%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV059^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 08:38:56 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV059^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:01:22 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 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
% 0.08/0.27 % (438410)Will run a generic schedule for satisfiability detection.
% 0.08/0.27 % (438415)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3797674767_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.27 % Exception at run slice level
% 0.08/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.27 % (438416)% WARNING: option uhcvi not known.
% 0.08/0.27 % (438416)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1711345353:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.27 % (438419)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3195844279:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.27 % (438418)dis+10_1_sil=32000:sp=arity:random_seed=762245551:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.27 % (438417)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3854913844:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.27 % (438419)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.27 % (438416)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.27 % (438416)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.27 % (438419) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-438410-438419"...
% 0.08/0.27 % (438418) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-438410-438418"...
% 0.08/0.27 % (438416) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-438410-438416"...
% 0.08/0.27 % (438417) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-438410-438417"...
% 0.08/0.27 % (438419)...printing done.
% 0.08/0.27 % (438421)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3626315685:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.27 % (438418)...printing done.
% 0.08/0.27 % (438416)...printing done.
% 0.08/0.27 % (438417)...printing done.
% 0.08/0.27 % (438419)Refutation found. Thanks to Tanya!
% 0.08/0.27 % SZS status Theorem for theBenchmark
% 0.08/0.27 % SZS output start Proof for theBenchmark
% 0.08/0.27 thf(type_def_5, type, b: $tType).
% 0.08/0.27 thf(type_def_6, type, a: $tType).
% 0.08/0.27 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.27 thf(func_def_0, type, cG: (b > b)).
% 0.08/0.27 thf(func_def_1, type, cA: (b > a)).
% 0.08/0.27 thf(func_def_2, type, c_less_: (a > a > $o)).
% 0.08/0.27 thf(func_def_3, type, cF: (b > b)).
% 0.08/0.27 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.27 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.27 thf(func_def_9, type, sK0: b).
% 0.08/0.27 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.08/0.27 thf(f1,conjecture,(
% 0.08/0.27 ((cG = (^[X4 : b] : ((cF @ (cF @ X4))))) & ! [X3 : b] : (c_less_ @ (cA @ X3) @ (cA @ (cF @ X3))) & ! [X0 : a,X1 : a,X2 : a] : (((c_less_ @ X1 @ X2) & (c_less_ @ X0 @ X1)) => (c_less_ @ X0 @ X2))) => ! [X5 : b] : (c_less_ @ (cA @ X5) @ (cA @ (cG @ X5)))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM89A_pme)).
% 0.08/0.27 thf(f2,negated_conjecture,(
% 0.08/0.27 ~(((cG = (^[X4 : b] : ((cF @ (cF @ X4))))) & ! [X3 : b] : (c_less_ @ (cA @ X3) @ (cA @ (cF @ X3))) & ! [X0 : a,X1 : a,X2 : a] : (((c_less_ @ X1 @ X2) & (c_less_ @ X0 @ X1)) => (c_less_ @ X0 @ X2))) => ! [X5 : b] : (c_less_ @ (cA @ X5) @ (cA @ (cG @ X5))))),
% 0.08/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.27 thf(f3,plain,(
% 0.08/0.27 ~(((cG = (^[X0 : b] : ((cF @ (cF @ X0))))) & ! [X1 : b] : (c_less_ @ (cA @ X1) @ (cA @ (cF @ X1))) & ! [X2 : a,X3 : a,X4 : a] : (((c_less_ @ X3 @ X4) & (c_less_ @ X2 @ X3)) => (c_less_ @ X2 @ X4))) => ! [X5 : b] : (c_less_ @ (cA @ X5) @ (cA @ (cG @ X5))))),
% 0.08/0.27 inference(rectify,[],[f2])).
