%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM667^1 : 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 : n026.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 08:18:28 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM667^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n026.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 12:36:12 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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
% 0.21/0.29 % (534441)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (534451)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=659646045:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (534451) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-534441-534451"...
% 0.21/0.29 % (534451)...printing done.
% 0.21/0.29 % (534451)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, nat: $tType).
% 0.21/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, x: nat).
% 0.21/0.29 thf(func_def_1, type, y: nat).
% 0.21/0.29 thf(func_def_2, type, z: nat).
% 0.21/0.29 thf(func_def_3, type, less: (nat > nat > $o)).
% 0.21/0.29 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 ~(less @ x @ y) => (x = y)),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l)).
% 0.21/0.29 thf(f2,axiom,(
% 0.21/0.29 ~(less @ y @ z) => (y = z)),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',k)).
% 0.21/0.29 thf(f4,axiom,(
% 0.21/0.29 ! [X2 : nat,X1 : nat,X0 : nat] : ((~(less @ X0 @ X1) => (X0 = X1)) => ((less @ X1 @ X2) => (less @ X0 @ X2)))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16a)).
% 0.21/0.29 thf(f6,conjecture,(
% 0.21/0.29 ~(less @ x @ z) => (x = z)),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz17)).
% 0.21/0.29 thf(f7,negated_conjecture,(
% 0.21/0.29 ~(~(less @ x @ z) => (x = z))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ~(less @ y @ z) => (y = z)),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ~ (((less @ y @ z)) = $true) => (y = z)),
% 0.21/0.29 inference(fool_elimination,[],[f8])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ~(less @ x @ y) => (x = y)),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ~ (((less @ x @ y)) = $true) => (x = y)),
% 0.21/0.29 inference(fool_elimination,[],[f10])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 ~(~(less @ x @ z) => (x = z))),
% 0.21/0.29 inference(rectify,[],[f7])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 ~(~ (((less @ x @ z)) = $true) => (x = z))),
% 0.21/0.29 inference(fool_elimination,[],[f12])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 ! [X0 : nat,X1 : nat,X2 : nat] : ((~(less @ X2 @ X1) => (X1 = X2)) => ((less @ X1 @ X0) => (less @ X2 @ X0)))),
% 0.21/0.29 inference(rectify,[],[f4])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 ! [X0 : nat,X1 : nat,X2 : nat] : ((~ (((less @ X2 @ X1)) = $true) => (X1 = X2)) => ((((less @ X1 @ X0)) = $true) => (((less @ X2 @ X0)) = $true)))),
% 0.21/0.29 inference(fool_elimination,[],[f16])).
% 0.21/0.29 thf(f20,plain,(
% 0.21/0.29 (((less @ y @ z)) != $true) => (y = z)),
% 0.21/0.29 inference(flattening,[],[f9])).
% 0.21/0.29 thf(f21,plain,(
% 0.21/0.29 (((less @ x @ y)) != $true) => (x = y)),
% 0.21/0.29 inference(flattening,[],[f11])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 ~((((less @ x @ z)) != $true) => (x = z))),
% 0.21/0.29 inference(flattening,[],[f13])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 ! [X2 : nat,X1 : nat,X0 : nat] : (((((less @ X2 @ X1)) != $true) => (X1 = X2)) => ((((less @ X1 @ X0)) = $true) => (((less @ X2 @ X0)) = $true)))),
% 0.21/0.29 inference(flattening,[],[f17])).
% 0.21/0.29 thf(f26,plain,(
% 0.21/0.29 (((less @ x @ z)) != $true) & (x != z)),
% 0.21/0.29 inference(ennf_transformation,[],[f22])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 (((less @ x @ y)) = $true) | (x = y)),
% 0.21/0.29 inference(ennf_transformation,[],[f21])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 ! [X2 : nat,X1 : nat,X0 : nat] : (((((less @ X2 @ X0)) = $true) | (((less @ X1 @ X0)) != $true)) | ((((less @ X2 @ X1)) != $true) & (X1 != X2)))),
% 0.21/0.29 inference(ennf_transformation,[],[f24])).
% 0.21/0.29 thf(f30,plain,(
% 0.21/0.29 ! [X2 : nat,X1 : nat,X0 : nat] : ((((less @ X2 @ X0)) = $true) | ((((less @ X2 @ X1)) != $true) & (X1 != X2)) | (((less @ X1 @ X0)) != $true))),
% 0.21/0.29 inference(flattening,[],[f29])).
