%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM637^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 08:18:20 AM UTC 2026
% Result : Theorem 0.36s 0.43s
% Output : Refutation 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM637^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.28 % Computer : n017.cluster.edu
% 0.12/0.28 % Model : x86_64 x86_64
% 0.12/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.28 % Memory : 8046.5625MB
% 0.12/0.28 % OS : Linux 6.8.0-71-generic
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Tue Sep 29 12:06:22 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.30/0.34 Running higher-order theorem proving
% 0.30/0.35 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.36/0.43 % (252768)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.36/0.43 % (252773)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2741700748:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.36/0.43 % (252773) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-252768-252773"...
% 0.36/0.43 % (252773)...printing done.
% 0.36/0.43 % (252773)Refutation found. Thanks to Tanya!
% 0.36/0.43 % SZS status Theorem for theBenchmark
% 0.36/0.43 % SZS output start Proof for theBenchmark
% 0.36/0.43 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.36/0.43 thf(func_def_1, type, succ: ($i > $i)).
% 0.36/0.43 thf(func_def_5, type, sK0: (($i > $o) > $i)).
% 0.36/0.43 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.36/0.43 thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.36/0.43 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.36/0.43 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.36/0.43 thf(f3,axiom,(
% 0.36/0.43 ! [X0 : ($i > $o)] : (((X0 @ one) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1)))) => ! [X2 : $i] : (X0 @ X2))),
% 0.36/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction)).
% 0.36/0.43 thf(f4,conjecture,(
% 0.36/0.43 ! [X0 : $i] : ((X0 != one) => ? [X1 : $i] : (X0 = ((succ @ X1))))),
% 0.36/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3)).
% 0.36/0.43 thf(f5,negated_conjecture,(
% 0.36/0.43 ~ ! [X0 : $i] : ((X0 != one) => ? [X1 : $i] : (X0 = ((succ @ X1))))),
% 0.36/0.43 inference(negated_conjecture,[status(cth)],[f4])).
% 0.36/0.43 thf(f6,plain,(
% 0.36/0.43 ! [X0 : ($i > $o)] : (((X0 @ one) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1)))) => ! [X2 : $i] : (X0 @ X2))),
% 0.36/0.43 inference(rectify,[],[f3])).
% 0.36/0.43 thf(f7,plain,(
% 0.36/0.43 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((((X0 @ X1)) = $true) => (((X0 @ (succ @ X1))) = $true)) & (((X0 @ one)) = $true)) => ! [X2 : $i] : (((X0 @ X2)) = $true))),
% 0.36/0.43 inference(fool_elimination,[],[f6])).
% 0.36/0.43 thf(f8,plain,(
% 0.36/0.43 ? [X0 : $i] : (! [X1 : $i] : (((succ @ X1)) != X0) & (X0 != one))),
% 0.36/0.43 inference(ennf_transformation,[],[f5])).
% 0.36/0.43 thf(f10,plain,(
% 0.36/0.43 ! [X0 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) = $true) | (? [X1 : $i] : ((((X0 @ X1)) = $true) & (((X0 @ (succ @ X1))) != $true)) | (((X0 @ one)) != $true)))),
% 0.36/0.43 inference(ennf_transformation,[],[f7])).
% 0.36/0.43 thf(f11,plain,(
% 0.36/0.43 ! [X0 : ($i > $o)] : ((((X0 @ one)) != $true) | ! [X2 : $i] : (((X0 @ X2)) = $true) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & (((X0 @ (succ @ X1))) != $true)))),
% 0.36/0.43 inference(flattening,[],[f10])).
% 0.36/0.43 thf(f12,plain,(
% 0.36/0.43 ! [X0 : ($i > $o)] : ((((X0 @ one)) != $true) | ! [X1 : $i] : (((X0 @ X1)) = $true) | ? [X2 : $i] : ((((X0 @ X2)) = $true) & (((X0 @ (succ @ X2))) != $true)))),
% 0.36/0.43 inference(rectify,[],[f11])).
