%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM700^1 : 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 : n010.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 08:19:21 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM700^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n010.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 12:41:48 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.22/0.29 % (2796966)Will run a generic schedule for satisfiability detection.
% 0.22/0.29 % (2796971)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2961851032_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.29 % Exception at run slice level
% 0.22/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.29 % (2796972)% WARNING: option uhcvi not known.
% 0.22/0.29 % (2796976)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=180811957:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.29 % (2796972)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3039557847:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.29 % (2796973)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=538185838:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.29 % (2796974)dis+10_1_sil=32000:sp=arity:random_seed=773578183:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.29 % (2796975)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2338489809:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.29 % (2796972)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.29 % (2796977)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4118629277:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.29 % (2796972)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.29 % (2796975)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.29 % (2796976) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2796966-2796976"...
% 0.22/0.29 % (2796974) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2796966-2796974"...
% 0.22/0.29 % (2796975) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2796966-2796975"...
% 0.22/0.29 % (2796972) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2796966-2796972"...
% 0.22/0.29 % (2796977) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2796966-2796977"...
% 0.22/0.29 % (2796979)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1990302928:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.29 % (2796976)...printing done.
% 0.22/0.29 % (2796975)...printing done.
% 0.22/0.29 % (2796974)...printing done.
% 0.22/0.29 % Exception at run slice level
% 0.22/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.29 % (2796972)...printing done.
% 0.22/0.29 % (2796977)...printing done.
% 0.22/0.29 % (2796976)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% 0.22/0.29 thf(type_def_5, type, nat: $tType).
% 0.22/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.29 thf(func_def_0, type, x: nat).
% 0.22/0.29 thf(func_def_1, type, y: nat).
% 0.22/0.29 thf(func_def_2, type, less: (nat > nat > $o)).
% 0.22/0.29 thf(func_def_3, type, pl: (nat > nat > nat)).
% 0.22/0.29 thf(func_def_4, type, n_1: nat).
% 0.22/0.29 thf(func_def_6, type, lessis: (nat > nat > $o)).
% 0.22/0.29 thf(func_def_7, type, more: (nat > nat > $o)).
% 0.22/0.29 thf(func_def_8, type, moreis: (nat > nat > $o)).
% 0.22/0.29 thf(f1,axiom,(
% 0.22/0.29 (less @ y @ (pl @ x @ n_1))),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',l)).
% 0.22/0.29 thf(f2,axiom,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : (~(more @ X0 @ X1) => (lessis @ X0 @ X1))),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10e)).
% 0.22/0.29 thf(f3,axiom,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : ((less @ X0 @ X1) => ~(moreis @ X0 @ X1))),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10h)).
% 0.22/0.29 thf(f4,axiom,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : ((more @ X1 @ X0) => (moreis @ X1 @ (pl @ X0 @ n_1)))),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz25)).
% 0.22/0.29 thf(f5,conjecture,(
% 0.22/0.29 (lessis @ y @ x)),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz26)).
% 0.22/0.29 thf(f6,negated_conjecture,(
% 0.22/0.29 ~(lessis @ y @ x)),
% 0.22/0.29 inference(negated_conjecture,[status(cth)],[f5])).
% 0.22/0.29 thf(f7,plain,(
% 0.22/0.29 (less @ y @ (pl @ x @ n_1))),
% 0.22/0.29 inference(rectify,[],[f1])).
% 0.22/0.29 thf(f8,plain,(
% 0.22/0.29 (((less @ y @ (pl @ x @ n_1))) = $true)),
% 0.22/0.29 inference(fool_elimination,[],[f7])).
% 0.22/0.29 thf(f9,plain,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : (~(more @ X0 @ X1) => (lessis @ X0 @ X1))),
% 0.22/0.29 inference(rectify,[],[f2])).
% 0.22/0.29 thf(f10,plain,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : (~ (((more @ X0 @ X1)) = $true) => (((lessis @ X0 @ X1)) = $true))),
% 0.22/0.29 inference(fool_elimination,[],[f9])).
% 0.22/0.29 thf(f11,plain,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : ((less @ X0 @ X1) => ~(moreis @ X0 @ X1))),
% 0.22/0.29 inference(rectify,[],[f3])).
% 0.22/0.29 thf(f12,plain,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : ((((less @ X0 @ X1)) = $true) => ~ (((moreis @ X0 @ X1)) = $true))),
% 0.22/0.29 inference(fool_elimination,[],[f11])).
% 0.22/0.29 thf(f13,plain,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : ((more @ X1 @ X0) => (moreis @ X1 @ (pl @ X0 @ n_1)))),
% 0.22/0.29 inference(rectify,[],[f4])).
% 0.22/0.29 thf(f14,plain,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : ((((more @ X1 @ X0)) = $true) => (((moreis @ X1 @ (pl @ X0 @ n_1))) = $true))),
% 0.22/0.29 inference(fool_elimination,[],[f13])).
% 0.22/0.29 thf(f15,plain,(
% 0.22/0.29 ~(lessis @ y @ x)),
% 0.22/0.29 inference(rectify,[],[f6])).
% 0.22/0.29 thf(f16,plain,(
% 0.22/0.29 ~ (((lessis @ y @ x)) = $true)),
% 0.22/0.29 inference(fool_elimination,[],[f15])).
