%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM705^1 : 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 : 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 08:19:22 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM705^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 % Computer : n013.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 12:41:51 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.25 Running first-order model finding
% 0.09/0.25 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
% 0.23/0.31 % (2047279)Will run a generic schedule for satisfiability detection.
% 0.23/0.31 % (2047285)% WARNING: option uhcvi not known.
% 0.23/0.31 % (2047285)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1450352017:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.31 % (2047286)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=81439536:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.31 % (2047287)dis+10_1_sil=32000:sp=arity:random_seed=1322968850:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.31 % (2047288)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=863225886:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.31 % (2047285)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.31 % (2047288)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.31 % (2047285)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.23/0.31 % (2047284)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1305726465_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.31 % (2047288) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2047279-2047288"...
% 0.23/0.31 % (2047285) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2047279-2047285"...
% 0.23/0.31 % (2047287) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2047279-2047287"...
% 0.23/0.31 % Exception at run slice level
% 0.23/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.31 % (2047285)...printing done.
% 0.23/0.31 % (2047288)...printing done.
% 0.23/0.31 % (2047289)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1227020890:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.31 % (2047287)...printing done.
% 0.23/0.31 % (2047288)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% 0.23/0.31 thf(type_def_5, type, nat: $tType).
% 0.23/0.31 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.31 thf(func_def_0, type, p: (nat > $o)).
% 0.23/0.31 thf(func_def_1, type, some: ((nat > $o) > $o)).
% 0.23/0.31 thf(func_def_3, type, lessis: (nat > nat > $o)).
% 0.23/0.31 thf(func_def_4, type, more: (nat > nat > $o)).
% 0.23/0.31 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.23/0.31 thf(func_def_8, type, vIMP: ($o > $o > $o)).
% 0.23/0.31 thf(func_def_9, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.23/0.31 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.31 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.31 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.31 thf(func_def_13, type, sK0: nat).
% 0.23/0.31 thf(func_def_14, type, sK1: nat).
% 0.23/0.31 thf(f1,axiom,(
% 0.23/0.31 (some @ p)),
% 0.23/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',s)).
% 0.23/0.31 thf(f2,axiom,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : ((lessis @ X0 @ X1) => (~(more @ X1 @ X0) => (X1 = X0)))),
% 0.23/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz14)).
% 0.23/0.31 thf(f4,axiom,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : ((lessis @ X0 @ X1) => ~(more @ X0 @ X1))),
% 0.23/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10d)).
% 0.23/0.31 thf(f5,axiom,(
% 0.23/0.31 ! [X0 : (nat > $o)] : ((some @ X0) => (some @ (^[X1 : nat] : (~(! [X2 : nat] : ((X0 @ X2) => (lessis @ X1 @ X2)) => ~(X0 @ X1))))))),
% 0.23/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz27)).
% 0.23/0.31 thf(f6,conjecture,(
% 0.23/0.31 ~(! [X0 : nat,X1 : nat] : (~(! [X2 : nat] : ((p @ X2) => (lessis @ X0 @ X2)) => ~(p @ X0)) => (~(! [X2 : nat] : ((p @ X2) => (lessis @ X1 @ X2)) => ~(p @ X1)) => (X0 = X1))) => ~(some @ (^[X0 : nat] : (~(! [X2 : nat] : ((p @ X2) => (lessis @ X0 @ X2)) => ~(p @ X0))))))),
% 0.23/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz27a)).
% 0.23/0.31 thf(f7,negated_conjecture,(
% 0.23/0.31 ~ ~(! [X0 : nat,X1 : nat] : (~(! [X2 : nat] : ((p @ X2) => (lessis @ X0 @ X2)) => ~(p @ X0)) => (~(! [X2 : nat] : ((p @ X2) => (lessis @ X1 @ X2)) => ~(p @ X1)) => (X0 = X1))) => ~(some @ (^[X0 : nat] : (~(! [X2 : nat] : ((p @ X2) => (lessis @ X0 @ X2)) => ~(p @ X0))))))),
% 0.23/0.31 inference(negated_conjecture,[status(cth)],[f6])).