% 0.36/0.43 thf(f13,plain,(
% 0.36/0.43 ! [X0 : ($i > $o)] : ((((X0 @ one)) != $true) | ! [X1 : $i] : (((X0 @ X1)) = $true) | ((((X0 @ (sK0 @ X0))) = $true) & (((X0 @ (succ @ (sK0 @ X0)))) != $true)))),
% 0.36/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f12])).
% 0.36/0.43 thf(f14,plain,(
% 0.36/0.43 ! [X1 : $i] : (((succ @ X1)) != sK1) & (one != sK1)),
% 0.36/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f8])).
% 0.36/0.43 thf(f16,plain,(
% 0.36/0.43 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (succ @ (sK0 @ X0)))) != $true) | (((X0 @ one)) != $true) | (((X0 @ X1)) = $true)) )),
% 0.36/0.43 inference(cnf_transformation,[],[f13])).
% 0.36/0.43 thf(f18,plain,(
% 0.36/0.43 (one != sK1)),
% 0.36/0.43 inference(cnf_transformation,[],[f14])).
% 0.36/0.43 thf(f19,plain,(
% 0.36/0.43 ( ! [X1 : $i] : ((((succ @ X1)) != sK1)) )),
% 0.36/0.43 inference(cnf_transformation,[],[f14])).
% 0.36/0.43 thf(f64,plain,(
% 0.36/0.43 ( ! [X0 : $i] : ((((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | ((((^[Y0 : $i]: (~ (Y0 = X0))) @ one)) != $true)) )),
% 0.36/0.43 inference(leibniz_equality_elimination,[],[f16])).
% 0.36/0.43 thf(f78,plain,(
% 0.36/0.43 ( ! [X0 : $i] : ((((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (((~ (one = X0))) != $true)) )),
% 0.36/0.43 inference(beta-eta_normalization,[],[f64])).
% 0.36/0.43 thf(f79,plain,(
% 0.36/0.43 ( ! [X0 : $i] : ((((one = X0)) = $true) | (((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0)) )),
% 0.36/0.43 inference(not_proxy_clausification,[],[f78])).
% 0.36/0.43 thf(f80,plain,(
% 0.36/0.43 ( ! [X0 : $i] : ((((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (one = X0)) )),
% 0.36/0.43 inference(equality_proxy_clausification,[],[f79])).
% 0.36/0.43 thf(f91,plain,(
% 0.36/0.43 ( ! [X0 : $i] : ((sK1 != X0) | (one = X0)) )),
% 0.36/0.43 inference(constrained_superposition,[],[f19,f80])).
% 0.36/0.43 thf(f101,plain,(
% 0.36/0.43 (one = sK1) | (sK1 != sK1)),
% 0.36/0.43 inference(imitation,[],[f91])).
% 0.36/0.43 thf(f103,plain,(
% 0.36/0.43 (one = sK1)),
% 0.36/0.43 inference(trivial_inequality_removal,[],[f101])).
% 0.36/0.43 thf(f104,plain,(
% 0.36/0.43 $false),
% 0.36/0.43 inference(forward_subsumption_resolution,[],[f103,f18])).
% 0.36/0.43 % SZS output end Proof for theBenchmark
% 0.36/0.43 % (252773)------------------------------
% 0.36/0.43 % (252773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.43 % (252773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.43 % (252773)CaDiCaL version: 2.1.3
% 0.36/0.43 % (252773)Termination reason: Refutation
% 0.36/0.43 % (252773)Time elapsed: 0.006 s
% 0.36/0.43 % (252773)Peak memory usage: 12 MB
% 0.36/0.43 % (252773)Instructions burned: 4 (million)
% 0.36/0.43 % (252768)Success in time 0.056 s
% 0.36/0.43 % Vampire exiting
%------------------------------------------------------------------------------