%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM682^1 : 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 : n013.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 08:18:31 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% 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.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n013.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
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 12:37:06 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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
% 0.21/0.30 % (2041219)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (2041229)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1741198799:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (2041229) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2041219-2041229"...
% 0.21/0.30 % (2041229)...printing done.
% 0.21/0.30 % (2041230)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (2041230)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.30 % (2041229)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% 0.21/0.30 thf(type_def_5, type, nat: $tType).
% 0.21/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.30 thf(func_def_0, type, x: nat).
% 0.21/0.30 thf(func_def_1, type, y: nat).
% 0.21/0.30 thf(func_def_2, type, z: nat).
% 0.21/0.30 thf(func_def_3, type, less: (nat > nat > $o)).
% 0.21/0.30 thf(func_def_4, type, pl: (nat > nat > nat)).
% 0.21/0.30 thf(func_def_6, type, more: (nat > nat > $o)).
% 0.21/0.30 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.21/0.30 thf(f1,axiom,(
% 0.21/0.30 (less @ (pl @ x @ z) @ (pl @ y @ z))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l)).
% 0.21/0.30 thf(f3,axiom,(
% 0.21/0.30 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~(more @ X0 @ X1)) => ~ ~(((more @ X0 @ X1) => ~(less @ X0 @ X1)) => ~((less @ X0 @ X1) => (X0 != X1))))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10b)).
% 0.21/0.30 thf(f4,axiom,(
% 0.21/0.30 ! [X0 : nat,X1 : nat,X2 : nat] : ((more @ X0 @ X1) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2)))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a)).
% 0.21/0.30 thf(f6,axiom,(
% 0.21/0.30 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10a)).
% 0.21/0.30 thf(f7,conjecture,(
% 0.21/0.30 (less @ x @ y)),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz20c)).
% 0.21/0.30 thf(f8,negated_conjecture,(
% 0.21/0.30 ~(less @ x @ y)),
% 0.21/0.30 inference(negated_conjecture,[status(cth)],[f7])).
% 0.21/0.30 thf(f9,plain,(
% 0.21/0.30 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(more @ X0 @ X1) => (less @ X0 @ X1)))),
% 0.21/0.30 inference(rectify,[],[f6])).
% 0.21/0.30 thf(f10,plain,(
% 0.21/0.30 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~ (((more @ X0 @ X1)) = $true) => (((less @ X0 @ X1)) = $true)))),
% 0.21/0.30 inference(fool_elimination,[],[f9])).
% 0.21/0.30 thf(f11,plain,(
% 0.21/0.30 ~(less @ x @ y)),
% 0.21/0.30 inference(rectify,[],[f8])).
% 0.21/0.30 thf(f12,plain,(
% 0.21/0.30 ~ (((less @ x @ y)) = $true)),
% 0.21/0.30 inference(fool_elimination,[],[f11])).
% 0.21/0.30 thf(f15,plain,(
% 0.21/0.30 (less @ (pl @ x @ z) @ (pl @ y @ z))),
% 0.21/0.30 inference(rectify,[],[f1])).
% 0.21/0.30 thf(f16,plain,(
% 0.21/0.30 (((less @ (pl @ x @ z) @ (pl @ y @ z))) = $true)),
% 0.21/0.30 inference(fool_elimination,[],[f15])).
% 0.21/0.30 thf(f17,plain,(
% 0.21/0.30 ! [X0 : nat,X1 : nat,X2 : nat] : ((more @ X0 @ X1) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2)))),
% 0.21/0.30 inference(rectify,[],[f4])).
% 0.21/0.30 thf(f18,plain,(
% 0.21/0.30 ! [X1 : nat,X2 : nat,X0 : nat] : ((((more @ X0 @ X1)) = $true) => (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true))),
% 0.21/0.30 inference(fool_elimination,[],[f17])).
% 0.21/0.30 thf(f19,plain,(
% 0.21/0.30 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~(more @ X0 @ X1)) => ~ ~(((more @ X0 @ X1) => ~(less @ X0 @ X1)) => ~((less @ X0 @ X1) => (X0 != X1))))),
% 0.21/0.30 inference(rectify,[],[f3])).
% 0.21/0.30 thf(f20,plain,(
% 0.21/0.30 ! [X0 : nat,X1 : nat] : ~(((X0 = X1) => ~ (((more @ X0 @ X1)) = $true)) => ~ ~(((((more @ X0 @ X1)) = $true) => ~ (((less @ X0 @ X1)) = $true)) => ~((((less @ X0 @ X1)) = $true) => (X0 != X1))))),
% 0.21/0.30 inference(fool_elimination,[],[f19])).
