%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU625^2 : 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 : n015.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 08:32:44 AM UTC 2026
% Result : Theorem 1.56s 0.47s
% Output : Refutation 1.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU625^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n015.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 14:02:18 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
% 1.56/0.47 % (3569254)Will run a generic schedule for satisfiability detection.
% 1.56/0.47 % (3569274)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3561782235:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.56/0.47 % (3569274)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.56/0.47 % (3569271)% WARNING: option uhcvi not known.
% 1.56/0.47 % (3569271)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=595284:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.56/0.47 % (3569272)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1798503663:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.56/0.47 % (3569270)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2319401330_2999 on theBenchmark for (2999ds/0Mi)
% 1.56/0.47 % (3569275)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3087983164:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.56/0.47 % (3569271)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.56/0.47 % (3569276)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=130826008:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.56/0.47 % (3569271)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.56/0.47 % Exception at run slice level
% 1.56/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.56/0.47 % (3569273)dis+10_1_sil=32000:sp=arity:random_seed=3811475901:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.56/0.47 % (3569284)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2711137021:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.56/0.47 % Exception at run slice level
% 1.56/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.56/0.47 % (3569274)Instruction limit reached!
% 1.56/0.47 % (3569274)------------------------------
% 1.56/0.47 % (3569274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.47 % (3569274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.47 % (3569274)CaDiCaL version: 2.1.3
% 1.56/0.47 % (3569274)Termination reason: Instruction limit
% 1.56/0.47 % (3569274)Termination phase: Saturation
% 1.56/0.47 % (3569274)Time elapsed: 0.030 s
% 1.56/0.47 % (3569274)Peak memory usage: 12 MB
% 1.56/0.47 % (3569274)Instructions burned: 116 (million)
% 1.56/0.47 % (3569292)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3699361717:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.56/0.47 % (3569292)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.56/0.47 % (3569292)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.56/0.47 % (3569291)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3947991939:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.56/0.47 % (3569273)Instruction limit reached!
% 1.56/0.47 % (3569273)------------------------------
% 1.56/0.47 % (3569273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.47 % (3569273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.47 % (3569273)CaDiCaL version: 2.1.3
% 1.56/0.47 % (3569273)Termination reason: Instruction limit
% 1.56/0.47 % (3569273)Termination phase: Saturation
% 1.56/0.47 % (3569273)Time elapsed: 0.050 s
% 1.56/0.47 % (3569273)Peak memory usage: 12 MB
% 1.56/0.47 % (3569273)Instructions burned: 105 (million)
% 1.56/0.47 % (3569275)Instruction limit reached!
% 1.56/0.47 % (3569275)------------------------------
% 1.56/0.47 % (3569275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.47 % (3569275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.47 % (3569275)CaDiCaL version: 2.1.3
% 1.56/0.47 % (3569275)Termination reason: Instruction limit
% 1.56/0.47 % (3569275)Termination phase: Saturation
% 1.56/0.47 % (3569275)Time elapsed: 0.063 s
% 1.56/0.47 % (3569275)Peak memory usage: 12 MB
% 1.56/0.47 % (3569275)Instructions burned: 132 (million)
% 1.56/0.47 % (3569302)ott-21_1_sil=16000:fs=off:random_seed=3544043052:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.56/0.47 % (3569276)Instruction limit reached!
% 1.56/0.47 % (3569276)------------------------------
% 1.56/0.47 % (3569276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.47 % (3569276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.47 % (3569276)CaDiCaL version: 2.1.3
% 1.56/0.47 % (3569276)Termination reason: Instruction limit
% 1.56/0.47 % (3569276)Termination phase: Saturation
% 1.56/0.47 % (3569276)Time elapsed: 0.084 s
% 1.56/0.47 % (3569276)Peak memory usage: 12 MB
% 1.56/0.47 % (3569276)Instructions burned: 159 (million)
% 1.56/0.47 % (3569305)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3848869151:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.56/0.47 % (3569291)Instruction limit reached!
% 1.56/0.47 % (3569291)------------------------------
% 1.56/0.47 % (3569291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.47 % (3569291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.47 % (3569291)CaDiCaL version: 2.1.3
% 1.56/0.47 % (3569291)Termination reason: Instruction limit
% 1.56/0.47 % (3569291)Termination phase: Saturation
% 1.56/0.47 % (3569291)Time elapsed: 0.063 s
% 1.56/0.47 % (3569291)Peak memory usage: 12 MB
% 1.56/0.47 % (3569291)Instructions burned: 132 (million)
% 1.56/0.47 % (3569312)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2125427751:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.56/0.47 % Exception at run slice level
% 1.56/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.56/0.47 % (3569319)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3456689430:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.56/0.47 % (3569323)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2870019244:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.56/0.47 % Exception at run slice level
% 1.56/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.56/0.47 % (3569328)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1877098311:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 1.56/0.47 % (3569328)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.56/0.47 % (3569302)Instruction limit reached!
% 1.56/0.47 % (3569302)------------------------------
% 1.56/0.47 % (3569302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.47 % (3569302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.47 % (3569302)CaDiCaL version: 2.1.3
% 1.56/0.47 % (3569302)Termination reason: Instruction limit
% 1.56/0.47 % (3569302)Termination phase: Saturation
% 1.56/0.47 % (3569302)Time elapsed: 0.084 s
% 1.56/0.47 % (3569302)Peak memory usage: 12 MB
% 1.56/0.47 % (3569302)Instructions burned: 188 (million)
% 1.56/0.47 % (3569335)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1170131333:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 1.56/0.47 % (3569335)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.56/0.47 % (3569271) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3569254-3569271"...
