%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM692^1 : 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 : n016.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 08:19:19 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM692^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:44:34 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.29 % (289229)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (289235)% WARNING: option uhcvi not known.
% 0.20/0.29 % (289235)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1135089258:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (289234)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3210594035_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (289236)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1156468293:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (289237)dis+10_1_sil=32000:sp=arity:random_seed=2615297300:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (289238)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3435050205:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (289235)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (289235)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (289238)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (289237) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-289229-289237"...
% 0.20/0.29 % (289235) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-289229-289235"...
% 0.20/0.29 % (289238) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-289229-289238"...
% 0.20/0.29 % (289235)...printing done.
% 0.20/0.29 % (289237)...printing done.
% 0.20/0.29 % (289238)...printing done.
% 0.20/0.29 % (289237)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, nat: $tType).
% 0.20/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_0, type, x: nat).
% 0.20/0.29 thf(func_def_1, type, y: nat).
% 0.20/0.29 thf(func_def_2, type, z: nat).
% 0.20/0.29 thf(func_def_3, type, u: nat).
% 0.20/0.29 thf(func_def_4, type, lessis: (nat > nat > $o)).
% 0.20/0.29 thf(func_def_6, type, ts: (nat > nat > nat)).
% 0.20/0.29 thf(func_def_7, type, moreis: (nat > nat > $o)).
% 0.20/0.29 thf(f1,axiom,(
% 0.20/0.29 (lessis @ x @ y)),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l)).
% 0.20/0.29 thf(f2,axiom,(
% 0.20/0.29 (lessis @ z @ u)),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k)).
% 0.20/0.29 thf(f3,axiom,(
% 0.20/0.29 ! [X0 : nat,X1 : nat] : ((moreis @ X0 @ X1) => (lessis @ X1 @ X0))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13)).
% 0.20/0.29 thf(f4,axiom,(
% 0.20/0.29 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((moreis @ X0 @ X1) => ((moreis @ X2 @ X3) => (moreis @ (ts @ X0 @ X2) @ (ts @ X1 @ X3))))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz23)).
% 0.20/0.29 thf(f5,axiom,(
% 0.20/0.29 ! [X0 : nat,X1 : nat] : ((lessis @ X0 @ X1) => (moreis @ X1 @ X0))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz14)).
% 0.20/0.29 thf(f6,conjecture,(
% 0.20/0.29 (lessis @ (ts @ x @ z) @ (ts @ y @ u))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz23a)).
% 0.20/0.29 thf(f7,negated_conjecture,(
% 0.20/0.29 ~(lessis @ (ts @ x @ z) @ (ts @ y @ u))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 (lessis @ x @ y)),
% 0.20/0.29 inference(rectify,[],[f1])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 (((lessis @ x @ y)) = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f8])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 (lessis @ z @ u)),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 (((lessis @ z @ u)) = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f10])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ! [X0 : nat,X1 : nat] : ((moreis @ X0 @ X1) => (lessis @ X1 @ X0))),
% 0.20/0.29 inference(rectify,[],[f3])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ! [X0 : nat,X1 : nat] : ((((moreis @ X0 @ X1)) = $true) => (((lessis @ X1 @ X0)) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f12])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((moreis @ X0 @ X1) => ((moreis @ X2 @ X3) => (moreis @ (ts @ X0 @ X2) @ (ts @ X1 @ X3))))),
% 0.20/0.29 inference(rectify,[],[f4])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((((moreis @ X0 @ X1)) = $true) => ((((moreis @ X2 @ X3)) = $true) => (((moreis @ (ts @ X0 @ X2) @ (ts @ X1 @ X3))) = $true)))),
% 0.20/0.29 inference(fool_elimination,[],[f14])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ! [X0 : nat,X1 : nat] : ((lessis @ X0 @ X1) => (moreis @ X1 @ X0))),
% 0.20/0.29 inference(rectify,[],[f5])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ! [X0 : nat,X1 : nat] : ((((lessis @ X0 @ X1)) = $true) => (((moreis @ X1 @ X0)) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f16])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 ~(lessis @ (ts @ x @ z) @ (ts @ y @ u))),
% 0.20/0.29 inference(rectify,[],[f7])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ~ (((lessis @ (ts @ x @ z) @ (ts @ y @ u))) = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f18])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 (((lessis @ (ts @ x @ z) @ (ts @ y @ u))) != $true)),
% 0.20/0.29 inference(flattening,[],[f19])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ! [X0 : nat,X1 : nat] : ((((lessis @ X1 @ X0)) = $true) | (((moreis @ X0 @ X1)) != $true))),
% 0.20/0.29 inference(ennf_transformation,[],[f13])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (((((moreis @ (ts @ X0 @ X2) @ (ts @ X1 @ X3))) = $true) | (((moreis @ X2 @ X3)) != $true)) | (((moreis @ X0 @ X1)) != $true))),
% 0.20/0.29 inference(ennf_transformation,[],[f15])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((((moreis @ (ts @ X0 @ X2) @ (ts @ X1 @ X3))) = $true) | (((moreis @ X2 @ X3)) != $true) | (((moreis @ X0 @ X1)) != $true))),
% 0.20/0.29 inference(flattening,[],[f22])).