% 0.23/0.31 thf(f8,plain,(
% 0.23/0.31 (some @ p)),
% 0.23/0.31 inference(rectify,[],[f1])).
% 0.23/0.31 thf(f9,plain,(
% 0.23/0.31 (((some @ p)) = $true)),
% 0.23/0.31 inference(fool_elimination,[],[f8])).
% 0.23/0.31 thf(f10,plain,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : ((lessis @ X0 @ X1) => (~(more @ X1 @ X0) => (X1 = X0)))),
% 0.23/0.31 inference(rectify,[],[f2])).
% 0.23/0.31 thf(f11,plain,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : ((((lessis @ X0 @ X1)) = $true) => (~ (((more @ X1 @ X0)) = $true) => (X0 = X1)))),
% 0.23/0.31 inference(fool_elimination,[],[f10])).
% 0.23/0.31 thf(f14,plain,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : ((lessis @ X0 @ X1) => ~(more @ X0 @ X1))),
% 0.23/0.31 inference(rectify,[],[f4])).
% 0.23/0.31 thf(f15,plain,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : ((((lessis @ X0 @ X1)) = $true) => ~ (((more @ X0 @ X1)) = $true))),
% 0.23/0.31 inference(fool_elimination,[],[f14])).
% 0.23/0.31 thf(f16,plain,(
% 0.23/0.31 ! [X0 : (nat > $o)] : ((some @ X0) => (some @ (^[X1 : nat] : (~(! [X2 : nat] : ((X0 @ X2) => (lessis @ X1 @ X2)) => ~(X0 @ X1))))))),
% 0.23/0.31 inference(rectify,[],[f5])).
% 0.23/0.31 thf(f17,plain,(
% 0.23/0.31 ! [X0 : (nat > $o)] : ((((some @ X0)) = $true) => ($true = ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((X0 @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (X0 @ Y0)))))))))),
% 0.23/0.31 inference(fool_elimination,[],[f16])).
% 0.23/0.31 thf(f18,plain,(
% 0.23/0.31 ~ ~(! [X0 : nat,X1 : nat] : (~(! [X2 : nat] : ((p @ X2) => (lessis @ X0 @ X2)) => ~(p @ X0)) => (~(! [X3 : nat] : ((p @ X3) => (lessis @ X1 @ X3)) => ~(p @ X1)) => (X0 = X1))) => ~(some @ (^[X4 : nat] : (~(! [X5 : nat] : ((p @ X5) => (lessis @ X4 @ X5)) => ~(p @ X4))))))),
% 0.23/0.31 inference(rectify,[],[f7])).
% 0.23/0.31 thf(f19,plain,(
% 0.23/0.31 ~ ~(! [X0 : nat,X1 : nat] : (~(! [X2 : nat] : ((((p @ X2)) = $true) => (((lessis @ X0 @ X2)) = $true)) => ~ (((p @ X0)) = $true)) => (~(! [X3 : nat] : (($true = ((p @ X3))) => ($true = ((lessis @ X1 @ X3)))) => ~ (((p @ X1)) = $true)) => (X0 = X1))) => ~ ($true = ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))))))),
% 0.23/0.31 inference(fool_elimination,[],[f18])).
% 0.23/0.31 thf(f20,plain,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : ((((lessis @ X0 @ X1)) = $true) => ((((more @ X1 @ X0)) != $true) => (X0 = X1)))),
% 0.23/0.31 inference(flattening,[],[f11])).
% 0.23/0.31 thf(f22,plain,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : ((((lessis @ X0 @ X1)) = $true) => (((more @ X0 @ X1)) != $true))),
% 0.23/0.31 inference(flattening,[],[f15])).
% 0.23/0.31 thf(f23,plain,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : (~(! [X2 : nat] : ((((p @ X2)) = $true) => (((lessis @ X0 @ X2)) = $true)) => (((p @ X0)) != $true)) => (~(! [X3 : nat] : (($true = ((p @ X3))) => ($true = ((lessis @ X1 @ X3)))) => (((p @ X1)) != $true)) => (X0 = X1))) => ($true != ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0))))))))),
% 0.23/0.31 inference(flattening,[],[f19])).