% 0.21/0.29 thf(f31,plain,(
% 0.21/0.29 (((less @ y @ z)) = $true) | (y = z)),
% 0.21/0.29 inference(ennf_transformation,[],[f20])).
% 0.21/0.29 thf(f35,plain,(
% 0.21/0.29 ! [X0 : nat,X1 : nat,X2 : nat] : ((((less @ X0 @ X2)) = $true) | ((((less @ X0 @ X1)) != $true) & (X0 != X1)) | (((less @ X1 @ X2)) != $true))),
% 0.21/0.29 inference(rectify,[],[f30])).
% 0.21/0.29 thf(f38,plain,(
% 0.21/0.29 (x != z)),
% 0.21/0.29 inference(cnf_transformation,[],[f26])).
% 0.21/0.29 thf(f39,plain,(
% 0.21/0.29 (((less @ x @ z)) != $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f26])).
% 0.21/0.29 thf(f41,plain,(
% 0.21/0.29 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((less @ X1 @ X2)) != $true) | (((less @ X0 @ X2)) = $true) | (((less @ X0 @ X1)) != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f35])).
% 0.21/0.29 thf(f42,plain,(
% 0.21/0.29 (y = z) | (((less @ y @ z)) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f31])).
% 0.21/0.29 thf(f44,plain,(
% 0.21/0.29 (((less @ x @ y)) = $true) | (x = y)),
% 0.21/0.29 inference(cnf_transformation,[],[f27])).
% 0.21/0.29 thf(f46,definition,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.29 thf(f51,definition,(
% 0.21/0.29 spl0_1 <=> (((less @ x @ y)) = $true)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.21/0.29 thf(f52,plain,(
% 0.21/0.29 (((less @ x @ y)) = $true) | ~spl0_1),
% 0.21/0.29 inference(avatar_component_clause,[],[f51])).
% 0.21/0.29 thf(f54,definition,(
% 0.21/0.29 spl0_2 <=> (x = y)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.21/0.29 thf(f55,plain,(
% 0.21/0.29 (x = y) | ~spl0_2),
% 0.21/0.29 inference(avatar_component_clause,[],[f54])).
% 0.21/0.29 thf(f56,plain,(
% 0.21/0.29 spl0_1 | spl0_2),
% 0.21/0.29 inference(avatar_split_clause,[],[f44,f54,f51])).
% 0.21/0.29 thf(f58,definition,(
% 0.21/0.29 spl0_3 <=> (((less @ y @ z)) = $true)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.21/0.29 thf(f59,plain,(
% 0.21/0.29 (((less @ y @ z)) = $true) | ~spl0_3),
% 0.21/0.29 inference(avatar_component_clause,[],[f58])).
% 0.21/0.29 thf(f61,definition,(
% 0.21/0.29 spl0_4 <=> (y = z)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.21/0.29 thf(f62,plain,(
% 0.21/0.29 (y = z) | ~spl0_4),
% 0.21/0.29 inference(avatar_component_clause,[],[f61])).
% 0.21/0.29 thf(f63,plain,(
% 0.21/0.29 spl0_3 | spl0_4),
% 0.21/0.29 inference(avatar_split_clause,[],[f42,f61,f58])).
% 0.21/0.29 thf(f65,plain,(
% 0.21/0.29 (((less @ y @ z)) != $true) | ~spl0_2),
% 0.21/0.29 inference(backward_demodulation,[],[f39,f55])).
% 0.21/0.29 thf(f66,plain,(
% 0.21/0.29 $false | (~spl0_2 | ~spl0_3)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f65,f59])).
% 0.21/0.29 thf(f67,plain,(
% 0.21/0.29 ~spl0_2 | ~spl0_3),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f66])).
% 0.21/0.29 thf(f70,plain,(
% 0.21/0.29 ($true != $true) | (((less @ x @ z)) = $false)),
% 0.21/0.29 inference(constrained_superposition,[],[f39,f46])).
% 0.21/0.29 thf(f76,plain,(
% 0.21/0.29 (((less @ x @ z)) = $false)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f70])).
% 0.21/0.29 thf(f82,plain,(
% 0.21/0.29 ( ! [X0 : nat] : (($true != $true) | (((less @ X0 @ z)) = $true) | (((less @ X0 @ y)) != $true)) ) | ~spl0_3),
% 0.21/0.29 inference(constrained_superposition,[],[f41,f59])).