% 0.08/0.27 thf(f4,plain,(
% 0.08/0.27 ~(((cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X1 : b] : (((c_less_ @ (cA @ X1) @ (cA @ (cF @ X1)))) = $true) & ! [X2 : a,X3 : a,X4 : a] : (((((c_less_ @ X3 @ X4)) = $true) & (((c_less_ @ X2 @ X3)) = $true)) => (((c_less_ @ X2 @ X4)) = $true))) => ! [X5 : b] : (((c_less_ @ (cA @ X5) @ (cA @ (cG @ X5)))) = $true))),
% 0.08/0.27 inference(fool_elimination,[],[f3])).
% 0.08/0.27 thf(f5,plain,(
% 0.08/0.27 ~(((cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X0 : b] : ($true = ((c_less_ @ (cA @ X0) @ (cA @ (cF @ X0))))) & ! [X1 : a,X2 : a,X3 : a] : (((((c_less_ @ X2 @ X3)) = $true) & (((c_less_ @ X1 @ X2)) = $true)) => ($true = ((c_less_ @ X1 @ X3))))) => ! [X4 : b] : ($true = ((c_less_ @ (cA @ X4) @ (cA @ (cG @ X4))))))),
% 0.08/0.27 inference(rectify,[],[f4])).
% 0.08/0.27 thf(f6,plain,(
% 0.08/0.27 ? [X4 : b] : ($true != ((c_less_ @ (cA @ X4) @ (cA @ (cG @ X4))))) & ((cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X0 : b] : ($true = ((c_less_ @ (cA @ X0) @ (cA @ (cF @ X0))))) & ! [X1 : a,X2 : a,X3 : a] : (($true = ((c_less_ @ X1 @ X3))) | ((((c_less_ @ X2 @ X3)) != $true) | (((c_less_ @ X1 @ X2)) != $true))))),
% 0.08/0.27 inference(ennf_transformation,[],[f5])).
% 0.08/0.27 thf(f7,plain,(
% 0.08/0.27 ? [X4 : b] : ($true != ((c_less_ @ (cA @ X4) @ (cA @ (cG @ X4))))) & (cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X0 : b] : ($true = ((c_less_ @ (cA @ X0) @ (cA @ (cF @ X0))))) & ! [X1 : a,X2 : a,X3 : a] : (($true = ((c_less_ @ X1 @ X3))) | (((c_less_ @ X2 @ X3)) != $true) | (((c_less_ @ X1 @ X2)) != $true))),
% 0.08/0.27 inference(flattening,[],[f6])).
% 0.08/0.27 thf(f8,plain,(
% 0.08/0.27 ? [X0 : b] : ($true != ((c_less_ @ (cA @ X0) @ (cA @ (cG @ X0))))) & (cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X1 : b] : (((c_less_ @ (cA @ X1) @ (cA @ (cF @ X1)))) = $true) & ! [X2 : a,X3 : a,X4 : a] : ((((c_less_ @ X2 @ X4)) = $true) | (((c_less_ @ X3 @ X4)) != $true) | (((c_less_ @ X2 @ X3)) != $true))),
% 0.08/0.27 inference(rectify,[],[f7])).
% 0.08/0.27 thf(f9,plain,(
% 0.08/0.27 ($true != ((c_less_ @ (cA @ sK0) @ (cA @ (cG @ sK0))))) & (cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X1 : b] : (((c_less_ @ (cA @ X1) @ (cA @ (cF @ X1)))) = $true) & ! [X2 : a,X3 : a,X4 : a] : ((((c_less_ @ X2 @ X4)) = $true) | (((c_less_ @ X3 @ X4)) != $true) | (((c_less_ @ X2 @ X3)) != $true))),
% 0.08/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8])).
% 0.08/0.27 thf(f10,plain,(
% 0.08/0.27 ( ! [X2 : a,X3 : a,X4 : a] : ((((c_less_ @ X2 @ X4)) = $true) | (((c_less_ @ X3 @ X4)) != $true) | (((c_less_ @ X2 @ X3)) != $true)) )),
% 0.08/0.27 inference(cnf_transformation,[],[f9])).
% 0.08/0.27 thf(f11,plain,(
% 0.08/0.27 ( ! [X1 : b] : ((((c_less_ @ (cA @ X1) @ (cA @ (cF @ X1)))) = $true)) )),
% 0.08/0.27 inference(cnf_transformation,[],[f9])).