% 0.20/0.29 thf(f24,plain,(
% 0.20/0.29 ! [X0 : nat,X1 : nat] : ((((moreis @ X1 @ X0)) = $true) | (((lessis @ X0 @ X1)) != $true))),
% 0.20/0.29 inference(ennf_transformation,[],[f17])).
% 0.20/0.29 thf(f25,plain,(
% 0.20/0.29 (((lessis @ x @ y)) = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f9])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 (((lessis @ z @ u)) = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f11])).
% 0.20/0.29 thf(f27,plain,(
% 0.20/0.29 ( ! [X0 : nat,X1 : nat] : ((((moreis @ X0 @ X1)) != $true) | (((lessis @ X1 @ X0)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f21])).
% 0.20/0.29 thf(f28,plain,(
% 0.20/0.29 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((((moreis @ X2 @ X3)) != $true) | (((moreis @ (ts @ X0 @ X2) @ (ts @ X1 @ X3))) = $true) | (((moreis @ X0 @ X1)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f23])).
% 0.20/0.29 thf(f29,plain,(
% 0.20/0.29 ( ! [X0 : nat,X1 : nat] : ((((lessis @ X0 @ X1)) != $true) | (((moreis @ X1 @ X0)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f24])).
% 0.20/0.29 thf(f30,plain,(
% 0.20/0.29 (((lessis @ (ts @ x @ z) @ (ts @ y @ u))) != $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f20])).
% 0.20/0.29 thf(f32,definition,(
% 0.20/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.29 thf(f45,plain,(
% 0.20/0.29 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (((lessis @ X1 @ X0)) = $true) | (((moreis @ X0 @ X1)) = $false)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f27,f32])).
% 0.20/0.29 thf(f46,plain,(
% 0.20/0.29 ( ! [X0 : nat,X1 : nat] : ((((lessis @ X1 @ X0)) = $true) | (((moreis @ X0 @ X1)) = $false)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f45])).
% 0.20/0.29 thf(f48,plain,(
% 0.20/0.29 ($true != $true) | ($true = ((moreis @ y @ x)))),
% 0.20/0.29 inference(constrained_superposition,[],[f29,f25])).
% 0.20/0.29 thf(f50,plain,(
% 0.20/0.29 ($true != $true) | ($true = ((moreis @ u @ z)))),
% 0.20/0.29 inference(constrained_superposition,[],[f29,f26])).
% 0.20/0.29 thf(f51,plain,(
% 0.20/0.29 ($true = ((moreis @ u @ z)))),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f50])).
% 0.20/0.29 thf(f52,plain,(
% 0.20/0.29 ($true = ((moreis @ y @ x)))),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f48])).
% 0.20/0.29 thf(f57,plain,(
% 0.20/0.29 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = ((moreis @ (ts @ X0 @ u) @ (ts @ X1 @ z)))) | (((moreis @ X0 @ X1)) != $true)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f28,f51])).
% 0.20/0.29 thf(f58,plain,(
% 0.20/0.29 ( ! [X0 : nat,X1 : nat] : ((((moreis @ X0 @ X1)) != $true) | ($true = ((moreis @ (ts @ X0 @ u) @ (ts @ X1 @ z))))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f57])).
% 0.20/0.29 thf(f106,plain,(
% 0.20/0.29 ($true != $true) | ($true = ((moreis @ (ts @ y @ u) @ (ts @ x @ z))))),
% 0.20/0.29 inference(constrained_superposition,[],[f58,f52])).
% 0.20/0.29 thf(f110,plain,(
% 0.20/0.29 ($true = ((moreis @ (ts @ y @ u) @ (ts @ x @ z))))),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f106])).
% 0.20/0.29 thf(f125,plain,(
% 0.20/0.29 ($true = $false) | (((lessis @ (ts @ x @ z) @ (ts @ y @ u))) = $true)),
% 0.20/0.29 inference(constrained_superposition,[],[f46,f110])).
% 0.20/0.29 thf(f132,plain,(
% 0.20/0.29 (((lessis @ (ts @ x @ z) @ (ts @ y @ u))) = $true)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f125])).
% 0.20/0.29 thf(f136,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f132,f30])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (289237)------------------------------
% 0.20/0.29 % (289237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (289237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (289237)CaDiCaL version: 2.1.3
% 0.20/0.29 % (289237)Termination reason: Refutation
% 0.20/0.29 % (289237)Time elapsed: 0.006 s
% 0.20/0.29 % (289237)Peak memory usage: 12 MB
% 0.20/0.29 % (289237)Instructions burned: 9 (million)
% 0.20/0.29 % (289229)Success in time 0.05 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------