% 0.21/0.30 thf(f21,plain,(
% 0.21/0.30 ! [X1 : nat,X0 : nat] : ((X0 != X1) => ((((more @ X0 @ X1)) != $true) => (((less @ X0 @ X1)) = $true)))),
% 0.21/0.30 inference(flattening,[],[f10])).
% 0.21/0.30 thf(f22,plain,(
% 0.21/0.30 (((less @ x @ y)) != $true)),
% 0.21/0.30 inference(flattening,[],[f12])).
% 0.21/0.30 thf(f24,plain,(
% 0.21/0.30 ! [X1 : nat,X0 : nat] : ~(((X0 = X1) => (((more @ X0 @ X1)) != $true)) => (((((more @ X0 @ X1)) = $true) => (((less @ X0 @ X1)) != $true)) => ~((((less @ X0 @ X1)) = $true) => (X0 != X1))))),
% 0.21/0.30 inference(flattening,[],[f20])).
% 0.21/0.30 thf(f27,plain,(
% 0.21/0.30 ! [X1 : nat,X0 : nat,X2 : nat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (((more @ X0 @ X1)) != $true))),
% 0.21/0.30 inference(ennf_transformation,[],[f18])).
% 0.21/0.30 thf(f28,plain,(
% 0.21/0.30 ! [X1 : nat,X0 : nat] : (((((less @ X0 @ X1)) = $true) | (((more @ X0 @ X1)) = $true)) | (X0 = X1))),
% 0.21/0.30 inference(ennf_transformation,[],[f21])).
% 0.21/0.30 thf(f29,plain,(
% 0.21/0.30 ! [X1 : nat,X0 : nat] : ((((more @ X0 @ X1)) = $true) | (((less @ X0 @ X1)) = $true) | (X0 = X1))),
% 0.21/0.30 inference(flattening,[],[f28])).
% 0.21/0.30 thf(f30,plain,(
% 0.21/0.30 ! [X1 : nat,X0 : nat] : ((((X0 != X1) | (((less @ X0 @ X1)) != $true)) & ((((less @ X0 @ X1)) != $true) | (((more @ X0 @ X1)) != $true))) & ((((more @ X0 @ X1)) != $true) | (X0 != X1)))),
% 0.21/0.30 inference(ennf_transformation,[],[f24])).
% 0.21/0.30 thf(f31,plain,(
% 0.21/0.30 ! [X1 : nat,X0 : nat] : (((((more @ X0 @ X1)) != $true) | (X0 != X1)) & ((((less @ X0 @ X1)) != $true) | (((more @ X0 @ X1)) != $true)) & ((X0 != X1) | (((less @ X0 @ X1)) != $true)))),
% 0.21/0.30 inference(flattening,[],[f30])).
% 0.21/0.30 thf(f33,plain,(
% 0.21/0.30 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = ((more @ (pl @ X1 @ X2) @ (pl @ X0 @ X2)))) | ($true != ((more @ X1 @ X0))))),
% 0.21/0.30 inference(rectify,[],[f27])).
% 0.21/0.30 thf(f35,plain,(
% 0.21/0.30 ! [X0 : nat,X1 : nat] : (($true = ((more @ X1 @ X0))) | ($true = ((less @ X1 @ X0))) | (X0 = X1))),
% 0.21/0.30 inference(rectify,[],[f29])).
% 0.21/0.30 thf(f36,plain,(
% 0.21/0.30 ! [X0 : nat,X1 : nat] : ((($true != ((more @ X1 @ X0))) | (X0 != X1)) & (($true != ((less @ X1 @ X0))) | ($true != ((more @ X1 @ X0)))) & ((X0 != X1) | ($true != ((less @ X1 @ X0)))))),
% 0.21/0.30 inference(rectify,[],[f31])).
% 0.21/0.30 thf(f37,plain,(
% 0.21/0.30 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != ((more @ X1 @ X0))) | ($true = ((more @ (pl @ X1 @ X2) @ (pl @ X0 @ X2))))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f33])).
% 0.21/0.30 thf(f39,plain,(
% 0.21/0.30 ( ! [X0 : nat,X1 : nat] : (($true = ((more @ X1 @ X0))) | (X0 = X1) | ($true = ((less @ X1 @ X0)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f35])).
