%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV481^1 : TPTP v9.3.1. Released v7.0.0.
% 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 08:39:34 AM UTC 2026
% Result : Theorem 0.27s 0.37s
% Output : Refutation 0.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV481^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.26 % Computer : n017.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 15:48:37 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.27/0.31 Running first-order model finding
% 0.27/0.31 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
% 0.27/0.37 % (495350)Will run a generic schedule for satisfiability detection.
% 0.27/0.37 % (495361)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1758489204:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.27/0.37 % (495356)% WARNING: option uhcvi not known.
% 0.27/0.37 % (495355)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4075922971_2999 on theBenchmark for (2999ds/0Mi)
% 0.27/0.37 % (495356)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3512097605:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.27/0.37 % (495357)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1756174982:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.27/0.37 % (495360)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3619661175:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.27/0.37 % (495356)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.27/0.37 % (495358)dis+10_1_sil=32000:sp=arity:random_seed=1794622473:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.27/0.37 % Exception at run slice level
% 0.27/0.37 % (495361) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-495350-495361"...
% 0.27/0.37 User error: % (495356)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.27/0.37 Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.27/0.37 % (495359)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=552309325:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.27/0.37 % (495359)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.27/0.37 % (495361)...printing done.
% 0.27/0.37 % (495361)Refutation found. Thanks to Tanya!
% 0.27/0.37 % SZS status Theorem for theBenchmark
% 0.27/0.37 % SZS output start Proof for theBenchmark
% 0.27/0.37 thf(type_def_5, type, 'type/pair/prod': ($tType * $tType) > $tType).
% 0.27/0.37 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.27/0.37 thf(type_def_7, type, sK1: $tType).
% 0.27/0.37 thf(type_def_8, type, sK2: $tType).
% 0.27/0.37 thf(func_def_0, type, 'const/sets/SETSPEC': !>[X0: $tType]:((X0 > $o > X0 > $o))).
% 0.27/0.37 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.27/0.37 thf(func_def_2, type, 'const/sets/GSPEC': !>[X0: $tType]:(((X0 > $o) > X0 > $o))).
% 0.27/0.37 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.27/0.37 thf(func_def_4, type, 'const/pair/,': !>[X0: $tType, X1: $tType]:((X0 > X1 > 'type/pair/prod' @ X0 @ X1))).
% 0.27/0.37 thf(func_def_8, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.27/0.37 thf(func_def_9, type, db2: !>[X0: $tType]:(X0)).
% 0.27/0.37 thf(func_def_10, type, vAND: ($o > $o > $o)).
% 0.27/0.37 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.27/0.37 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.27/0.37 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.27/0.37 thf(func_def_14, type, sK0: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > $o) > X0))).
% 0.27/0.37 thf(func_def_15, type, sK3: (sK1 > $o)).
% 0.27/0.37 thf(func_def_16, type, sK4: (sK2 > $o)).
% 0.27/0.37 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.27/0.37 thf(func_def_18, type, sK5: ((sK1 > sK2 > sK1) > 'type/pair/prod' @ sK1 @ sK2)).
% 0.27/0.37 thf(f1,axiom,(
% 0.27/0.37 ! [X2 : $tType,X0 : $tType,X1 : $tType,X3 : (X0 > X1 > X2),X4 : (X0 > $o),X5 : (X0 > X1 > $o)] : ((! [X6 : X0] : (('const/sets/IN' @ X0 @ X6 @ X4) => ('const/sets/FINITE' @ X1 @ (X5 @ X6))) & ('const/sets/FINITE' @ X0 @ X4)) => ('const/sets/FINITE' @ X2 @ ('const/sets/GSPEC' @ X2 @ (^[X6 : X2] : (? [X7 : X0,X8 : X1] : ('const/sets/SETSPEC' @ X2 @ X6 @ ('const/sets/IN' @ X1 @ X8 @ (X5 @ X7)) & ('const/sets/IN' @ X0 @ X7 @ X4) @ (X3 @ X7 @ X8)))))))),
% 0.27/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_PRODUCT_DEPENDENT_')).
% 0.27/0.37 thf(f2,conjecture,(
% 0.27/0.37 ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > $o)] : ((('const/sets/FINITE' @ X1 @ X3) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ 'type/pair/prod' @ X0 @ X1 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X0 @ X1 @ (^[X4 : 'type/pair/prod' @ X0 @ X1] : (? [X5 : X0,X6 : X1] : ('const/sets/SETSPEC' @ 'type/pair/prod' @ X0 @ X1 @ X4 @ ('const/sets/IN' @ X1 @ X6 @ X3) & ('const/sets/IN' @ X0 @ X5 @ X2) @ ('const/pair/,' @ X0 @ X1 @ X5 @ X6)))))))),
% 0.27/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_PRODUCT_')).
