%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV604^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:39:39 AM UTC 2026
% Result : Theorem 0.37s 0.29s
% Output : Refutation 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV604^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n014.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 15:59:30 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 0.37/0.29 % (2849047)Will run a generic schedule for satisfiability detection.
% 0.37/0.29 % (2849052)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1194774614_2999 on theBenchmark for (2999ds/0Mi)
% 0.37/0.29 % Exception at run slice level
% 0.37/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.37/0.29 % (2849053)% WARNING: option uhcvi not known.
% 0.37/0.29 % (2849053)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2648056682:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.37/0.29 % (2849054)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4077124337:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.37/0.29 % (2849053)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.37/0.29 % (2849053)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.37/0.29 % (2849058)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1616115868:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.37/0.29 % (2849055)dis+10_1_sil=32000:sp=arity:random_seed=4164993885:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.37/0.29 % (2849053) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2849047-2849053"...
% 0.37/0.29 % (2849060)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2355737737:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.37/0.29 % Exception at run slice level
% 0.37/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.37/0.29 % (2849053)...printing done.
% 0.37/0.29 % (2849053)Refutation found. Thanks to Tanya!
% 0.37/0.29 % SZS status Theorem for theBenchmark
% 0.37/0.29 % SZS output start Proof for theBenchmark
% 0.37/0.29 thf(type_def_5, type, set: $tType > $tType).
% 0.37/0.29 thf(type_def_6, type, itself: $tType > $tType).
% 0.37/0.29 thf(type_def_7, type, a: $tType).
% 0.37/0.29 thf(type_def_8, type, b: $tType).
% 0.37/0.29 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.37/0.29 thf(func_def_0, type, bot: !>[X0: $tType]:(X0)).
% 0.37/0.29 thf(func_def_1, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.37/0.29 thf(func_def_2, type, vimage: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0))).
% 0.37/0.29 thf(func_def_3, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.37/0.29 thf(func_def_4, type, a2: a).
% 0.37/0.29 thf(func_def_5, type, b2: b).
% 0.37/0.29 thf(func_def_6, type, f: (a > b)).
% 0.37/0.29 thf(func_def_10, type, vOR: ($o > $o > $o)).
% 0.37/0.29 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.37/0.29 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 0.37/0.29 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.37/0.29 thf(f1,axiom,(
% 0.37/0.29 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : (X0 > X1),X4 : set @ X1] : (((member @ X0 @ X2 @ (vimage @ X0 @ X1 @ X3 @ X4))) = ((member @ X1 @ (X3 @ X2) @ X4)))),
% 0.37/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',vimage_eq)).
% 0.37/0.29 thf(f2,axiom,(
% 0.37/0.29 ! [X0 : $tType,X1 : X0] : ~(member @ X0 @ X1 @ bot @ set @ X0)),
% 0.37/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_iff)).
% 0.37/0.29 thf(f3,axiom,(
% 0.37/0.29 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ X0] : (((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = (member @ X0 @ X1 @ X3) | (X1 = X2))),
% 0.37/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',insert_iff)).
% 0.37/0.29 thf(f4,conjecture,(
% 0.37/0.29 (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = (((f @ a2)) = b2))),
% 0.37/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',vimage_singleton_eq)).
% 0.37/0.29 thf(f5,negated_conjecture,(
% 0.37/0.29 ~ (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = (((f @ a2)) = b2))),
% 0.37/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.37/0.29 thf(f6,plain,(
% 0.37/0.29 ! [X0 : $tType,X1 : X0] : ~(member @ X0 @ X1 @ bot @ set @ X0)),
% 0.37/0.29 inference(rectify,[],[f2])).
% 0.37/0.29 thf(f7,plain,(
% 0.37/0.29 ! [X0 : $tType,X1 : X0] : ~ (((member @ X0 @ X1 @ bot @ set @ X0)) = $true)),
% 0.37/0.29 inference(fool_elimination,[],[f6])).