% 0.23/0.31 thf(f24,plain,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : (((X0 = X1) | (((more @ X1 @ X0)) = $true)) | (((lessis @ X0 @ X1)) != $true))),
% 0.23/0.31 inference(ennf_transformation,[],[f20])).
% 0.23/0.31 thf(f25,plain,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : ((X0 = X1) | (((more @ X1 @ X0)) = $true) | (((lessis @ X0 @ X1)) != $true))),
% 0.23/0.31 inference(flattening,[],[f24])).
% 0.23/0.31 thf(f27,plain,(
% 0.23/0.31 ! [X0 : nat,X1 : nat] : ((((more @ X0 @ X1)) != $true) | (((lessis @ X0 @ X1)) != $true))),
% 0.23/0.31 inference(ennf_transformation,[],[f22])).
% 0.23/0.31 thf(f28,plain,(
% 0.23/0.31 ! [X0 : (nat > $o)] : (($true = ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((X0 @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (X0 @ Y0)))))))) | (((some @ X0)) != $true))),
% 0.23/0.31 inference(ennf_transformation,[],[f17])).
% 0.23/0.31 thf(f29,plain,(
% 0.23/0.31 ($true != ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))))) | ? [X0 : nat,X1 : nat] : (((X0 != X1) & ((((p @ X1)) = $true) & ! [X3 : nat] : (($true = ((lessis @ X1 @ X3))) | ($true != ((p @ X3)))))) & ((((p @ X0)) = $true) & ! [X2 : nat] : ((((lessis @ X0 @ X2)) = $true) | (((p @ X2)) != $true))))),
% 0.23/0.31 inference(ennf_transformation,[],[f23])).
% 0.23/0.31 thf(f30,plain,(
% 0.23/0.31 ($true != ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))))) | ? [X0 : nat,X1 : nat] : ((X0 != X1) & (((p @ X1)) = $true) & ! [X3 : nat] : (($true = ((lessis @ X1 @ X3))) | ($true != ((p @ X3)))) & (((p @ X0)) = $true) & ! [X2 : nat] : ((((lessis @ X0 @ X2)) = $true) | (((p @ X2)) != $true)))),
% 0.23/0.31 inference(flattening,[],[f29])).
% 0.23/0.31 thf(f31,plain,(
% 0.23/0.31 ($true != ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))))) | ? [X0 : nat,X1 : nat] : ((X0 != X1) & (((p @ X1)) = $true) & ! [X2 : nat] : ((((lessis @ X1 @ X2)) = $true) | (((p @ X2)) != $true)) & (((p @ X0)) = $true) & ! [X3 : nat] : (($true = ((lessis @ X0 @ X3))) | ($true != ((p @ X3)))))),
% 0.23/0.31 inference(rectify,[],[f30])).
% 0.23/0.31 thf(f32,plain,(
% 0.23/0.31 ($true != ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))))) | ((sK0 != sK1) & ($true = ((p @ sK1))) & ! [X2 : nat] : (($true = ((lessis @ sK1 @ X2))) | (((p @ X2)) != $true)) & ($true = ((p @ sK0))) & ! [X3 : nat] : (($true = ((lessis @ sK0 @ X3))) | ($true != ((p @ X3)))))),
% 0.23/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f31])).
% 0.23/0.31 thf(f33,plain,(
% 0.23/0.31 (((some @ p)) = $true)),
% 0.23/0.31 inference(cnf_transformation,[],[f9])).
% 0.23/0.31 thf(f34,plain,(
% 0.23/0.31 ( ! [X0 : nat,X1 : nat] : ((((more @ X1 @ X0)) = $true) | (((lessis @ X0 @ X1)) != $true) | (X0 = X1)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f25])).
% 0.23/0.31 thf(f36,plain,(
% 0.23/0.31 ( ! [X0 : nat,X1 : nat] : ((((more @ X0 @ X1)) != $true) | (((lessis @ X0 @ X1)) != $true)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f27])).