% 0.27/0.37 thf(f3,negated_conjecture,(
% 0.27/0.37 ~ ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > $o)] : ((('const/sets/FINITE' @ X1 @ X3) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ 'type/pair/prod' @ X0 @ X1 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X0 @ X1 @ (^[X4 : 'type/pair/prod' @ X0 @ X1] : (? [X5 : X0,X6 : X1] : ('const/sets/SETSPEC' @ 'type/pair/prod' @ X0 @ X1 @ X4 @ ('const/sets/IN' @ X1 @ X6 @ X3) & ('const/sets/IN' @ X0 @ X5 @ X2) @ ('const/pair/,' @ X0 @ X1 @ X5 @ X6)))))))),
% 0.27/0.37 inference(negated_conjecture,[status(cth)],[f2])).
% 0.27/0.37 thf(f4,plain,(
% 0.27/0.37 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X1 > X2 > X0),X4 : (X1 > $o),X5 : (X1 > X2 > $o)] : ((! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ X4) => ('const/sets/FINITE' @ X2 @ (X5 @ X6))) & ('const/sets/FINITE' @ X1 @ X4)) => ('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X7 : X0] : (? [X8 : X1,X9 : X2] : ('const/sets/SETSPEC' @ X0 @ X7 @ ('const/sets/IN' @ X2 @ X9 @ (X5 @ X8)) & ('const/sets/IN' @ X1 @ X8 @ X4) @ (X3 @ X8 @ X9)))))))),
% 0.27/0.37 inference(rectify,[],[f1])).
% 0.27/0.37 thf(f5,plain,(
% 0.27/0.37 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X1 > X2 > X0),X4 : (X1 > $o),X5 : (X1 > X2 > $o)] : ((! [X6 : X1] : (((('const/sets/IN' @ X1 @ X6 @ X4)) = $true) => ((('const/sets/FINITE' @ X2 @ (X5 @ X6))) = $true)) & ((('const/sets/FINITE' @ X1 @ X4)) = $true)) => ($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X2 @ (^[Y1 : X2]: (?? @ X1 @ (^[Y2 : X1]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y2 @ X4) & ('const/sets/IN' @ X2 @ Y1 @ (X5 @ Y2))) @ (X3 @ Y2 @ Y1))))))))))))),
% 0.27/0.37 inference(fool_elimination,[],[f4])).
% 0.27/0.37 thf(f6,plain,(
% 0.27/0.37 ~ ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > $o)] : ((('const/sets/FINITE' @ X1 @ X3) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ 'type/pair/prod' @ X0 @ X1 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X0 @ X1 @ (^[X4 : 'type/pair/prod' @ X0 @ X1] : (? [X5 : X0,X6 : X1] : ('const/sets/SETSPEC' @ 'type/pair/prod' @ X0 @ X1 @ X4 @ ('const/sets/IN' @ X1 @ X6 @ X3) & ('const/sets/IN' @ X0 @ X5 @ X2) @ ('const/pair/,' @ X0 @ X1 @ X5 @ X6)))))))),
% 0.27/0.37 inference(rectify,[],[f3])).
% 0.27/0.37 thf(f7,plain,(
% 0.27/0.37 ~ ! [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > $o)] : ((((('const/sets/FINITE' @ X1 @ X3)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)) => ($true = (('const/sets/FINITE' @ 'type/pair/prod' @ X0 @ X1 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X0 @ X1 @ (^[Y0 : 'type/pair/prod' @ X0 @ X1]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X0 @ (^[Y2 : X0]: ('const/sets/SETSPEC' @ 'type/pair/prod' @ X0 @ X1 @ Y0 @ (('const/sets/IN' @ X0 @ Y2 @ X2) & ('const/sets/IN' @ X1 @ Y1 @ X3)) @ ('const/pair/,' @ X0 @ X1 @ Y2 @ Y1))))))))))))),
% 0.27/0.37 inference(fool_elimination,[],[f6])).
