) | ((@+ [A:$i]: ((((s @ zero) = zero) => (A = (s @ zero))) & (((s @ zero) = (s @ zero)) => (A = zero)))) != zero)),introduced(choice instance)).
% 48.46/12.60 thf(147,plain,(((@+ [A:$i]: ((A = (s @ zero)) & ((zero = (s @ zero)) => (A = zero)))) != (s @ zero)) | ((@+ [A:$i]: ((((s @ zero) = zero) => (A = (s @ zero))) & (A = zero))) != zero)),inference(simp,[status(thm)],[127])).
% 48.46/12.60 thf(24959,plain,(! [A:$i] : ((~ ((((s @ zero) = zero) => (A = (s @ zero))) & (A = zero))) | ((((s @ zero) = zero) => ((@+ [B:$i]: ((((s @ zero) = zero) => (B = (s @ zero))) & (B = zero))) = (s @ zero))) & ((@+ [B:$i]: ((((s @ zero) = zero) => (B = (s @ zero))) & (B = zero))) = zero)))),inference(choice,[status(esa)],[24957])).
% 48.46/12.60 thf(25040,plain,(! [A:$i] : (((((s @ zero) = zero) | ~ (A = zero) | ~ ((s @ zero) = zero) | ((@+ [B:$i]: ((((s @ zero) = zero) => (B = (s @ zero))) & (B = zero))) = (s @ zero))) & (((s @ zero) = zero) | ~ (A = zero) | ((@+ [B:$i]: ((((s @ zero) = zero) => (B = (s @ zero))) & (B = zero))) = zero)) & (~ (A = (s @ zero)) | ~ (A = zero) | ~ ((s @ zero) = zero) | ((@+ [B:$i]: ((((s @ zero) = zero) => (B = (s @ zero))) & (B = zero))) = (s @ zero))) & (~ (A = (s @ zero)) | ~ (A = zero) | ((@+ [B:$i]: ((((s @ zero) = zero) => (B = (s @ zero))) & (B = zero))) = zero))))),inference(cnf,[status(esa)],[24959])).
% 48.46/12.60 thf(25042,plain,(! [A:$i] : (((s @ zero) = zero) | (~ (A = zero)) | ((@+ [B:$i]: ((((s @ zero) = zero) => (B = (s @ zero))) & (B = zero))) = zero))),inference(cnfConj,[status(thm)],[25040])).
% 48.46/12.60 thf(25047,plain,(! [A:$i] : (((s @ zero) = zero) | (A != zero) | ((@+ [B:$i]: ((((s @ zero) = zero) => (B = (s @ zero))) & (B = zero))) = zero))),inference(lifteq,[status(thm)],[25042])).
% 48.46/12.60 thf(25048,plain,(((s @ zero) = zero) | ((@+ [A:$i]: ((((s @ zero) = zero) => (A = (s @ zero))) & (A = zero))) = zero)),inference(simp,[status(thm)],[25047])).
% 48.46/12.60 thf(1,conjecture,(((! [A:$o,B:$i,C:$i]: ((A) => ((ite @ A @ B @ C) = B)) & ! [A:$o,B:$i,C:$i]: ((~ (A)) => ((ite @ A @ B @ C) = C))) => (? [A:($i > $i)]: (((A @ zero) = (s @ zero)) & ((A @ (s @ zero)) = zero))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',n8)).
% 48.46/12.60 thf(2,negated_conjecture,((~ ((! [A:$o,B:$i,C:$i]: ((A) => ((ite @ A @ B @ C) = B)) & ! [A:$o,B:$i,C:$i]: ((~ (A)) => ((ite @ A @ B @ C) = C))) => (? [A:($i > $i)]: (((A @ zero) = (s @ zero)) & ((A @ (s @ zero)) = zero)))))),inference(neg_conjecture,[status(cth)],[1])).
% 48.46/12.60 thf(3,plain,((~ ((! [A:$o,B:$i,C:$i]: ((A) => ((ite @ A @ B @ C) = B)) & ! [A:$o,B:$i,C:$i]: ((~ (A)) => ((ite @ A @ B @ C) = C))) => (? [A:($i > $i)]: (((A @ zero) = (s @ zero)) & ((A @ (s @ zero)) = zero)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 48.46/12.60 thf(4,plain,((~ ((! [A:$i,B:$i]: ((($true)) => ((ite @ ($true) @ A @ B) = A)) & ! [A:$i,B:$i]: ((~ (($true))) => ((ite @ ($true) @ A @ B) = B))) => (? [A:($i > $i)]: (((A @ zero) = (s @ zero)) & ((A @ (s @ zero)) = zero)))))),inference(instance,[status(thm)],[3])).
% 48.46/12.60 thf(5,plain,((~ ((! [A:$i,B:$i]: ((ite @ ($true) @ A @ B) = A)) => (? [A:($i > $i)]: (((A @ zero) = (s @ zero)) & ((A @ (s @ zero)) = zero)))))),inference(simp,[status(thm)],[4])).
% 48.46/12.60 thf(12,plain,(! [C:($i > $i),B:$i,A:$i] : ((((ite @ ($true) @ A @ B) = A) & (~ ((C @ zero) = (s @ zero)) | ~ ((C @ (s @ zero)) = zero))))),inference(cnf,[status(esa)],[5])).
% 48.46/12.60 thf(14,plain,(! [A:($i > $i)] : ((~ ((A @ zero) = (s @ zero))) | (~ ((A @ (s @ zero)) = zero)))),inference(cnfConj,[status(thm)],[12])).
% 48.46/12.60 thf(23,plain,(! [A:($i > $i)] : (((A @ zero) != (s @ zero)) | ((A @ (s @ zero)) != zero))),inference(lifteq,[status(thm)],[14])).
% 48.46/12.60 thf(24,plain,(! [A:($i > $i)] : (((A @ zero) != (s @ zero)) | ((A @ (s @ zero)) != zero))),inference(simp,[status(thm)],[23])).
% 48.46/12.60 thf(49,plain,(! [A:($i > $i)] : (((A @ zero) != (s @ zero)) | ((A @ (s @ zero)) != (s @ zero)) | ((A @ zero) != zero))),inference(eqfactor_ordered,[status(thm)],[24])).
% 48.46/12.60 thf(81,plain,(((s @ zero) != zero)),inference(pre_uni,[status(thm)],[49:[bind(A, $thf(^ [B:$i]: (B)))]])).
% 48.46/12.60 thf(25103,plain,(((@+ [A:$i]: ((((s @ zero) = zero) => (A = (s @ zero))) & (A = zero))) = zero)),inference(simplifyReflect,[status(thm)],[25048,81])).
% 48.46/12.60 thf(25104,plain,(((@+ [A:$i]: ((A = (s @ zero)) & ((zero = (s @ zero)) => (A = zero)))) != (s @ zero))),inference(simplifyReflect,[status(thm)],[147,25103])).
% 48.46/12.60 thf(27776,plain,(($false)),inference(simplifyReflect,[status(thm)],[25033,25104,81])).
% 48.46/12.60 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.46/12.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------