% 0.23/0.31 thf(f37,plain,(
% 0.23/0.31 ( ! [X0 : (nat > $o)] : (($true = ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((X0 @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (X0 @ Y0)))))))) | (((some @ X0)) != $true)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f28])).
% 0.23/0.31 thf(f38,plain,(
% 0.23/0.31 ( ! [X3 : nat] : (($true != ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))))) | ($true = ((lessis @ sK0 @ X3))) | ($true != ((p @ X3)))) )),
% 0.23/0.31 inference(cnf_transformation,[],[f32])).
% 0.23/0.31 thf(f39,plain,(
% 0.23/0.31 ($true != ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))))) | ($true = ((p @ sK0)))),
% 0.23/0.31 inference(cnf_transformation,[],[f32])).
% 0.23/0.31 thf(f40,plain,(
% 0.23/0.31 ( ! [X2 : nat] : (($true != ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))))) | ($true = ((lessis @ sK1 @ X2))) | (((p @ X2)) != $true)) )),
% 0.23/0.31 inference(cnf_transformation,[],[f32])).
% 0.23/0.31 thf(f41,plain,(
% 0.23/0.31 ($true != ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))))) | ($true = ((p @ sK1)))),
% 0.23/0.31 inference(cnf_transformation,[],[f32])).
% 0.23/0.31 thf(f42,plain,(
% 0.23/0.31 ($true != ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))))) | (sK0 != sK1)),
% 0.23/0.31 inference(cnf_transformation,[],[f32])).
% 0.23/0.31 thf(f44,definition,(
% 0.23/0.31 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.23/0.31 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.23/0.31 thf(f47,definition,(
% 0.23/0.31 spl2_1 <=> ! [X3 : nat] : (($true = ((lessis @ sK0 @ X3))) | ($true != ((p @ X3))))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.23/0.31 thf(f48,plain,(
% 0.23/0.31 ( ! [X3 : nat] : (($true = ((lessis @ sK0 @ X3))) | ($true != ((p @ X3)))) ) | ~spl2_1),
% 0.23/0.31 inference(avatar_component_clause,[],[f47])).
% 0.23/0.31 thf(f50,definition,(
% 0.23/0.31 spl2_2 <=> ($true = ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0))))))))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.23/0.31 thf(f52,plain,(
% 0.23/0.31 ($true != ((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0)))))))) | spl2_2),
% 0.23/0.31 inference(avatar_component_clause,[],[f50])).
% 0.23/0.31 thf(f53,plain,(
% 0.23/0.31 spl2_1 | ~spl2_2),
% 0.23/0.31 inference(avatar_split_clause,[],[f38,f50,f47])).
% 0.23/0.31 thf(f55,definition,(
% 0.23/0.31 spl2_3 <=> ($true = ((p @ sK0)))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.23/0.31 thf(f57,plain,(
% 0.23/0.31 ($true = ((p @ sK0))) | ~spl2_3),
% 0.23/0.31 inference(avatar_component_clause,[],[f55])).
% 0.23/0.31 thf(f58,plain,(
% 0.23/0.31 spl2_3 | ~spl2_2),
% 0.23/0.31 inference(avatar_split_clause,[],[f39,f50,f55])).
% 0.23/0.31 thf(f60,definition,(
% 0.23/0.31 spl2_4 <=> ! [X2 : nat] : (($true = ((lessis @ sK1 @ X2))) | (((p @ X2)) != $true))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.23/0.31 thf(f61,plain,(
% 0.23/0.31 ( ! [X2 : nat] : (($true = ((lessis @ sK1 @ X2))) | (((p @ X2)) != $true)) ) | ~spl2_4),
% 0.23/0.31 inference(avatar_component_clause,[],[f60])).
% 0.23/0.31 thf(f62,plain,(
% 0.23/0.31 spl2_4 | ~spl2_2),
% 0.23/0.31 inference(avatar_split_clause,[],[f40,f50,f60])).