% 0.27/0.37 thf(f8,plain,(
% 0.27/0.37 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X1 > X2 > X0),X4 : (X1 > $o),X5 : (X1 > X2 > $o)] : (($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X2 @ (^[Y1 : X2]: (?? @ X1 @ (^[Y2 : X1]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y2 @ X4) & ('const/sets/IN' @ X2 @ Y1 @ (X5 @ Y2))) @ (X3 @ Y2 @ Y1))))))))))) | (? [X6 : X1] : (((('const/sets/FINITE' @ X2 @ (X5 @ X6))) != $true) & ((('const/sets/IN' @ X1 @ X6 @ X4)) = $true)) | ((('const/sets/FINITE' @ X1 @ X4)) != $true)))),
% 0.27/0.37 inference(ennf_transformation,[],[f5])).
% 0.27/0.37 thf(f9,plain,(
% 0.27/0.37 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X1 > X2 > X0),X4 : (X1 > $o),X5 : (X1 > X2 > $o)] : (($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X2 @ (^[Y1 : X2]: (?? @ X1 @ (^[Y2 : X1]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y2 @ X4) & ('const/sets/IN' @ X2 @ Y1 @ (X5 @ Y2))) @ (X3 @ Y2 @ Y1))))))))))) | ? [X6 : X1] : (((('const/sets/FINITE' @ X2 @ (X5 @ X6))) != $true) & ((('const/sets/IN' @ X1 @ X6 @ X4)) = $true)) | ((('const/sets/FINITE' @ X1 @ X4)) != $true))),
% 0.27/0.37 inference(flattening,[],[f8])).
% 0.27/0.37 thf(f10,plain,(
% 0.27/0.37 ? [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > $o)] : (($true != (('const/sets/FINITE' @ 'type/pair/prod' @ X0 @ X1 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X0 @ X1 @ (^[Y0 : 'type/pair/prod' @ X0 @ X1]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X0 @ (^[Y2 : X0]: ('const/sets/SETSPEC' @ 'type/pair/prod' @ X0 @ X1 @ Y0 @ (('const/sets/IN' @ X0 @ Y2 @ X2) & ('const/sets/IN' @ X1 @ Y1 @ X3)) @ ('const/pair/,' @ X0 @ X1 @ Y2 @ Y1))))))))))) & (((('const/sets/FINITE' @ X1 @ X3)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)))),
% 0.27/0.37 inference(ennf_transformation,[],[f7])).
% 0.27/0.37 thf(f11,plain,(
% 0.27/0.37 ? [X0 : $tType,X1 : $tType,X2 : (X0 > $o),X3 : (X1 > $o)] : (($true != (('const/sets/FINITE' @ 'type/pair/prod' @ X0 @ X1 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ X0 @ X1 @ (^[Y0 : 'type/pair/prod' @ X0 @ X1]: (?? @ X1 @ (^[Y1 : X1]: (?? @ X0 @ (^[Y2 : X0]: ('const/sets/SETSPEC' @ 'type/pair/prod' @ X0 @ X1 @ Y0 @ (('const/sets/IN' @ X0 @ Y2 @ X2) & ('const/sets/IN' @ X1 @ Y1 @ X3)) @ ('const/pair/,' @ X0 @ X1 @ Y2 @ Y1))))))))))) & ((('const/sets/FINITE' @ X1 @ X3)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true))),
% 0.27/0.37 inference(flattening,[],[f10])).
% 0.27/0.37 thf(f12,plain,(
% 0.27/0.37 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : (X1 > X2 > X0),X4 : (X1 > $o),X5 : (X1 > X2 > $o)] : (($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X2 @ (^[Y1 : X2]: (?? @ X1 @ (^[Y2 : X1]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y2 @ X4) & ('const/sets/IN' @ X2 @ Y1 @ (X5 @ Y2))) @ (X3 @ Y2 @ Y1))))))))))) | (($true != (('const/sets/FINITE' @ X2 @ (X5 @ (sK0 @ X1 @ X2 @ X5 @ X4))))) & ($true = (('const/sets/IN' @ X1 @ (sK0 @ X1 @ X2 @ X5 @ X4) @ X4)))) | ((('const/sets/FINITE' @ X1 @ X4)) != $true))),
% 0.27/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X6,sK0 @ X1 @ X2 @ X5 @ X4)],[f9])).