% 0.21/0.30 thf(f40,plain,(
% 0.21/0.30 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | ($true != ((less @ X1 @ X0)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f36])).
% 0.21/0.30 thf(f41,plain,(
% 0.21/0.30 ( ! [X0 : nat,X1 : nat] : (($true != ((more @ X1 @ X0))) | ($true != ((less @ X1 @ X0)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f36])).
% 0.21/0.30 thf(f43,plain,(
% 0.21/0.30 (((less @ (pl @ x @ z) @ (pl @ y @ z))) = $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f16])).
% 0.21/0.30 thf(f45,plain,(
% 0.21/0.30 (((less @ x @ y)) != $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f22])).
% 0.21/0.30 thf(f47,definition,(
% 0.21/0.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.30 thf(f50,plain,(
% 0.21/0.30 ( ! [X1 : nat] : (($true != ((less @ X1 @ X1)))) )),
% 0.21/0.30 inference(equality_resolution,[],[f40])).
% 0.21/0.30 thf(f54,plain,(
% 0.21/0.30 ($true != $true) | (((less @ x @ y)) = $false)),
% 0.21/0.30 inference(constrained_superposition,[],[f45,f47])).
% 0.21/0.30 thf(f55,plain,(
% 0.21/0.30 ( ! [X0 : nat] : ((((less @ X0 @ X0)) = $false) | ($true != $true)) )),
% 0.21/0.30 inference(constrained_superposition,[],[f50,f47])).
% 0.21/0.30 thf(f58,plain,(
% 0.21/0.30 ( ! [X0 : nat] : ((((less @ X0 @ X0)) = $false)) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f55])).
% 0.21/0.30 thf(f64,plain,(
% 0.21/0.30 (((less @ x @ y)) = $false)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f54])).
% 0.21/0.30 thf(f79,plain,(
% 0.21/0.30 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((less @ X0 @ X1)) = $true) | (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (X0 = X1) | ($true != $true)) )),
% 0.21/0.30 inference(constrained_superposition,[],[f37,f39])).
% 0.21/0.30 thf(f81,plain,(
% 0.21/0.30 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X2))) = $true) | (((less @ X0 @ X1)) = $true) | (X0 = X1)) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f79])).
% 0.21/0.30 thf(f90,plain,(
% 0.21/0.30 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (X0 = X2) | ($true = ((less @ X0 @ X2))) | ($true != ((less @ (pl @ X0 @ X1) @ (pl @ X2 @ X1))))) )),
% 0.21/0.30 inference(constrained_superposition,[],[f41,f81])).
% 0.21/0.30 thf(f92,plain,(
% 0.21/0.30 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != ((less @ (pl @ X0 @ X1) @ (pl @ X2 @ X1)))) | (X0 = X2) | ($true = ((less @ X0 @ X2)))) )),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f90])).
% 0.21/0.30 thf(f106,plain,(
% 0.21/0.30 (((less @ x @ y)) = $true) | (x = y) | ($true != $true)),
% 0.21/0.30 inference(constrained_superposition,[],[f92,f43])).
% 0.21/0.30 thf(f108,plain,(
% 0.21/0.30 (x = y) | (((less @ x @ y)) = $true)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f106])).
% 0.21/0.30 thf(f109,plain,(
% 0.21/0.30 ($true = $false) | (x = y)),
% 0.21/0.30 inference(forward_demodulation,[],[f108,f64])).
% 0.21/0.30 thf(f110,plain,(
% 0.21/0.30 (x = y)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f109])).
% 0.21/0.30 thf(f113,plain,(
% 0.21/0.30 ($true = ((less @ (pl @ y @ z) @ (pl @ y @ z))))),
% 0.21/0.30 inference(backward_demodulation,[],[f43,f110])).
% 0.21/0.30 thf(f114,plain,(
% 0.21/0.30 ($true = $false)),
% 0.21/0.30 inference(forward_demodulation,[],[f113,f58])).
% 0.21/0.30 thf(f115,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f114])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (2041229)------------------------------
% 0.21/0.30 % (2041229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2041229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2041229)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2041229)Termination reason: Refutation
% 0.21/0.30 % (2041229)Time elapsed: 0.003 s
% 0.21/0.30 % (2041229)Peak memory usage: 12 MB
% 0.21/0.30 % (2041229)Instructions burned: 8 (million)
% 0.21/0.30 % (2041219)Success in time 0.038 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------