% 0.37/0.29 thf(f8,plain,(
% 0.37/0.29 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ X0] : (((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = (member @ X0 @ X1 @ X3) | (X1 = X2))),
% 0.37/0.29 inference(rectify,[],[f3])).
% 0.37/0.29 thf(f9,plain,(
% 0.37/0.29 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ X0] : (((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = (((X1 = X2) | (member @ X0 @ X1 @ X3))))),
% 0.37/0.29 inference(fool_elimination,[],[f8])).
% 0.37/0.29 thf(f10,plain,(
% 0.37/0.29 ~ (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = ((b2 = (f @ a2))))),
% 0.37/0.29 inference(fool_elimination,[],[f5])).
% 0.37/0.29 thf(f11,plain,(
% 0.37/0.29 ! [X0 : $tType,X1 : X0] : (((member @ X0 @ X1 @ bot @ set @ X0)) != $true)),
% 0.37/0.29 inference(flattening,[],[f7])).
% 0.37/0.29 thf(f12,plain,(
% 0.37/0.29 (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) != ((b2 = (f @ a2))))),
% 0.37/0.29 inference(flattening,[],[f10])).
% 0.37/0.29 thf(f13,plain,(
% 0.37/0.29 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : (X0 > X1),X4 : set @ X1] : ((((member @ X0 @ X2 @ (vimage @ X0 @ X1 @ X3 @ X4))) = ((member @ X1 @ (X3 @ X2) @ X4)))) )),
% 0.37/0.29 inference(cnf_transformation,[],[f1])).
% 0.37/0.29 thf(f14,plain,(
% 0.37/0.29 ( ! [X0 : $tType,X1 : X0] : ((((member @ X0 @ X1 @ bot @ set @ X0)) != $true)) )),
% 0.37/0.29 inference(cnf_transformation,[],[f11])).
% 0.37/0.29 thf(f15,plain,(
% 0.37/0.29 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : ((((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = (((X1 = X2) | (member @ X0 @ X1 @ X3))))) )),
% 0.37/0.29 inference(cnf_transformation,[],[f9])).
% 0.37/0.29 thf(f16,plain,(
% 0.37/0.29 (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) != ((b2 = (f @ a2))))),
% 0.37/0.29 inference(cnf_transformation,[],[f12])).
% 0.37/0.29 thf(f19,plain,(
% 0.37/0.29 (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = $true) | ($true = ((b2 = (f @ a2))))),
% 0.37/0.29 inference(xor_proxy_clausification,[],[f16])).
% 0.37/0.29 thf(f20,plain,(
% 0.37/0.29 (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = $false) | (((b2 = (f @ a2))) = $false)),
% 0.37/0.29 inference(xor_proxy_clausification,[],[f16])).
% 0.37/0.29 thf(f21,plain,(
% 0.37/0.29 (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = $false) | (b2 != ((f @ a2)))),
% 0.37/0.29 inference(equality_proxy_clausification,[],[f20])).
% 0.37/0.29 thf(f22,plain,(
% 0.37/0.29 (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = $true) | (b2 = ((f @ a2)))),
% 0.37/0.29 inference(equality_proxy_clausification,[],[f19])).
% 0.37/0.29 thf(f23,plain,(
% 0.37/0.29 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : ((((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = $true) | ((((X1 = X2) | (member @ X0 @ X1 @ X3))) = $false)) )),
% 0.37/0.29 inference(iff_proxy_clausification,[],[f15])).
% 0.37/0.29 thf(f24,plain,(
% 0.37/0.29 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : ((((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = $false) | ($true = (((X1 = X2) | (member @ X0 @ X1 @ X3))))) )),
% 0.37/0.29 inference(iff_proxy_clausification,[],[f15])).
% 0.37/0.29 thf(f25,plain,(
% 0.37/0.29 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : ((((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = $false) | (((member @ X0 @ X1 @ X3)) = $true) | ($true = ((X1 = X2)))) )),
% 0.37/0.29 inference(or_proxy_clausification,[],[f24])).