% 0.27/0.37 thf(f13,plain,(
% 0.27/0.37 ($true != (('const/sets/FINITE' @ 'type/pair/prod' @ sK1 @ sK2 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ sK1 @ sK2 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK2]: (?? @ sK2 @ (^[Y1 : sK2]: (?? @ sK1 @ (^[Y2 : sK1]: ('const/sets/SETSPEC' @ 'type/pair/prod' @ sK1 @ sK2 @ Y0 @ (('const/sets/IN' @ sK1 @ Y2 @ sK3) & ('const/sets/IN' @ sK2 @ Y1 @ sK4)) @ ('const/pair/,' @ sK1 @ sK2 @ Y2 @ Y1))))))))))) & ($true = (('const/sets/FINITE' @ sK2 @ sK4))) & ($true = (('const/sets/FINITE' @ sK1 @ sK3)))),
% 0.27/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f11])).
% 0.27/0.37 thf(f15,plain,(
% 0.27/0.37 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : (X1 > X2 > X0),X4 : (X1 > $o),X5 : (X1 > X2 > $o)] : (((('const/sets/FINITE' @ X1 @ X4)) != $true) | ($true != (('const/sets/FINITE' @ X2 @ (X5 @ (sK0 @ X1 @ X2 @ X5 @ X4))))) | ($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X2 @ (^[Y1 : X2]: (?? @ X1 @ (^[Y2 : X1]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X1 @ Y2 @ X4) & ('const/sets/IN' @ X2 @ Y1 @ (X5 @ Y2))) @ (X3 @ Y2 @ Y1)))))))))))) )),
% 0.27/0.37 inference(cnf_transformation,[],[f12])).
% 0.27/0.37 thf(f16,plain,(
% 0.27/0.37 ($true = (('const/sets/FINITE' @ sK1 @ sK3)))),
% 0.27/0.37 inference(cnf_transformation,[],[f13])).
% 0.27/0.37 thf(f17,plain,(
% 0.27/0.37 ($true = (('const/sets/FINITE' @ sK2 @ sK4)))),
% 0.27/0.37 inference(cnf_transformation,[],[f13])).
% 0.27/0.37 thf(f18,plain,(
% 0.27/0.37 ($true != (('const/sets/FINITE' @ 'type/pair/prod' @ sK1 @ sK2 @ ('const/sets/GSPEC' @ 'type/pair/prod' @ sK1 @ sK2 @ (^[Y0 : 'type/pair/prod' @ sK1 @ sK2]: (?? @ sK2 @ (^[Y1 : sK2]: (?? @ sK1 @ (^[Y2 : sK1]: ('const/sets/SETSPEC' @ 'type/pair/prod' @ sK1 @ sK2 @ Y0 @ (('const/sets/IN' @ sK1 @ Y2 @ sK3) & ('const/sets/IN' @ sK2 @ Y1 @ sK4)) @ ('const/pair/,' @ sK1 @ sK2 @ Y2 @ Y1)))))))))))),
% 0.27/0.37 inference(cnf_transformation,[],[f13])).
% 0.27/0.37 thf(f33,plain,(
% 0.27/0.37 ( ! [X0 : $tType,X2 : $tType,X3 : (sK1 > X0 > X2),X1 : (sK1 > X0 > $o)] : (($true != $true) | ($true != (('const/sets/FINITE' @ X0 @ (X1 @ (sK0 @ sK1 @ X0 @ X1 @ sK3))))) | ($true = (('const/sets/FINITE' @ X2 @ ('const/sets/GSPEC' @ X2 @ (^[Y0 : X2]: (?? @ X0 @ (^[Y1 : X0]: (?? @ sK1 @ (^[Y2 : sK1]: ('const/sets/SETSPEC' @ X2 @ Y0 @ (('const/sets/IN' @ sK1 @ Y2 @ sK3) & ('const/sets/IN' @ X0 @ Y1 @ (X1 @ Y2))) @ (X3 @ Y2 @ Y1)))))))))))) )),
% 0.27/0.37 inference(constrained_superposition,[],[f15,f16])).
% 0.27/0.37 thf(f39,plain,(
% 0.27/0.37 ( ! [X0 : $tType,X2 : $tType,X3 : (sK1 > X0 > X2),X1 : (sK1 > X0 > $o)] : (($true != (('const/sets/FINITE' @ X0 @ (X1 @ (sK0 @ sK1 @ X0 @ X1 @ sK3))))) | ($true = (('const/sets/FINITE' @ X2 @ ('const/sets/GSPEC' @ X2 @ (^[Y0 : X2]: (?? @ X0 @ (^[Y1 : X0]: (?? @ sK1 @ (^[Y2 : sK1]: ('const/sets/SETSPEC' @ X2 @ Y0 @ (('const/sets/IN' @ sK1 @ Y2 @ sK3) & ('const/sets/IN' @ X0 @ Y1 @ (X1 @ Y2))) @ (X3 @ Y2 @ Y1)))))))))))) )),
% 0.27/0.37 inference(trivial_inequality_removal,[],[f33])).
