%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PHI045^6 : TPTP v9.3.1. Released v9.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 08:20:22 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 : PHI045^6 : TPTP v9.3.1. Released v9.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n006.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:19:54 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.24 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
% 0.21/0.29 % (694380)Will run a generic schedule for satisfiability detection.
% 0.21/0.29 % (694386)% WARNING: option uhcvi not known.
% 0.21/0.29 % (694387)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2212785703:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.29 % (694385)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=464482136_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.29 % (694386)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2912237186:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.29 % (694388)dis+10_1_sil=32000:sp=arity:random_seed=2024679447:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.29 % (694390)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2443195449:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.29 % (694389)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3740628593:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.29 % (694386)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.29 % (694391)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2791612929:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.29 % Exception at run slice level
% 0.21/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs% (694386)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.29
% 0.21/0.29 % (694389)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.29 % (694390) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-694380-694390"...
% 0.21/0.29 % (694388) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-694380-694388"...
% 0.21/0.29 % (694391) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-694380-694391"...
% 0.21/0.29 % (694387) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-694380-694387"...
% 0.21/0.29 % (694386) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-694380-694386"...
% 0.21/0.29 % (694388)...printing done.
% 0.21/0.29 % (694390)...printing done.
% 0.21/0.29 % (694391)...printing done.
% 0.21/0.29 % (694388)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, entity: $tType).
% 0.21/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, god_like: (entity > $o)).
% 0.21/0.29 thf(func_def_1, type, positive_property: ((entity > $o) > $o)).
% 0.21/0.29 thf(func_def_3, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.29 thf(func_def_4, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.29 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.21/0.29 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.29 thf(func_def_9, type, sK0: ((entity > $o) > (entity > $o) > entity)).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 ~(positive_property @ (^[X0 : entity] : ((X0 != X0))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coro1)).
% 0.21/0.29 thf(f2,axiom,(
% 0.21/0.29 ! [X0 : (entity > $o),X1 : (entity > $o)] : ((! [X2 : entity] : ((X0 @ X2) => (X1 @ X2)) & (positive_property @ X0)) => (positive_property @ X1))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coro2)).
% 0.21/0.29 thf(f3,axiom,(
% 0.21/0.29 (positive_property @ god_like)),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3)).
% 0.21/0.29 thf(f4,conjecture,(
% 0.21/0.29 ? [X0 : entity] : (god_like @ X0)),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.21/0.29 thf(f5,negated_conjecture,(
% 0.21/0.29 ~ ? [X0 : entity] : (god_like @ X0)),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 ~(positive_property @ (^[X0 : entity] : ((X0 != X0))))),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ~ (((positive_property @ (^[Y0 : entity]: (~ (Y0 = Y0))))) = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ! [X0 : (entity > $o),X1 : (entity > $o)] : ((! [X2 : entity] : ((X0 @ X2) => (X1 @ X2)) & (positive_property @ X0)) => (positive_property @ X1))),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ! [X0 : (entity > $o),X1 : (entity > $o)] : ((! [X2 : entity] : ((((X0 @ X2)) = $true) => (((X1 @ X2)) = $true)) & (((positive_property @ X0)) = $true)) => (((positive_property @ X1)) = $true))),
% 0.21/0.29 inference(fool_elimination,[],[f8])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 (positive_property @ god_like)),
% 0.21/0.29 inference(rectify,[],[f3])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 (((positive_property @ god_like)) = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f10])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 ~ ? [X0 : entity] : (god_like @ X0)),
% 0.21/0.29 inference(rectify,[],[f5])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 ~ ? [X0 : entity] : (((god_like @ X0)) = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f12])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 (((positive_property @ (^[Y0 : entity]: (~ (Y0 = Y0))))) != $true)),
% 0.21/0.29 inference(flattening,[],[f7])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 ! [X0 : (entity > $o),X1 : (entity > $o)] : ((((positive_property @ X1)) = $true) | (? [X2 : entity] : ((((X1 @ X2)) != $true) & (((X0 @ X2)) = $true)) | (((positive_property @ X0)) != $true)))),
% 0.21/0.29 inference(ennf_transformation,[],[f9])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 ! [X0 : (entity > $o),X1 : (entity > $o)] : ((((positive_property @ X1)) = $true) | ? [X2 : entity] : ((((X1 @ X2)) != $true) & (((X0 @ X2)) = $true)) | (((positive_property @ X0)) != $true))),
% 0.21/0.29 inference(flattening,[],[f15])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 ! [X0 : entity] : (((god_like @ X0)) != $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f13])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 ! [X0 : (entity > $o),X1 : (entity > $o)] : ((((positive_property @ X1)) = $true) | (($true != ((X1 @ (sK0 @ X1 @ X0)))) & ($true = ((X0 @ (sK0 @ X1 @ X0))))) | (((positive_property @ X0)) != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1 @ X0)],[f16])).
% 0.21/0.29 thf(f19,plain,(
% 0.21/0.29 (((positive_property @ (^[Y0 : entity]: (~ (Y0 = Y0))))) != $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f14])).
% 0.21/0.29 thf(f20,plain,(
% 0.21/0.29 ( ! [X0 : (entity > $o),X1 : (entity > $o)] : ((((positive_property @ X0)) != $true) | ($true = ((X0 @ (sK0 @ X1 @ X0)))) | (((positive_property @ X1)) = $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f18])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 (((positive_property @ god_like)) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f11])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 ( ! [X0 : entity] : ((((god_like @ X0)) != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f17])).
% 0.21/0.29 thf(f26,plain,(
% 0.21/0.29 ($true != ((positive_property @ (^[Y0 : entity]: (~ $true)))))),
% 0.21/0.29 inference(boolean_simplification,[],[f19])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 ($true != ((positive_property @ (^[Y0 : entity]: ($false)))))),
% 0.21/0.29 inference(boolean_simplification,[],[f26])).
% 0.21/0.29 thf(f46,plain,(
% 0.21/0.29 ( ! [X0 : (entity > $o)] : (($true != $true) | ($true = ((god_like @ (sK0 @ X0 @ god_like)))) | (((positive_property @ X0)) = $true)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f20,f22])).
% 0.21/0.29 thf(f49,plain,(
% 0.21/0.29 ( ! [X0 : (entity > $o)] : (($true = ((god_like @ (sK0 @ X0 @ god_like)))) | (((positive_property @ X0)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f46])).
% 0.21/0.29 thf(f51,plain,(
% 0.21/0.29 ( ! [X0 : (entity > $o)] : ((((positive_property @ X0)) = $true)) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f49,f23])).
% 0.21/0.29 thf(f54,plain,(
% 0.21/0.29 ($true != $true)),
% 0.21/0.29 inference(constrained_superposition,[],[f27,f51])).
% 0.21/0.29 thf(f57,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f54])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (694388)------------------------------
% 0.21/0.29 % (694388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (694388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (694388)CaDiCaL version: 2.1.3
% 0.21/0.29 % (694388)Termination reason: Refutation
% 0.21/0.29 % (694388)Time elapsed: 0.003 s
% 0.21/0.29 % (694388)Peak memory usage: 12 MB
% 0.21/0.29 % (694388)Instructions burned: 3 (million)
% 0.21/0.29 % (694380)Success in time 0.043 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------