% 0.37/0.29 thf(f26,plain,(
% 0.37/0.29 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : ((((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = $false) | (((member @ X0 @ X1 @ X3)) = $true) | (X1 = X2)) )),
% 0.37/0.29 inference(equality_proxy_clausification,[],[f25])).
% 0.37/0.29 thf(f28,plain,(
% 0.37/0.29 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : ((((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = $true) | (((X1 = X2)) = $false)) )),
% 0.37/0.29 inference(or_proxy_clausification,[],[f23])).
% 0.37/0.29 thf(f29,plain,(
% 0.37/0.29 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : ((((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3))) = $true) | (X1 != X2)) )),
% 0.37/0.29 inference(equality_proxy_clausification,[],[f28])).
% 0.37/0.29 thf(f30,plain,(
% 0.37/0.29 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : (X0 > X1),X4 : set @ X1] : ((((member @ X0 @ X2 @ (vimage @ X0 @ X1 @ X3 @ X4))) = $true) | (((member @ X1 @ (X3 @ X2) @ X4)) = $false)) )),
% 0.37/0.29 inference(iff_proxy_clausification,[],[f13])).
% 0.37/0.29 thf(f31,plain,(
% 0.37/0.29 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : (X0 > X1),X4 : set @ X1] : ((((member @ X0 @ X2 @ (vimage @ X0 @ X1 @ X3 @ X4))) = $false) | (((member @ X1 @ (X3 @ X2) @ X4)) = $true)) )),
% 0.37/0.29 inference(iff_proxy_clausification,[],[f13])).
% 0.37/0.29 thf(f33,definition,(
% 0.37/0.29 spl0_1 <=> (b2 = ((f @ a2)))),
% 0.37/0.29 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.37/0.29 thf(f34,plain,(
% 0.37/0.29 (b2 = ((f @ a2))) | ~spl0_1),
% 0.37/0.29 inference(avatar_component_clause,[],[f33])).
% 0.37/0.29 thf(f37,definition,(
% 0.37/0.29 spl0_2 <=> (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = $false)),
% 0.37/0.29 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.37/0.29 thf(f39,plain,(
% 0.37/0.29 (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = $false) | ~spl0_2),
% 0.37/0.29 inference(avatar_component_clause,[],[f37])).
% 0.37/0.29 thf(f40,plain,(
% 0.37/0.29 ~spl0_1 | spl0_2),
% 0.37/0.29 inference(avatar_split_clause,[],[f21,f37,f33])).
% 0.37/0.29 thf(f42,definition,(
% 0.37/0.29 spl0_3 <=> (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = $true)),
% 0.37/0.29 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.37/0.29 thf(f44,plain,(
% 0.37/0.29 (((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b)))) = $true) | ~spl0_3),
% 0.37/0.29 inference(avatar_component_clause,[],[f42])).
% 0.37/0.29 thf(f45,plain,(
% 0.37/0.29 spl0_1 | spl0_3),
% 0.37/0.29 inference(avatar_split_clause,[],[f22,f42,f33])).
% 0.37/0.29 thf(f89,plain,(
% 0.37/0.29 ($true = $false) | ($true = ((member @ b @ (f @ a2) @ (insert @ b @ b2 @ bot @ set @ b)))) | ~spl0_3),
% 0.37/0.29 inference(constrained_superposition,[],[f44,f31])).
% 0.37/0.29 thf(f100,plain,(
% 0.37/0.29 ($true = ((member @ b @ (f @ a2) @ (insert @ b @ b2 @ bot @ set @ b)))) | ~spl0_3),
% 0.37/0.29 inference(trivial_inequality_removal,[],[f89])).
% 0.37/0.29 thf(f110,plain,(
% 0.37/0.29 ($true = $false) | ($true = ((member @ b @ (f @ a2) @ bot @ set @ b))) | (b2 = ((f @ a2))) | ~spl0_3),
% 0.37/0.29 inference(constrained_superposition,[],[f26,f100])).
