%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM681^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:19:17 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM681^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 12:37:31 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.27 % (2592625)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (2592631)% WARNING: option uhcvi not known.
% 0.18/0.27 % (2592631)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1855891008:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (2592631)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (2592631)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.27 % (2592631) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2592625-2592631"...
% 0.18/0.27 % (2592631)...printing done.
% 0.18/0.27 % (2592631)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% 0.18/0.27 thf(type_def_5, type, nat: $tType).
% 0.18/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.27 thf(func_def_0, type, x: nat).
% 0.18/0.27 thf(func_def_1, type, y: nat).
% 0.18/0.27 thf(func_def_2, type, z: nat).
% 0.18/0.27 thf(func_def_3, type, pl: (nat > nat > nat)).
% 0.18/0.27 thf(func_def_5, type, less: (nat > nat > $o)).
% 0.18/0.27 thf(func_def_6, type, more: (nat > nat > $o)).
% 0.18/0.27 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.18/0.27 thf(f1,axiom,(
% 0.18/0.27 (((pl @ x @ z)) = ((pl @ y @ z)))),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',i)).
% 0.18/0.27 thf(f3,axiom,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~(more @ X0 @ X1)) => ~ ~(((more @ X0 @ X1) => ~(less @ X0 @ X1)) => ~((less @ X0 @ X1) => (X0 != X1))))),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10b)).
% 0.18/0.27 thf(f4,axiom,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((less @ X0 @ X1) => (less @ (pl @ X0 @ X2) @ (pl @ X1 @ X2)))),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19c)).
% 0.18/0.27 thf(f5,axiom,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10a)).
% 0.18/0.27 thf(f6,axiom,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((more @ X0 @ X1) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2)))),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a)).
% 0.18/0.27 thf(f7,conjecture,(
% 0.18/0.27 (x = y)),
% 0.18/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz20b)).
% 0.18/0.27 thf(f8,negated_conjecture,(
% 0.18/0.27 ~ (x = y)),
% 0.18/0.27 inference(negated_conjecture,[status(cth)],[f7])).
% 0.18/0.27 thf(f11,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~(more @ X0 @ X1)) => ~ ~(((more @ X0 @ X1) => ~(less @ X0 @ X1)) => ~((less @ X0 @ X1) => (X0 != X1))))),
% 0.18/0.27 inference(rectify,[],[f3])).
% 0.18/0.27 thf(f12,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~ (((more @ X0 @ X1)) = $true)) => ~ ~(((((more @ X0 @ X1)) = $true) => ~ (((less @ X0 @ X1)) = $true)) => ~((((less @ X0 @ X1)) = $true) => (X0 != X1))))),
% 0.18/0.27 inference(fool_elimination,[],[f11])).
% 0.18/0.27 thf(f13,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((less @ X0 @ X1) => (less @ (pl @ X0 @ X2) @ (pl @ X1 @ X2)))),
% 0.18/0.27 inference(rectify,[],[f4])).
% 0.18/0.27 thf(f14,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((((less @ X0 @ X1)) = $true) => (((less @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true))),
% 0.18/0.27 inference(fool_elimination,[],[f13])).
% 0.18/0.27 thf(f15,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.18/0.27 inference(rectify,[],[f5])).
% 0.18/0.27 thf(f16,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~ (((more @ X0 @ X1)) = $true) => (((less @ X0 @ X1)) = $true)))),
% 0.18/0.27 inference(fool_elimination,[],[f15])).
% 0.18/0.27 thf(f17,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((more @ X0 @ X1) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2)))),
% 0.18/0.27 inference(rectify,[],[f6])).
% 0.18/0.27 thf(f18,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((((more @ X0 @ X1)) = $true) => (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true))),
% 0.18/0.27 inference(fool_elimination,[],[f17])).
% 0.18/0.27 thf(f20,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => (((more @ X0 @ X1)) != $true)) => (((((more @ X0 @ X1)) = $true) => (((less @ X0 @ X1)) != $true)) => ~((((less @ X0 @ X1)) = $true) => (X0 != X1))))),
% 0.18/0.27 inference(flattening,[],[f12])).
% 0.18/0.27 thf(f21,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : ((X0 != X1) => ((((more @ X0 @ X1)) != $true) => (((less @ X0 @ X1)) = $true)))),
% 0.18/0.27 inference(flattening,[],[f16])).
% 0.18/0.27 thf(f22,plain,(
% 0.18/0.27 (x != y)),
% 0.18/0.27 inference(flattening,[],[f8])).
% 0.18/0.27 thf(f24,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : ((((X0 != X1) | (((less @ X0 @ X1)) != $true)) & ((((less @ X0 @ X1)) != $true) | (((more @ X0 @ X1)) != $true))) & ((((more @ X0 @ X1)) != $true) | (X0 != X1)))),
% 0.18/0.27 inference(ennf_transformation,[],[f20])).
% 0.18/0.27 thf(f25,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : (((X0 != X1) | (((less @ X0 @ X1)) != $true)) & ((((less @ X0 @ X1)) != $true) | (((more @ X0 @ X1)) != $true)) & ((((more @ X0 @ X1)) != $true) | (X0 != X1)))),
% 0.18/0.27 inference(flattening,[],[f24])).
% 0.18/0.27 thf(f26,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((((less @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (((less @ X0 @ X1)) != $true))),
% 0.18/0.27 inference(ennf_transformation,[],[f14])).
% 0.18/0.27 thf(f27,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : (((((less @ X0 @ X1)) = $true) | (((more @ X0 @ X1)) = $true)) | (X0 = X1))),
% 0.18/0.27 inference(ennf_transformation,[],[f21])).
