%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU597^2 : 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 : n002.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 08:32:36 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU597^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n002.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:58:53 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.20/0.26 % (1323680)Will run a generic schedule for satisfiability detection.
% 0.20/0.26 % (1323685)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3151682934_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.26 % Exception at run slice level
% 0.20/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.26 % (1323686)% WARNING: option uhcvi not known.
% 0.20/0.26 % (1323686)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=882479406:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.26 % (1323689)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=765786189:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.26 % (1323687)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1531864539:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.26 % (1323688)dis+10_1_sil=32000:sp=arity:random_seed=469786159:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.26 % (1323690)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3097815394:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.26 % (1323691)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=612671427:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.26 % (1323686)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.26 % (1323689)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.26 % (1323686)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.26 % (1323693)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2487123161:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.26 % Exception at run slice level
% 0.20/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.26 % (1323689) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1323680-1323689"...
% 0.20/0.26 % (1323688) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1323680-1323688"...
% 0.20/0.26 % (1323686) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1323680-1323686"...
% 0.20/0.26 % (1323691) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1323680-1323691"...
% 0.20/0.26 % (1323690) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1323680-1323690"...
% 0.20/0.26 % (1323687) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1323680-1323687"...
% 0.20/0.26 % (1323689)...printing done.
% 0.20/0.26 % (1323688)...printing done.
% 0.20/0.26 % (1323686)...printing done.
% 0.20/0.26 % (1323691)...printing done.
% 0.20/0.26 % (1323690)...printing done.
% 0.20/0.26 % (1323686)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% 0.20/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.26 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.26 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.20/0.26 thf(func_def_2, type, subsetI2: $o).
% 0.20/0.26 thf(func_def_4, type, binintersect: ($i > $i > $i)).
% 0.20/0.26 thf(func_def_5, type, binintersectER: $o).
% 0.20/0.26 thf(func_def_6, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.26 thf(func_def_7, type, vIMP: ($o > $o > $o)).
% 0.20/0.26 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_10, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.26 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.20/0.26 thf(func_def_17, type, sK2: ($i > $i > $i)).
% 0.20/0.26 thf(f1,axiom,(
% 0.20/0.26 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 0.20/0.26 thf(f2,axiom,(
% 0.20/0.26 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER)).
% 0.20/0.26 thf(f3,conjecture,(
% 0.20/0.26 subsetI2 => (binintersectER => ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub)).
% 0.20/0.26 thf(f4,negated_conjecture,(
% 0.20/0.26 ~(subsetI2 => (binintersectER => ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1)))),
% 0.20/0.26 inference(negated_conjecture,[status(cth)],[f3])).
% 0.20/0.26 thf(f5,plain,(
% 0.20/0.26 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.20/0.26 inference(rectify,[],[f1])).
% 0.20/0.26 thf(f6,plain,(
% 0.20/0.26 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 0.20/0.26 inference(fool_elimination,[],[f5])).
% 0.20/0.26 thf(f7,plain,(
% 0.20/0.26 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 0.20/0.26 inference(rectify,[],[f2])).
% 0.20/0.26 thf(f8,plain,(
% 0.20/0.26 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))))))),
% 0.20/0.26 inference(fool_elimination,[],[f7])).
% 0.20/0.26 thf(f9,plain,(
% 0.20/0.26 ~(subsetI2 => (binintersectER => ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1)))),
% 0.20/0.26 inference(rectify,[],[f4])).
% 0.20/0.26 thf(f10,plain,(
% 0.20/0.26 ~((subsetI2 = $true) => ((binintersectER = $true) => ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X1)) = $true)))),
% 0.20/0.26 inference(fool_elimination,[],[f9])).
% 0.20/0.26 thf(f11,plain,(
% 0.20/0.26 (? [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X1)) != $true) & (binintersectER = $true)) & (subsetI2 = $true)),
% 0.20/0.26 inference(ennf_transformation,[],[f10])).
% 0.20/0.26 thf(f12,plain,(
% 0.20/0.26 ? [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X1)) != $true) & (binintersectER = $true) & (subsetI2 = $true)),
% 0.20/0.26 inference(flattening,[],[f11])).
% 0.20/0.26 thf(f13,plain,(
% 0.20/0.26 ($true != ((subset @ (binintersect @ sK0 @ sK1) @ sK1))) & (binintersectER = $true) & (subsetI2 = $true)),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12])).
% 0.20/0.26 thf(f14,plain,(
% 0.20/0.26 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 0.20/0.26 inference(cnf_transformation,[],[f6])).
% 0.20/0.26 thf(f15,plain,(
% 0.20/0.26 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))))))),
% 0.20/0.26 inference(cnf_transformation,[],[f8])).
% 0.20/0.26 thf(f16,plain,(
% 0.20/0.26 (subsetI2 = $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f13])).
% 0.20/0.26 thf(f17,plain,(
% 0.20/0.26 (binintersectER = $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f13])).
% 0.20/0.26 thf(f18,plain,(
% 0.20/0.26 ($true != ((subset @ (binintersect @ sK0 @ sK1) @ sK1)))),
% 0.20/0.26 inference(cnf_transformation,[],[f13])).
% 0.20/0.26 thf(f20,definition,(
% 0.20/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.26 thf(f21,plain,(
% 0.20/0.26 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))) = $true)),
% 0.20/0.26 inference(definition_unfolding,[],[f14,f16])).
% 0.20/0.26 thf(f22,plain,(
% 0.20/0.26 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))))) = $true)),
% 0.20/0.26 inference(definition_unfolding,[],[f15,f17])).