% 0.27/0.37 thf(f64,plain,(
% 0.27/0.37 ( ! [X0 : $tType,X1 : (sK1 > sK2 > X0)] : (($true != $true) | ($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ sK2 @ (^[Y1 : sK2]: (?? @ sK1 @ (^[Y2 : sK1]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ sK1 @ Y2 @ sK3) & ('const/sets/IN' @ sK2 @ Y1 @ ((^[Y3 : sK1]: ((^[Y4 : sK2]: (sK4 @ ((^[Y5 : sK1]: ((^[Y6 : sK2]: (Y6)))) @ Y3 @ Y4))))) @ Y2))) @ (X1 @ Y2 @ Y1)))))))))))) )),
% 0.27/0.37 inference(constrained_superposition,[],[f39,f17])).
% 0.27/0.37 thf(f67,plain,(
% 0.27/0.37 ( ! [X0 : $tType,X1 : (sK1 > sK2 > X0)] : (($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ sK2 @ (^[Y1 : sK2]: (?? @ sK1 @ (^[Y2 : sK1]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ sK1 @ Y2 @ sK3) & ('const/sets/IN' @ sK2 @ Y1 @ ((^[Y3 : sK1]: ((^[Y4 : sK2]: (sK4 @ ((^[Y5 : sK1]: ((^[Y6 : sK2]: (Y6)))) @ Y3 @ Y4))))) @ Y2))) @ (X1 @ Y2 @ Y1)))))))))))) )),
% 0.27/0.37 inference(trivial_inequality_removal,[],[f64])).
% 0.27/0.37 thf(f68,plain,(
% 0.27/0.37 ( ! [X0 : $tType,X1 : (sK1 > sK2 > X0)] : (($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ sK2 @ (^[Y1 : sK2]: (?? @ sK1 @ (^[Y2 : sK1]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ sK1 @ Y2 @ sK3) & ('const/sets/IN' @ sK2 @ Y1 @ sK4)) @ (X1 @ Y2 @ Y1)))))))))))) )),
% 0.27/0.37 inference(beta-eta_normalization,[],[f67])).
% 0.27/0.37 thf(f81,plain,(
% 0.27/0.37 ( ! [X0 : (sK1 > sK2 > sK1)] : (($true != $true) | ((^[Y0 : 'type/pair/prod' @ sK1 @ sK2]: ((^[Y1 : sK2]: ((^[Y2 : sK1]: (Y2)))))) != (^[Y0 : 'type/pair/prod' @ sK1 @ sK2]: ((^[Y1 : sK2]: ((^[Y2 : sK1]: (X0 @ Y2 @ Y1)))))))) )),
% 0.27/0.37 inference(constrained_superposition,[],[f18,f68])).
% 0.27/0.37 thf(f82,plain,(
% 0.27/0.37 ( ! [X0 : (sK1 > sK2 > sK1)] : (((^[Y0 : 'type/pair/prod' @ sK1 @ sK2]: ((^[Y1 : sK2]: ((^[Y2 : sK1]: (Y2)))))) != (^[Y0 : 'type/pair/prod' @ sK1 @ sK2]: ((^[Y1 : sK2]: ((^[Y2 : sK1]: (X0 @ Y2 @ Y1)))))))) )),
% 0.27/0.37 inference(trivial_inequality_removal,[],[f81])).
% 0.27/0.37 thf(f91,plain,(
% 0.27/0.37 $false),
% 0.27/0.37 inference(equality_resolution,[],[f82])).
% 0.27/0.37 % SZS output end Proof for theBenchmark
% 0.27/0.37 % (495361)------------------------------
% 0.27/0.37 % (495361)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.37 % (495361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.37 % (495361)CaDiCaL version: 2.1.3
% 0.27/0.37 % (495361)Termination reason: Refutation
% 0.27/0.37 % (495361)Time elapsed: 0.014 s
% 0.27/0.37 % (495361)Peak memory usage: 12 MB
% 0.27/0.37 % (495361)Instructions burned: 25 (million)
% 0.27/0.37 % (495350)Success in time 0.042 s
% 0.27/0.37 % Vampire exiting
%------------------------------------------------------------------------------