% 0.23/0.31 thf(f64,definition,(
% 0.23/0.31 spl2_5 <=> ($true = ((p @ sK1)))),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition])).
% 0.23/0.31 thf(f66,plain,(
% 0.23/0.31 ($true = ((p @ sK1))) | ~spl2_5),
% 0.23/0.31 inference(avatar_component_clause,[],[f64])).
% 0.23/0.31 thf(f67,plain,(
% 0.23/0.31 spl2_5 | ~spl2_2),
% 0.23/0.31 inference(avatar_split_clause,[],[f41,f50,f64])).
% 0.23/0.31 thf(f69,definition,(
% 0.23/0.31 spl2_6 <=> (sK0 = sK1)),
% 0.23/0.31 introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition])).
% 0.23/0.31 thf(f71,plain,(
% 0.23/0.31 (sK0 != sK1) | spl2_6),
% 0.23/0.31 inference(avatar_component_clause,[],[f69])).
% 0.23/0.31 thf(f72,plain,(
% 0.23/0.31 ~spl2_6 | ~spl2_2),
% 0.23/0.31 inference(avatar_split_clause,[],[f42,f50,f69])).
% 0.23/0.31 thf(f80,plain,(
% 0.23/0.31 ($true != $true) | (((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0))))))) = $false) | spl2_2),
% 0.23/0.31 inference(constrained_superposition,[],[f52,f44])).
% 0.23/0.31 thf(f81,plain,(
% 0.23/0.31 (((some @ (^[Y0 : nat]: (~ ((!! @ nat @ (^[Y1 : nat]: ((p @ Y1) => (lessis @ Y0 @ Y1)))) => (~ (p @ Y0))))))) = $false) | spl2_2),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f80])).
% 0.23/0.31 thf(f94,plain,(
% 0.23/0.31 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (((lessis @ X0 @ X1)) != $true) | ($true != ((lessis @ X1 @ X0))) | (X0 = X1)) )),
% 0.23/0.31 inference(constrained_superposition,[],[f36,f34])).
% 0.23/0.31 thf(f95,plain,(
% 0.23/0.31 ( ! [X0 : nat,X1 : nat] : ((((lessis @ X0 @ X1)) != $true) | ($true != ((lessis @ X1 @ X0))) | (X0 = X1)) )),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f94])).
% 0.23/0.31 thf(f103,plain,(
% 0.23/0.31 ($true = $false) | ($true != ((some @ (^[Y0 : nat]: (p @ ((^[Y1 : nat]: (Y1)) @ Y0)))))) | spl2_2),
% 0.23/0.31 inference(constrained_superposition,[],[f37,f81])).
% 0.23/0.31 thf(f110,plain,(
% 0.23/0.31 ($true != ((some @ (^[Y0 : nat]: (p @ ((^[Y1 : nat]: (Y1)) @ Y0)))))) | spl2_2),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f103])).
% 0.23/0.31 thf(f111,plain,(
% 0.23/0.31 (((some @ p)) != $true) | spl2_2),
% 0.23/0.31 inference(beta-eta_normalization,[],[f110])).
% 0.23/0.31 thf(f116,plain,(
% 0.23/0.31 $false | spl2_2),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f111,f33])).
% 0.23/0.31 thf(f117,plain,(
% 0.23/0.31 spl2_2),
% 0.23/0.31 inference(avatar_contradiction_clause,[],[f116])).
% 0.23/0.31 thf(f119,plain,(
% 0.23/0.31 ( ! [X0 : nat] : (($true != $true) | ($true != ((lessis @ X0 @ sK0))) | (sK0 = X0) | (((p @ X0)) != $true)) ) | ~spl2_1),
% 0.23/0.31 inference(constrained_superposition,[],[f95,f48])).
% 0.23/0.31 thf(f120,plain,(
% 0.23/0.31 ( ! [X0 : nat] : (($true != ((lessis @ X0 @ sK0))) | (sK0 = X0) | (((p @ X0)) != $true)) ) | ~spl2_1),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f119])).
