%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM669^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 08:19:16 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM669^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:37:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (1213417)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (1213423)% WARNING: option uhcvi not known.
% 0.21/0.28 % (1213423)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3852478630:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (1213423)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (1213423)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.28 % (1213423) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1213417-1213423"...
% 0.21/0.28 % (1213423)...printing done.
% 0.21/0.28 % (1213423)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, nat: $tType).
% 0.21/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, x: nat).
% 0.21/0.28 thf(func_def_1, type, more: (nat > nat > $o)).
% 0.21/0.28 thf(func_def_2, type, suc: (nat > nat)).
% 0.21/0.28 thf(func_def_3, type, pl: (nat > nat > nat)).
% 0.21/0.28 thf(func_def_4, type, n_1: nat).
% 0.21/0.28 thf(f1,axiom,(
% 0.21/0.28 ! [X0 : nat,X1 : nat] : (more @ (pl @ X0 @ X1) @ X0)),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz18)).
% 0.21/0.28 thf(f2,axiom,(
% 0.21/0.28 ! [X0 : nat] : (((pl @ X0 @ n_1)) = ((suc @ X0)))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4a)).
% 0.21/0.28 thf(f3,conjecture,(
% 0.21/0.28 (more @ (suc @ x) @ x)),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz18b)).
% 0.21/0.28 thf(f4,negated_conjecture,(
% 0.21/0.28 ~(more @ (suc @ x) @ x)),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ! [X0 : nat,X1 : nat] : (more @ (pl @ X0 @ X1) @ X0)),
% 0.21/0.28 inference(rectify,[],[f1])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ! [X0 : nat,X1 : nat] : (((more @ (pl @ X0 @ X1) @ X0)) = $true)),
% 0.21/0.28 inference(fool_elimination,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ~(more @ (suc @ x) @ x)),
% 0.21/0.28 inference(rectify,[],[f4])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ~ (((more @ (suc @ x) @ x)) = $true)),
% 0.21/0.28 inference(fool_elimination,[],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 (((more @ (suc @ x) @ x)) != $true)),
% 0.21/0.28 inference(flattening,[],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ( ! [X0 : nat,X1 : nat] : ((((more @ (pl @ X0 @ X1) @ X0)) = $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f6])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ( ! [X0 : nat] : ((((pl @ X0 @ n_1)) = ((suc @ X0)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f2])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 (((more @ (suc @ x) @ x)) != $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f14,definition,(
% 0.21/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 ($true != $true) | (((more @ (suc @ x) @ x)) = $false)),
% 0.21/0.28 inference(constrained_superposition,[],[f12,f14])).
% 0.21/0.28 thf(f19,plain,(
% 0.21/0.28 (((more @ (suc @ x) @ x)) = $false)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f17])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 ( ! [X0 : nat] : (($true = ((more @ (suc @ X0) @ X0)))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f10,f11])).
% 0.21/0.28 thf(f30,plain,(
% 0.21/0.28 ($true = $false)),
% 0.21/0.28 inference(constrained_superposition,[],[f19,f27])).
% 0.21/0.28 thf(f31,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f30])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (1213423)------------------------------
% 0.21/0.28 % (1213423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1213423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1213423)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1213423)Termination reason: Refutation
% 0.21/0.28 % (1213423)Time elapsed: 0.001 s
% 0.21/0.28 % (1213423)Peak memory usage: 12 MB
% 0.21/0.28 % (1213423)Instructions burned: 2 (million)
% 0.21/0.28 % (1213417)Success in time 0.037 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------