% 0.20/0.26 thf(f23,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))) @ X1)))) )),
% 0.20/0.26 inference(pi_proxy_clausification,[],[f22])).
% 0.20/0.26 thf(f24,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y0))))))))) )),
% 0.20/0.26 inference(beta-eta_normalization,[],[f23])).
% 0.20/0.26 thf(f25,plain,(
% 0.20/0.26 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y0))))) @ X2)))) )),
% 0.20/0.26 inference(pi_proxy_clausification,[],[f24])).
% 0.20/0.26 thf(f26,plain,(
% 0.20/0.26 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ X2))))))) )),
% 0.20/0.26 inference(beta-eta_normalization,[],[f25])).
% 0.20/0.26 thf(f27,plain,(
% 0.20/0.26 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ X2))) @ X3)))) )),
% 0.20/0.26 inference(pi_proxy_clausification,[],[f26])).
% 0.20/0.26 thf(f28,plain,(
% 0.20/0.26 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ (binintersect @ X3 @ X2)) => (in @ X1 @ X2))))) )),
% 0.20/0.26 inference(beta-eta_normalization,[],[f27])).
% 0.20/0.26 thf(f29,plain,(
% 0.20/0.26 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (binintersect @ X3 @ X2)))) | ($true = ((in @ X1 @ X2)))) )),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f28])).
% 0.20/0.26 thf(f30,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))) @ X1)))) )),
% 0.20/0.26 inference(pi_proxy_clausification,[],[f21])).
% 0.20/0.26 thf(f31,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))))))) )),
% 0.20/0.26 inference(beta-eta_normalization,[],[f30])).
% 0.20/0.26 thf(f32,plain,(
% 0.20/0.26 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))) @ X2)))) )),
% 0.20/0.26 inference(pi_proxy_clausification,[],[f31])).
% 0.20/0.26 thf(f33,plain,(
% 0.20/0.26 ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => (subset @ X2 @ X1))))) )),
% 0.20/0.26 inference(beta-eta_normalization,[],[f32])).
% 0.20/0.26 thf(f34,plain,(
% 0.20/0.26 ( ! [X2 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f33])).
% 0.20/0.26 thf(f35,plain,(
% 0.20/0.26 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK2 @ X1 @ X2)))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.20/0.26 inference(sigma_proxy_clausification,[],[f34])).
% 0.20/0.26 thf(f36,plain,(
% 0.20/0.26 ( ! [X2 : $i,X1 : $i] : (($false = (((in @ (sK2 @ X1 @ X2) @ X2) => (in @ (sK2 @ X1 @ X2) @ X1)))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.20/0.26 inference(beta-eta_normalization,[],[f35])).
% 0.20/0.26 thf(f37,plain,(
% 0.20/0.26 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ (sK2 @ X1 @ X2) @ X1))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f36])).
% 0.20/0.26 thf(f38,plain,(
% 0.20/0.26 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK2 @ X1 @ X2) @ X2))) | ($true = ((subset @ X2 @ X1)))) )),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f36])).
% 0.20/0.26 thf(f41,plain,(
% 0.20/0.26 ($true != $true) | (((subset @ (binintersect @ sK0 @ sK1) @ sK1)) = $false)),
% 0.20/0.26 inference(constrained_superposition,[],[f18,f20])).
% 0.20/0.26 thf(f47,plain,(
% 0.20/0.26 (((subset @ (binintersect @ sK0 @ sK1) @ sK1)) = $false)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f41])).
% 0.20/0.26 thf(f57,plain,(
% 0.20/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($true = ((in @ (sK2 @ X0 @ (binintersect @ X1 @ X2)) @ X2))) | ($true = ((subset @ (binintersect @ X1 @ X2) @ X0)))) )),
% 0.20/0.26 inference(constrained_superposition,[],[f29,f38])).
% 0.20/0.26 thf(f61,plain,(
% 0.20/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK2 @ X0 @ (binintersect @ X1 @ X2)) @ X2))) | ($true = ((subset @ (binintersect @ X1 @ X2) @ X0)))) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f57])).
% 0.20/0.26 thf(f68,plain,(
% 0.20/0.26 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = ((subset @ (binintersect @ X1 @ X0) @ X0))) | ($true = ((subset @ (binintersect @ X1 @ X0) @ X0)))) )),
% 0.20/0.26 inference(constrained_superposition,[],[f37,f61])).
% 0.20/0.26 thf(f69,plain,(
% 0.20/0.26 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = ((subset @ (binintersect @ X1 @ X0) @ X0)))) )),
% 0.20/0.26 inference(duplicate_literal_removal,[],[f68])).
% 0.20/0.26 thf(f70,plain,(
% 0.20/0.26 ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ (binintersect @ X1 @ X0) @ X0)))) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f69])).
% 0.20/0.26 thf(f77,plain,(
% 0.20/0.26 ($true = $false)),
% 0.20/0.26 inference(constrained_superposition,[],[f47,f70])).
% 0.20/0.26 thf(f78,plain,(
% 0.20/0.26 $false),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f77])).
% 0.20/0.26 % SZS output end Proof for theBenchmark
% 0.20/0.26 % (1323686)------------------------------
% 0.20/0.26 % (1323686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (1323686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (1323686)CaDiCaL version: 2.1.3
% 0.20/0.26 % (1323686)Termination reason: Refutation
% 0.20/0.26 % (1323686)Time elapsed: 0.005 s
% 0.20/0.26 % (1323686)Peak memory usage: 12 MB
% 0.20/0.26 % (1323686)Instructions burned: 7 (million)
% 0.20/0.26 % (1323680)Success in time 0.036 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------