%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM682^1 : 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 : n007.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 08:19:18 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM682^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n007.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 12:34:11 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.19/0.27 % (3295781)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (3295796)% WARNING: option uhcvi not known.
% 0.19/0.27 % (3295796)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3913647419:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (3295796)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (3295796)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.27 % (3295796) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3295781-3295796"...
% 0.19/0.27 % (3295796)...printing done.
% 0.19/0.27 % (3295796)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, nat: $tType).
% 0.19/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, x: nat).
% 0.19/0.27 thf(func_def_1, type, y: nat).
% 0.19/0.27 thf(func_def_2, type, z: nat).
% 0.19/0.27 thf(func_def_3, type, less: (nat > nat > $o)).
% 0.19/0.27 thf(func_def_4, type, pl: (nat > nat > nat)).
% 0.19/0.27 thf(func_def_6, type, more: (nat > nat > $o)).
% 0.19/0.27 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.19/0.27 thf(f1,axiom,(
% 0.19/0.27 (less @ (pl @ x @ z) @ (pl @ y @ z))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l)).
% 0.19/0.27 thf(f3,axiom,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~(more @ X0 @ X1)) => ~ ~(((more @ X0 @ X1) => ~(less @ X0 @ X1)) => ~((less @ X0 @ X1) => (X0 != X1))))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10b)).
% 0.19/0.27 thf(f4,axiom,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((more @ X0 @ X1) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2)))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a)).
% 0.19/0.27 thf(f6,axiom,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10a)).
% 0.19/0.27 thf(f7,conjecture,(
% 0.19/0.27 (less @ x @ y)),
% 0.19/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz20c)).
% 0.19/0.27 thf(f8,negated_conjecture,(
% 0.19/0.27 ~(less @ x @ y)),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f7])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 (less @ (pl @ x @ z) @ (pl @ y @ z))),
% 0.19/0.27 inference(rectify,[],[f1])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 (((less @ (pl @ x @ z) @ (pl @ y @ z))) = $true)),
% 0.19/0.27 inference(fool_elimination,[],[f9])).
% 0.19/0.27 thf(f13,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~(more @ X0 @ X1)) => ~ ~(((more @ X0 @ X1) => ~(less @ X0 @ X1)) => ~((less @ X0 @ X1) => (X0 != X1))))),
% 0.19/0.27 inference(rectify,[],[f3])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~ (((more @ X0 @ X1)) = $true)) => ~ ~(((((more @ X0 @ X1)) = $true) => ~ (((less @ X0 @ X1)) = $true)) => ~((((less @ X0 @ X1)) = $true) => (X0 != X1))))),
% 0.19/0.27 inference(fool_elimination,[],[f13])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((more @ X0 @ X1) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2)))),
% 0.19/0.27 inference(rectify,[],[f4])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((((more @ X0 @ X1)) = $true) => (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true))),
% 0.19/0.27 inference(fool_elimination,[],[f15])).
% 0.19/0.27 thf(f17,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.19/0.27 inference(rectify,[],[f6])).
% 0.19/0.27 thf(f18,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~ (((more @ X0 @ X1)) = $true) => (((less @ X0 @ X1)) = $true)))),
% 0.19/0.27 inference(fool_elimination,[],[f17])).
% 0.19/0.27 thf(f19,plain,(
% 0.19/0.27 ~(less @ x @ y)),
% 0.19/0.27 inference(rectify,[],[f8])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 ~ (((less @ x @ y)) = $true)),
% 0.19/0.27 inference(fool_elimination,[],[f19])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => (((more @ X0 @ X1)) != $true)) => (((((more @ X0 @ X1)) = $true) => (((less @ X0 @ X1)) != $true)) => ~((((less @ X0 @ X1)) = $true) => (X0 != X1))))),
% 0.19/0.27 inference(flattening,[],[f14])).
% 0.19/0.27 thf(f23,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : ((X0 != X1) => ((((more @ X0 @ X1)) != $true) => (((less @ X0 @ X1)) = $true)))),
% 0.19/0.27 inference(flattening,[],[f18])).
% 0.19/0.27 thf(f24,plain,(
% 0.19/0.27 (((less @ x @ y)) != $true)),
% 0.19/0.27 inference(flattening,[],[f20])).
% 0.19/0.27 thf(f26,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : ((((X0 != X1) | (((less @ X0 @ X1)) != $true)) & ((((less @ X0 @ X1)) != $true) | (((more @ X0 @ X1)) != $true))) & ((((more @ X0 @ X1)) != $true) | (X0 != X1)))),
% 0.19/0.27 inference(ennf_transformation,[],[f22])).