% 0.18/0.27 thf(f28,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat] : ((((less @ X0 @ X1)) = $true) | (((more @ X0 @ X1)) = $true) | (X0 = X1))),
% 0.18/0.27 inference(flattening,[],[f27])).
% 0.18/0.27 thf(f29,plain,(
% 0.18/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (((more @ X0 @ X1)) != $true))),
% 0.18/0.27 inference(ennf_transformation,[],[f18])).
% 0.18/0.27 thf(f30,plain,(
% 0.18/0.27 (((pl @ x @ z)) = ((pl @ y @ z)))),
% 0.18/0.27 inference(cnf_transformation,[],[f1])).
% 0.18/0.27 thf(f32,plain,(
% 0.18/0.27 ( ! [X0 : nat,X1 : nat] : ((((more @ X0 @ X1)) != $true) | (X0 != X1)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f25])).
% 0.18/0.27 thf(f34,plain,(
% 0.18/0.27 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | (((less @ X0 @ X1)) != $true)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f25])).
% 0.18/0.27 thf(f35,plain,(
% 0.18/0.27 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((less @ X0 @ X1)) != $true) | (((less @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f26])).
% 0.18/0.27 thf(f36,plain,(
% 0.18/0.27 ( ! [X0 : nat,X1 : nat] : ((((more @ X0 @ X1)) = $true) | (((less @ X0 @ X1)) = $true) | (X0 = X1)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f28])).
% 0.18/0.27 thf(f37,plain,(
% 0.18/0.27 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((more @ X0 @ X1)) != $true) | (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f29])).
% 0.18/0.27 thf(f38,plain,(
% 0.18/0.27 (x != y)),
% 0.18/0.27 inference(cnf_transformation,[],[f22])).
% 0.18/0.27 thf(f40,definition,(
% 0.18/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.18/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.18/0.27 thf(f42,plain,(
% 0.18/0.27 ( ! [X1 : nat] : (($true != ((less @ X1 @ X1)))) )),
% 0.18/0.27 inference(equality_resolution,[],[f34])).
% 0.18/0.27 thf(f43,plain,(
% 0.18/0.27 ( ! [X1 : nat] : (($true != ((more @ X1 @ X1)))) )),
% 0.18/0.27 inference(equality_resolution,[],[f32])).
% 0.18/0.27 thf(f65,plain,(
% 0.18/0.27 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (((less @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (((less @ X0 @ X1)) = $false)) )),
% 0.18/0.27 inference(constrained_superposition,[],[f35,f40])).
% 0.18/0.27 thf(f67,plain,(
% 0.18/0.27 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((less @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (((less @ X0 @ X1)) = $false)) )),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f65])).
% 0.18/0.27 thf(f71,plain,(
% 0.18/0.27 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (((more @ X0 @ X1)) = $false)) )),
% 0.18/0.27 inference(constrained_superposition,[],[f37,f40])).
% 0.18/0.27 thf(f75,plain,(
% 0.18/0.27 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (((more @ X0 @ X1)) = $false)) )),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f71])).
% 0.18/0.27 thf(f85,plain,(
% 0.18/0.27 ( ! [X0 : nat] : (($true = ((less @ (pl @ X0 @ z) @ (pl @ x @ z)))) | ($false = ((less @ X0 @ y)))) )),
% 0.18/0.27 inference(constrained_superposition,[],[f67,f30])).
% 0.18/0.27 thf(f97,plain,(
% 0.18/0.27 ( ! [X0 : nat] : (($true = ((more @ (pl @ X0 @ z) @ (pl @ x @ z)))) | ($false = ((more @ X0 @ y)))) )),
% 0.18/0.27 inference(constrained_superposition,[],[f75,f30])).
% 0.18/0.27 thf(f126,plain,(
% 0.18/0.27 ($true != $true) | ($false = ((less @ x @ y)))),
% 0.18/0.27 inference(constrained_superposition,[],[f42,f85])).
% 0.18/0.27 thf(f131,plain,(
% 0.18/0.27 ($false = ((less @ x @ y)))),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f126])).
% 0.18/0.27 thf(f177,plain,(
% 0.18/0.27 ($true != $true) | ($false = ((more @ x @ y)))),
% 0.18/0.27 inference(constrained_superposition,[],[f43,f97])).
% 0.18/0.27 thf(f186,plain,(
% 0.18/0.27 ($false = ((more @ x @ y)))),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f177])).
% 0.18/0.27 thf(f224,plain,(
% 0.18/0.27 ($true = $false) | ($true = ((less @ x @ y))) | (x = y)),
% 0.18/0.27 inference(constrained_superposition,[],[f36,f186])).
% 0.18/0.27 thf(f226,plain,(
% 0.18/0.27 ($true = ((less @ x @ y))) | (x = y)),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f224])).
% 0.18/0.27 thf(f229,plain,(
% 0.18/0.27 ($true = ((less @ x @ y)))),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f226,f38])).
% 0.18/0.27 thf(f231,plain,(
% 0.18/0.27 ($true = $false)),
% 0.18/0.27 inference(forward_demodulation,[],[f229,f131])).
% 0.18/0.27 thf(f232,plain,(
% 0.18/0.27 $false),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f231])).
% 0.18/0.27 % SZS output end Proof for theBenchmark
% 0.18/0.27 % (2592631)------------------------------
% 0.18/0.27 % (2592631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (2592631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (2592631)CaDiCaL version: 2.1.3
% 0.18/0.27 % (2592631)Termination reason: Refutation
% 0.18/0.27 % (2592631)Time elapsed: 0.006 s
% 0.18/0.27 % (2592631)Peak memory usage: 12 MB
% 0.18/0.27 % (2592631)Instructions burned: 18 (million)
% 0.18/0.27 % (2592625)Success in time 0.04 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------