% 0.21/0.29 thf(f86,plain,(
% 0.21/0.29 ( ! [X0 : nat] : ((((less @ X0 @ y)) != $true) | (((less @ X0 @ z)) = $true)) ) | ~spl0_3),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f82])).
% 0.21/0.29 thf(f89,plain,(
% 0.21/0.29 ($true != $true) | (((less @ x @ z)) = $true) | (~spl0_1 | ~spl0_3)),
% 0.21/0.29 inference(constrained_superposition,[],[f86,f52])).
% 0.21/0.29 thf(f92,plain,(
% 0.21/0.29 (((less @ x @ z)) = $true) | (~spl0_1 | ~spl0_3)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f89])).
% 0.21/0.29 thf(f93,plain,(
% 0.21/0.29 ($false = $true) | (~spl0_1 | ~spl0_3)),
% 0.21/0.29 inference(forward_demodulation,[],[f92,f76])).
% 0.21/0.29 thf(f94,plain,(
% 0.21/0.29 $false | (~spl0_1 | ~spl0_3)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f93])).
% 0.21/0.29 thf(f95,plain,(
% 0.21/0.29 ~spl0_1 | ~spl0_3),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f94])).
% 0.21/0.29 thf(f96,plain,(
% 0.21/0.29 (((less @ x @ y)) = $false) | ~spl0_4),
% 0.21/0.29 inference(backward_demodulation,[],[f76,f62])).
% 0.21/0.29 thf(f97,plain,(
% 0.21/0.29 (x != y) | ~spl0_4),
% 0.21/0.29 inference(backward_demodulation,[],[f38,f62])).
% 0.21/0.29 thf(f101,plain,(
% 0.21/0.29 $false | (~spl0_2 | ~spl0_4)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f97,f55])).
% 0.21/0.29 thf(f102,plain,(
% 0.21/0.29 ~spl0_2 | ~spl0_4),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f101])).
% 0.21/0.29 thf(f103,plain,(
% 0.21/0.29 ($false = $true) | (~spl0_1 | ~spl0_4)),
% 0.21/0.29 inference(forward_demodulation,[],[f52,f96])).
% 0.21/0.29 thf(f104,plain,(
% 0.21/0.29 $false | (~spl0_1 | ~spl0_4)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f103])).
% 0.21/0.29 thf(f105,plain,(
% 0.21/0.29 ~spl0_1 | ~spl0_4),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f104])).
% 0.21/0.29 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f56])).
% 0.21/0.29 cnf(s2, plain, spl0_3 | spl0_4, inference(sat_conversion,[],[f63])).
% 0.21/0.29 cnf(s3, plain, ~spl0_2 | ~spl0_3, inference(sat_conversion,[],[f67])).
% 0.21/0.29 cnf(s4, plain, ~spl0_1 | ~spl0_3, inference(sat_conversion,[],[f95])).
% 0.21/0.29 cnf(s6, plain, ~spl0_2 | ~spl0_4, inference(sat_conversion,[],[f102])).
% 0.21/0.29 cnf(s7, plain, ~spl0_1 | ~spl0_4, inference(sat_conversion,[],[f105])).
% 0.21/0.29 cnf(s8, plain, ~spl0_2, inference(rat,[],[s2,s3,s6])).
% 0.21/0.29 cnf(s9, plain, spl0_1, inference(rat,[],[s1,s8])).
% 0.21/0.29 cnf(s10, plain, ~spl0_4, inference(rat,[],[s7,s9])).
% 0.21/0.29 cnf(s11, plain, ~spl0_3, inference(rat,[],[s4,s9])).
% 0.21/0.29 cnf(s12, plain, $false, inference(rat,[],[s2,s10,s11])).
% 0.21/0.29 thf(f106,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(avatar_sat_refutation,[],[s12])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (534451)------------------------------
% 0.21/0.29 % (534451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (534451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (534451)CaDiCaL version: 2.1.3
% 0.21/0.29 % (534451)Termination reason: Refutation
% 0.21/0.29 % (534451)Time elapsed: 0.002 s
% 0.21/0.29 % (534451)Peak memory usage: 13 MB
% 0.21/0.29 % (534451)Instructions burned: 5 (million)
% 0.21/0.29 % (534441)Success in time 0.041 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------