% 0.37/0.29 thf(f111,plain,(
% 0.37/0.29 ($true = ((member @ b @ (f @ a2) @ bot @ set @ b))) | (b2 = ((f @ a2))) | ~spl0_3),
% 0.37/0.29 inference(trivial_inequality_removal,[],[f110])).
% 0.37/0.29 thf(f113,plain,(
% 0.37/0.29 (b2 = ((f @ a2))) | ~spl0_3),
% 0.37/0.29 inference(forward_subsumption_resolution,[],[f111,f14])).
% 0.37/0.29 thf(f119,plain,(
% 0.37/0.29 spl0_1 | ~spl0_3),
% 0.37/0.29 inference(avatar_split_clause,[],[f113,f42,f33])).
% 0.37/0.29 thf(f125,plain,(
% 0.37/0.29 ($true = $false) | ($false = ((member @ b @ (f @ a2) @ (insert @ b @ b2 @ bot @ set @ b)))) | ~spl0_2),
% 0.37/0.29 inference(constrained_superposition,[],[f30,f39])).
% 0.37/0.29 thf(f126,plain,(
% 0.37/0.29 ($false = ((member @ b @ (f @ a2) @ (insert @ b @ b2 @ bot @ set @ b)))) | ~spl0_2),
% 0.37/0.29 inference(trivial_inequality_removal,[],[f125])).
% 0.37/0.29 thf(f133,plain,(
% 0.37/0.29 ($false = ((member @ b @ b2 @ (insert @ b @ b2 @ bot @ set @ b)))) | (~spl0_1 | ~spl0_2)),
% 0.37/0.29 inference(forward_demodulation,[],[f126,f34])).
% 0.37/0.29 thf(f138,plain,(
% 0.37/0.29 ($true = $false) | (b2 != b2) | (~spl0_1 | ~spl0_2)),
% 0.37/0.29 inference(constrained_superposition,[],[f133,f29])).
% 0.37/0.29 thf(f144,plain,(
% 0.37/0.29 $false | (~spl0_1 | ~spl0_2)),
% 0.37/0.29 inference(trivial_inequality_removal,[],[f138])).
% 0.37/0.29 thf(f145,plain,(
% 0.37/0.29 ~spl0_1 | ~spl0_2),
% 0.37/0.29 inference(avatar_contradiction_clause,[],[f144])).
% 0.37/0.29 cnf(s1, plain, ~spl0_1 | spl0_2, inference(sat_conversion,[],[f40])).
% 0.37/0.29 cnf(s2, plain, spl0_1 | spl0_3, inference(sat_conversion,[],[f45])).
% 0.37/0.29 cnf(s5, plain, spl0_1 | ~spl0_3, inference(sat_conversion,[],[f119])).
% 0.37/0.29 cnf(s10, plain, ~spl0_1 | ~spl0_2, inference(sat_conversion,[],[f145])).
% 0.37/0.29 cnf(s11, plain, spl0_1, inference(rat,[],[s2,s5])).
% 0.37/0.29 cnf(s12, plain, ~spl0_2, inference(rat,[],[s10,s11])).
% 0.37/0.29 cnf(s13, plain, $false, inference(rat,[],[s1,s12,s11])).
% 0.37/0.29 thf(f148,plain,(
% 0.37/0.29 $false),
% 0.37/0.29 inference(avatar_sat_refutation,[],[s13])).
% 0.37/0.29 % SZS output end Proof for theBenchmark
% 0.37/0.29 % (2849053)------------------------------
% 0.37/0.29 % (2849053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.29 % (2849053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.29 % (2849053)CaDiCaL version: 2.1.3
% 0.37/0.29 % (2849053)Termination reason: Refutation
% 0.37/0.29 % (2849053)Time elapsed: 0.014 s
% 0.37/0.29 % (2849053)Peak memory usage: 13 MB
% 0.37/0.29 % (2849053)Instructions burned: 21 (million)
% 0.37/0.29 % (2849047)Success in time 0.052 s
% 0.37/0.29 % Vampire exiting
%------------------------------------------------------------------------------