% 0.22/0.29 thf(f17,plain,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : ((((more @ X0 @ X1)) != $true) => (((lessis @ X0 @ X1)) = $true))),
% 0.22/0.29 inference(flattening,[],[f10])).
% 0.22/0.29 thf(f18,plain,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : ((((less @ X0 @ X1)) = $true) => (((moreis @ X0 @ X1)) != $true))),
% 0.22/0.29 inference(flattening,[],[f12])).
% 0.22/0.29 thf(f19,plain,(
% 0.22/0.29 (((lessis @ y @ x)) != $true)),
% 0.22/0.29 inference(flattening,[],[f16])).
% 0.22/0.29 thf(f20,plain,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : ((((lessis @ X0 @ X1)) = $true) | (((more @ X0 @ X1)) = $true))),
% 0.22/0.29 inference(ennf_transformation,[],[f17])).
% 0.22/0.29 thf(f21,plain,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : ((((moreis @ X0 @ X1)) != $true) | (((less @ X0 @ X1)) != $true))),
% 0.22/0.29 inference(ennf_transformation,[],[f18])).
% 0.22/0.29 thf(f22,plain,(
% 0.22/0.29 ! [X0 : nat,X1 : nat] : ((((moreis @ X1 @ (pl @ X0 @ n_1))) = $true) | (((more @ X1 @ X0)) != $true))),
% 0.22/0.29 inference(ennf_transformation,[],[f14])).
% 0.22/0.29 thf(f23,plain,(
% 0.22/0.29 (((less @ y @ (pl @ x @ n_1))) = $true)),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 thf(f24,plain,(
% 0.22/0.29 ( ! [X0 : nat,X1 : nat] : ((((more @ X0 @ X1)) = $true) | (((lessis @ X0 @ X1)) = $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f20])).
% 0.22/0.29 thf(f25,plain,(
% 0.22/0.29 ( ! [X0 : nat,X1 : nat] : ((((moreis @ X0 @ X1)) != $true) | (((less @ X0 @ X1)) != $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f21])).
% 0.22/0.29 thf(f26,plain,(
% 0.22/0.29 ( ! [X0 : nat,X1 : nat] : ((((more @ X1 @ X0)) != $true) | (((moreis @ X1 @ (pl @ X0 @ n_1))) = $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f22])).
% 0.22/0.29 thf(f27,plain,(
% 0.22/0.29 (((lessis @ y @ x)) != $true)),
% 0.22/0.29 inference(cnf_transformation,[],[f19])).
% 0.22/0.29 thf(f29,definition,(
% 0.22/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.22/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.22/0.29 thf(f42,plain,(
% 0.22/0.29 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (((less @ X0 @ X1)) != $true) | (((moreis @ X0 @ X1)) = $false)) )),
% 0.22/0.29 inference(constrained_superposition,[],[f25,f29])).
% 0.22/0.29 thf(f43,plain,(
% 0.22/0.29 ( ! [X0 : nat,X1 : nat] : ((((less @ X0 @ X1)) != $true) | (((moreis @ X0 @ X1)) = $false)) )),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f42])).
% 0.22/0.29 thf(f45,plain,(
% 0.22/0.29 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = ((moreis @ X0 @ (pl @ X1 @ n_1)))) | (((lessis @ X0 @ X1)) = $true)) )),
% 0.22/0.29 inference(constrained_superposition,[],[f26,f24])).
% 0.22/0.29 thf(f46,plain,(
% 0.22/0.29 ( ! [X0 : nat,X1 : nat] : (($true = ((moreis @ X0 @ (pl @ X1 @ n_1)))) | (((lessis @ X0 @ X1)) = $true)) )),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f45])).
% 0.22/0.29 thf(f49,plain,(
% 0.22/0.29 ($true != $true) | ($false = ((moreis @ y @ (pl @ x @ n_1))))),
% 0.22/0.29 inference(constrained_superposition,[],[f43,f23])).
% 0.22/0.29 thf(f50,plain,(
% 0.22/0.29 ($false = ((moreis @ y @ (pl @ x @ n_1))))),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f49])).
% 0.22/0.29 thf(f57,plain,(
% 0.22/0.29 ($true = $false) | (((lessis @ y @ x)) = $true)),
% 0.22/0.29 inference(constrained_superposition,[],[f46,f50])).
% 0.22/0.29 thf(f58,plain,(
% 0.22/0.29 (((lessis @ y @ x)) = $true)),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f57])).
% 0.22/0.29 thf(f61,plain,(
% 0.22/0.29 $false),
% 0.22/0.29 inference(forward_subsumption_resolution,[],[f58,f27])).
% 0.22/0.29 % SZS output end Proof for theBenchmark
% 0.22/0.29 % (2796976)------------------------------
% 0.22/0.29 % (2796976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2796976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2796976)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2796976)Termination reason: Refutation
% 0.22/0.29 % (2796976)Time elapsed: 0.003 s
% 0.22/0.29 % (2796976)Peak memory usage: 12 MB
% 0.22/0.29 % (2796976)Instructions burned: 4 (million)
% 0.22/0.29 % (2796966)Success in time 0.049 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------