%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM693^1 : 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 : 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 08:18:34 AM UTC 2026
% Result : Theorem 0.08s 0.29s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM693^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:40:24 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.08/0.29 % (3087805)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.29 % (3087811)lrs+10_16_si=on:nwc=1.5:random_seed=2827883521:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.29 % (3087811) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3087805-3087811"...
% 0.08/0.29 % (3087810)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1184336293:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.29 % (3087811)...printing done.
% 0.08/0.29 % (3087811)Refutation found. Thanks to Tanya!
% 0.08/0.29 % SZS status Theorem for theBenchmark
% 0.08/0.29 % SZS output start Proof for theBenchmark
% 0.08/0.29 thf(type_def_5, type, nat: $tType).
% 0.08/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.29 thf(func_def_0, type, x: nat).
% 0.08/0.29 thf(func_def_1, type, more: (nat > nat > $o)).
% 0.08/0.29 thf(func_def_2, type, n_1: nat).
% 0.08/0.29 thf(func_def_3, type, suc: (nat > nat)).
% 0.08/0.29 thf(func_def_5, type, pl: (nat > nat > nat)).
% 0.08/0.29 thf(func_def_8, type, sK0: (nat > nat)).
% 0.08/0.29 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.08/0.29 thf(f2,axiom,(
% 0.08/0.29 ! [X0 : nat] : ((X0 != n_1) => ~ ! [X1 : nat] : (X0 != ((suc @ X1))))),
% 0.08/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3)).
% 0.08/0.29 thf(f3,axiom,(
% 0.08/0.29 ! [X1 : nat,X0 : nat] : (more @ (pl @ X0 @ X1) @ X0)),
% 0.08/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz18)).
% 0.08/0.29 thf(f4,axiom,(
% 0.08/0.29 ! [X0 : nat] : (((suc @ X0)) = ((pl @ n_1 @ X0)))),
% 0.08/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz4g)).
% 0.08/0.29 thf(f5,conjecture,(
% 0.08/0.29 ~(more @ x @ n_1) => (x = n_1)),
% 0.08/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz24)).
% 0.08/0.29 thf(f6,negated_conjecture,(
% 0.08/0.29 ~(~(more @ x @ n_1) => (x = n_1))),
% 0.08/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.08/0.29 thf(f7,plain,(
% 0.08/0.29 ! [X0 : nat,X1 : nat] : (more @ (pl @ X1 @ X0) @ X1)),
% 0.08/0.29 inference(rectify,[],[f3])).
% 0.08/0.29 thf(f8,plain,(
% 0.08/0.29 ! [X1 : nat,X0 : nat] : ($true = ((more @ (pl @ X1 @ X0) @ X1)))),
% 0.08/0.29 inference(fool_elimination,[],[f7])).
% 0.08/0.29 thf(f11,plain,(
% 0.08/0.29 ~(~(more @ x @ n_1) => (x = n_1))),
% 0.08/0.29 inference(rectify,[],[f6])).
% 0.08/0.29 thf(f12,plain,(
% 0.08/0.29 ~(~ (((more @ x @ n_1)) = $true) => (n_1 = x))),
% 0.08/0.29 inference(fool_elimination,[],[f11])).
% 0.08/0.29 thf(f14,plain,(
% 0.08/0.29 ~((((more @ x @ n_1)) != $true) => (n_1 = x))),
% 0.08/0.29 inference(flattening,[],[f12])).
% 0.08/0.29 thf(f16,plain,(
% 0.08/0.29 (n_1 != x) & (((more @ x @ n_1)) != $true)),
% 0.08/0.29 inference(ennf_transformation,[],[f14])).
% 0.08/0.29 thf(f17,plain,(
% 0.08/0.29 ! [X0 : nat] : (? [X1 : nat] : (((suc @ X1)) = X0) | (n_1 = X0))),
% 0.08/0.29 inference(ennf_transformation,[],[f2])).
% 0.08/0.29 thf(f18,plain,(
% 0.08/0.29 ! [X0 : nat,X1 : nat] : (((more @ (pl @ X0 @ X1) @ X0)) = $true)),
% 0.08/0.29 inference(rectify,[],[f8])).
% 0.08/0.29 thf(f19,plain,(
% 0.08/0.29 ! [X0 : nat] : ((((suc @ (sK0 @ X0))) = X0) | (n_1 = X0))),
% 0.08/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f17])).
% 0.08/0.29 thf(f20,plain,(
% 0.08/0.29 ( ! [X0 : nat] : ((((suc @ X0)) = ((pl @ n_1 @ X0)))) )),
% 0.08/0.29 inference(cnf_transformation,[],[f4])).
% 0.08/0.29 thf(f21,plain,(
% 0.08/0.29 ( ! [X0 : nat,X1 : nat] : ((((more @ (pl @ X0 @ X1) @ X0)) = $true)) )),
% 0.08/0.29 inference(cnf_transformation,[],[f18])).
% 0.08/0.29 thf(f22,plain,(
% 0.08/0.29 (((more @ x @ n_1)) != $true)),
% 0.08/0.29 inference(cnf_transformation,[],[f16])).
% 0.08/0.29 thf(f23,plain,(
% 0.08/0.29 (n_1 != x)),
% 0.08/0.29 inference(cnf_transformation,[],[f16])).
% 0.08/0.29 thf(f24,plain,(
% 0.08/0.29 ( ! [X0 : nat] : ((((suc @ (sK0 @ X0))) = X0) | (n_1 = X0)) )),
% 0.08/0.29 inference(cnf_transformation,[],[f19])).
% 0.08/0.29 thf(f29,plain,(
% 0.08/0.29 ( ! [X0 : nat] : ((((more @ (suc @ X0) @ n_1)) = $true)) )),
% 0.08/0.29 inference(constrained_superposition,[],[f21,f20])).
% 0.08/0.29 thf(f30,plain,(
% 0.08/0.29 ( ! [X0 : nat] : ((((more @ X0 @ n_1)) = $true) | (n_1 = X0)) )),
% 0.08/0.29 inference(constrained_superposition,[],[f29,f24])).
% 0.08/0.29 thf(f31,plain,(
% 0.08/0.29 (n_1 = x) | ($true != $true)),
% 0.08/0.29 inference(constrained_superposition,[],[f22,f30])).
% 0.08/0.29 thf(f32,plain,(
% 0.08/0.29 (n_1 = x)),
% 0.08/0.29 inference(trivial_inequality_removal,[],[f31])).
% 0.08/0.29 thf(f33,plain,(
% 0.08/0.29 $false),
% 0.08/0.29 inference(forward_subsumption_resolution,[],[f32,f23])).
% 0.08/0.29 % SZS output end Proof for theBenchmark
% 0.08/0.29 % (3087811)------------------------------
% 0.08/0.29 % (3087811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.29 % (3087811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.29 % (3087811)CaDiCaL version: 2.1.3
% 0.08/0.29 % (3087811)Termination reason: Refutation
% 0.08/0.29 % (3087811)Time elapsed: 0.002 s
% 0.08/0.29 % (3087811)Peak memory usage: 12 MB
% 0.08/0.29 % (3087811)Instructions burned: 2 (million)
% 0.08/0.29 % (3087805)Success in time 0.045 s
% 0.08/0.29 % Vampire exiting
%------------------------------------------------------------------------------