% 0.19/0.27 thf(f27,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : (((X0 != X1) | (((less @ X0 @ X1)) != $true)) & ((((less @ X0 @ X1)) != $true) | (((more @ X0 @ X1)) != $true)) & ((((more @ X0 @ X1)) != $true) | (X0 != X1)))),
% 0.19/0.27 inference(flattening,[],[f26])).
% 0.19/0.27 thf(f28,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (((more @ X0 @ X1)) != $true))),
% 0.19/0.27 inference(ennf_transformation,[],[f16])).
% 0.19/0.27 thf(f30,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : (((((less @ X0 @ X1)) = $true) | (((more @ X0 @ X1)) = $true)) | (X0 = X1))),
% 0.19/0.27 inference(ennf_transformation,[],[f23])).
% 0.19/0.27 thf(f31,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat] : ((((less @ X0 @ X1)) = $true) | (((more @ X0 @ X1)) = $true) | (X0 = X1))),
% 0.19/0.27 inference(flattening,[],[f30])).
% 0.19/0.27 thf(f32,plain,(
% 0.19/0.27 (((less @ (pl @ x @ z) @ (pl @ y @ z))) = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f10])).
% 0.19/0.27 thf(f35,plain,(
% 0.19/0.27 ( ! [X0 : nat,X1 : nat] : ((((more @ X0 @ X1)) != $true) | (((less @ X0 @ X1)) != $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f27])).
% 0.19/0.27 thf(f36,plain,(
% 0.19/0.27 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | (((less @ X0 @ X1)) != $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f27])).
% 0.19/0.27 thf(f37,plain,(
% 0.19/0.27 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((more @ X0 @ X1)) != $true) | (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f28])).
% 0.19/0.27 thf(f39,plain,(
% 0.19/0.27 ( ! [X0 : nat,X1 : nat] : ((((more @ X0 @ X1)) = $true) | (((less @ X0 @ X1)) = $true) | (X0 = X1)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f31])).
% 0.19/0.27 thf(f40,plain,(
% 0.19/0.27 (((less @ x @ y)) != $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f24])).
% 0.19/0.27 thf(f42,definition,(
% 0.19/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.27 thf(f44,plain,(
% 0.19/0.27 ( ! [X1 : nat] : (($true != ((less @ X1 @ X1)))) )),
% 0.19/0.27 inference(equality_resolution,[],[f36])).
% 0.19/0.27 thf(f63,plain,(
% 0.19/0.27 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (((less @ X0 @ X1)) != $true) | (((more @ X0 @ X1)) = $false)) )),
% 0.19/0.27 inference(constrained_superposition,[],[f35,f42])).
% 0.19/0.27 thf(f64,plain,(
% 0.19/0.27 ( ! [X0 : nat,X1 : nat] : ((((less @ X0 @ X1)) != $true) | (((more @ X0 @ X1)) = $false)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f63])).
% 0.19/0.27 thf(f67,plain,(
% 0.19/0.27 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (((less @ X0 @ X1)) = $true) | (X0 = X1)) )),
% 0.19/0.27 inference(constrained_superposition,[],[f37,f39])).
% 0.19/0.27 thf(f68,plain,(
% 0.19/0.27 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (((less @ X0 @ X1)) = $true) | (X0 = X1)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f67])).
% 0.19/0.27 thf(f80,plain,(
% 0.19/0.27 ($true != $true) | ($false = ((more @ (pl @ x @ z) @ (pl @ y @ z))))),
% 0.19/0.27 inference(constrained_superposition,[],[f64,f32])).
% 0.19/0.27 thf(f82,plain,(
% 0.19/0.27 ($false = ((more @ (pl @ x @ z) @ (pl @ y @ z))))),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f80])).
% 0.19/0.27 thf(f122,plain,(
% 0.19/0.27 ($true = $false) | (((less @ x @ y)) = $true) | (x = y)),
% 0.19/0.27 inference(constrained_superposition,[],[f68,f82])).
% 0.19/0.27 thf(f125,plain,(
% 0.19/0.27 (((less @ x @ y)) = $true) | (x = y)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f122])).
% 0.19/0.27 thf(f131,plain,(
% 0.19/0.27 (x = y)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f125,f40])).
% 0.19/0.27 thf(f134,plain,(
% 0.19/0.27 ($true = ((less @ (pl @ x @ z) @ (pl @ x @ z))))),
% 0.19/0.27 inference(constrained_superposition,[],[f32,f131])).
% 0.19/0.27 thf(f137,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f134,f44])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (3295796)------------------------------
% 0.19/0.27 % (3295796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3295796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3295796)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3295796)Termination reason: Refutation
% 0.19/0.27 % (3295796)Time elapsed: 0.003 s
% 0.19/0.27 % (3295796)Peak memory usage: 12 MB
% 0.19/0.27 % (3295796)Instructions burned: 9 (million)
% 0.19/0.27 % (3295781)Success in time 0.04 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------