% 0.08/0.27 thf(f12,plain,(
% 0.08/0.27 (cG = (^[Y0 : b]: (cF @ (cF @ Y0))))),
% 0.08/0.27 inference(cnf_transformation,[],[f9])).
% 0.08/0.27 thf(f13,plain,(
% 0.08/0.27 ($true != ((c_less_ @ (cA @ sK0) @ (cA @ (cG @ sK0)))))),
% 0.08/0.27 inference(cnf_transformation,[],[f9])).
% 0.08/0.27 thf(f15,definition,(
% 0.08/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.27 thf(f16,plain,(
% 0.08/0.27 ($true != ((c_less_ @ (cA @ sK0) @ (cA @ ((^[Y0 : b]: (cF @ (cF @ Y0))) @ sK0)))))),
% 0.08/0.27 inference(definition_unfolding,[],[f13,f12])).
% 0.08/0.27 thf(f17,plain,(
% 0.08/0.27 ($true != ((c_less_ @ (cA @ sK0) @ (cA @ (cF @ (cF @ sK0))))))),
% 0.08/0.27 inference(beta-eta_normalization,[],[f16])).
% 0.08/0.27 thf(f20,plain,(
% 0.08/0.27 ( ! [X0 : b,X1 : a] : (($true != $true) | ($true = ((c_less_ @ (cA @ X0) @ X1))) | ($true != ((c_less_ @ (cA @ (cF @ X0)) @ X1)))) )),
% 0.08/0.27 inference(constrained_superposition,[],[f10,f11])).
% 0.08/0.27 thf(f25,plain,(
% 0.08/0.27 ( ! [X0 : b,X1 : a] : (($true != ((c_less_ @ (cA @ (cF @ X0)) @ X1))) | ($true = ((c_less_ @ (cA @ X0) @ X1)))) )),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f20])).
% 0.08/0.27 thf(f28,plain,(
% 0.08/0.27 ( ! [X0 : b] : (($true != $true) | ($true = ((c_less_ @ (cA @ X0) @ (cA @ (cF @ (cF @ X0))))))) )),
% 0.08/0.27 inference(constrained_superposition,[],[f25,f11])).
% 0.08/0.27 thf(f31,plain,(
% 0.08/0.27 ( ! [X0 : b] : (($true = ((c_less_ @ (cA @ X0) @ (cA @ (cF @ (cF @ X0))))))) )),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f28])).
% 0.08/0.27 thf(f34,plain,(
% 0.08/0.27 ($true != $true) | ($false = ((c_less_ @ (cA @ sK0) @ (cA @ (cF @ (cF @ sK0))))))),
% 0.08/0.27 inference(constrained_superposition,[],[f17,f15])).
% 0.08/0.27 thf(f42,plain,(
% 0.08/0.27 ($false = ((c_less_ @ (cA @ sK0) @ (cA @ (cF @ (cF @ sK0))))))),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f34])).
% 0.08/0.27 thf(f47,plain,(
% 0.08/0.27 ($true = $false)),
% 0.08/0.27 inference(forward_demodulation,[],[f42,f31])).
% 0.08/0.27 thf(f48,plain,(
% 0.08/0.27 $false),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f47])).
% 0.08/0.27 % SZS output end Proof for theBenchmark
% 0.08/0.27 % (438419)------------------------------
% 0.08/0.27 % (438419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.27 % (438419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.27 % (438419)CaDiCaL version: 2.1.3
% 0.08/0.27 % (438419)Termination reason: Refutation
% 0.08/0.27 % (438419)Time elapsed: 0.004 s
% 0.08/0.27 % (438419)Peak memory usage: 12 MB
% 0.08/0.27 % (438419)Instructions burned: 5 (million)
% 0.08/0.27 % (438410)Success in time 0.037 s
% 0.08/0.27 % Vampire exiting
%------------------------------------------------------------------------------