% 0.23/0.31 thf(f127,plain,(
% 0.23/0.31 ($true != $true) | (sK0 = sK1) | ($true != ((p @ sK1))) | ($true != ((p @ sK0))) | (~spl2_1 | ~spl2_4)),
% 0.23/0.31 inference(constrained_superposition,[],[f120,f61])).
% 0.23/0.31 thf(f128,plain,(
% 0.23/0.31 (sK0 = sK1) | ($true != ((p @ sK1))) | ($true != ((p @ sK0))) | (~spl2_1 | ~spl2_4)),
% 0.23/0.31 inference(trivial_inequality_removal,[],[f127])).
% 0.23/0.31 thf(f130,plain,(
% 0.23/0.31 ($true != ((p @ sK1))) | ($true != ((p @ sK0))) | (~spl2_1 | ~spl2_4 | spl2_6)),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f128,f71])).
% 0.23/0.31 thf(f131,plain,(
% 0.23/0.31 ($true != ((p @ sK0))) | (~spl2_1 | ~spl2_4 | ~spl2_5 | spl2_6)),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f130,f66])).
% 0.23/0.31 thf(f132,plain,(
% 0.23/0.31 $false | (~spl2_1 | ~spl2_3 | ~spl2_4 | ~spl2_5 | spl2_6)),
% 0.23/0.31 inference(forward_subsumption_resolution,[],[f131,f57])).
% 0.23/0.31 thf(f133,plain,(
% 0.23/0.31 ~spl2_1 | ~spl2_3 | ~spl2_4 | ~spl2_5 | spl2_6),
% 0.23/0.31 inference(avatar_contradiction_clause,[],[f132])).
% 0.23/0.31 cnf(s1, plain, spl2_1 | ~spl2_2, inference(sat_conversion,[],[f53])).
% 0.23/0.31 cnf(s2, plain, ~spl2_2 | spl2_3, inference(sat_conversion,[],[f58])).
% 0.23/0.31 cnf(s3, plain, ~spl2_2 | spl2_4, inference(sat_conversion,[],[f62])).
% 0.23/0.31 cnf(s4, plain, ~spl2_2 | spl2_5, inference(sat_conversion,[],[f67])).
% 0.23/0.31 cnf(s5, plain, ~spl2_2 | ~spl2_6, inference(sat_conversion,[],[f72])).
% 0.23/0.31 cnf(s8, plain, spl2_2, inference(sat_conversion,[],[f117])).
% 0.23/0.31 cnf(s9, plain, ~spl2_1 | ~spl2_3 | ~spl2_4 | ~spl2_5 | spl2_6, inference(sat_conversion,[],[f133])).
% 0.23/0.31 cnf(s10, plain, ~spl2_6, inference(rat,[],[s5,s8])).
% 0.23/0.31 cnf(s11, plain, spl2_5, inference(rat,[],[s4,s8])).
% 0.23/0.31 cnf(s12, plain, spl2_4, inference(rat,[],[s3,s8])).
% 0.23/0.31 cnf(s13, plain, spl2_3, inference(rat,[],[s2,s8])).
% 0.23/0.31 cnf(s14, plain, ~spl2_1, inference(rat,[],[s9,s10,s11,s12,s13])).
% 0.23/0.31 cnf(s15, plain, $false, inference(rat,[],[s1,s8,s14])).
% 0.23/0.31 thf(f134,plain,(
% 0.23/0.31 $false),
% 0.23/0.31 inference(avatar_sat_refutation,[],[s15])).
% 0.23/0.31 % SZS output end Proof for theBenchmark
% 0.23/0.31 % (2047288)------------------------------
% 0.23/0.31 % (2047288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (2047288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (2047288)CaDiCaL version: 2.1.3
% 0.23/0.31 % (2047288)Termination reason: Refutation
% 0.23/0.31 % (2047288)Time elapsed: 0.008 s
% 0.23/0.31 % (2047288)Peak memory usage: 12 MB
% 0.23/0.31 % (2047288)Instructions burned: 12 (million)
% 0.23/0.31 % (2047279)Success in time 0.044 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------