% 1.56/0.47 % (3569271)...printing done.
% 1.56/0.47 % (3569271)Refutation found. Thanks to Tanya!
% 1.56/0.47 % SZS status Theorem for theBenchmark
% 1.56/0.47 % SZS output start Proof for theBenchmark
% 1.56/0.47 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 1.56/0.47 thf(func_def_0, type, in: ($i > $i > $o)).
% 1.56/0.47 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 1.56/0.47 thf(func_def_3, type, subset: ($i > $i > $o)).
% 1.56/0.47 thf(func_def_4, type, subsetI2: $o).
% 1.56/0.47 thf(func_def_6, type, subsetE: $o).
% 1.56/0.47 thf(func_def_7, type, binunion: ($i > $i > $i)).
% 1.56/0.47 thf(func_def_8, type, binunionLsub: $o).
% 1.56/0.47 thf(func_def_9, type, binunionRsub: $o).
% 1.56/0.47 thf(func_def_10, type, upairset2E: $o).
% 1.56/0.47 thf(func_def_11, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.56/0.47 thf(func_def_12, type, vIMP: ($o > $o > $o)).
% 1.56/0.47 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 1.56/0.47 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 1.56/0.47 thf(func_def_15, type, db2: !>[X0: $tType]:(X0)).
% 1.56/0.47 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.56/0.47 thf(func_def_17, type, vOR: ($o > $o > $o)).
% 1.56/0.47 thf(func_def_18, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.56/0.47 thf(func_def_25, type, vNOT: ($o > $o)).
% 1.56/0.47 thf(func_def_26, type, sK4: ($i > $i > $i)).
% 1.56/0.47 thf(f1,axiom,(
% 1.56/0.47 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.56/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 1.56/0.47 thf(f2,axiom,(
% 1.56/0.47 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 1.56/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
% 1.56/0.47 thf(f3,axiom,(
% 1.56/0.47 (binunionLsub = ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)))),
% 1.56/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub)).
% 1.56/0.47 thf(f4,axiom,(
% 1.56/0.47 (binunionRsub = ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)))),
% 1.56/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub)).
% 1.56/0.47 thf(f5,axiom,(
% 1.56/0.47 (upairset2E = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X2 = X1) | (X2 = X0))))),
% 1.56/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E)).
% 1.56/0.47 thf(f6,conjecture,(
% 1.56/0.47 subsetI2 => (subsetE => (binunionLsub => (binunionRsub => (upairset2E => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1))))))))),
% 1.56/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion)).
% 1.56/0.47 thf(f7,negated_conjecture,(
% 1.56/0.47 ~(subsetI2 => (subsetE => (binunionLsub => (binunionRsub => (upairset2E => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1)))))))))),
% 1.56/0.47 inference(negated_conjecture,[status(cth)],[f6])).
% 1.56/0.47 thf(f8,plain,(
% 1.56/0.47 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 1.56/0.47 inference(rectify,[],[f1])).
% 1.56/0.47 thf(f9,plain,(
% 1.56/0.47 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 1.56/0.47 inference(fool_elimination,[],[f8])).
% 1.56/0.47 thf(f10,plain,(
% 1.56/0.47 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 1.56/0.47 inference(rectify,[],[f2])).
% 1.56/0.47 thf(f11,plain,(
% 1.56/0.47 (subsetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))))))),
% 1.56/0.47 inference(fool_elimination,[],[f10])).
% 1.56/0.47 thf(f12,plain,(
% 1.56/0.47 (binunionLsub = ! [X0 : $i,X1 : $i] : (subset @ X0 @ (binunion @ X0 @ X1)))),
% 1.56/0.47 inference(rectify,[],[f3])).
% 1.56/0.47 thf(f13,plain,(
% 1.56/0.47 (binunionLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0))))))))),
% 1.56/0.47 inference(fool_elimination,[],[f12])).
% 1.56/0.47 thf(f14,plain,(
% 1.56/0.47 (binunionRsub = ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)))),
% 1.56/0.47 inference(rectify,[],[f4])).
% 1.56/0.47 thf(f15,plain,(
% 1.56/0.47 (binunionRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0))))))))),
% 1.56/0.47 inference(fool_elimination,[],[f14])).
% 1.56/0.47 thf(f16,plain,(
% 1.56/0.47 (upairset2E = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X2 = X1) | (X2 = X0))))),
% 1.56/0.47 inference(rectify,[],[f5])).
% 1.56/0.47 thf(f17,plain,(
% 1.56/0.47 (upairset2E = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0)))))))))))),
% 1.56/0.47 inference(fool_elimination,[],[f16])).
% 1.56/0.47 thf(f18,plain,(
% 1.56/0.47 ~(subsetI2 => (subsetE => (binunionLsub => (binunionRsub => (upairset2E => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1)))))))))),
% 1.56/0.47 inference(rectify,[],[f7])).
% 1.56/0.47 thf(f19,plain,(
% 1.56/0.47 ~((subsetI2 = $true) => ((subsetE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((upairset2E = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => (((subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1))) = $true))))))))),
% 1.56/0.47 inference(fool_elimination,[],[f18])).
% 1.56/0.47 thf(f20,plain,(
% 1.56/0.47 ((((? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1))) != $true) & (((in @ X3 @ X1)) = $true)) & (((in @ X2 @ X0)) = $true)) & (upairset2E = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (subsetE = $true)) & (subsetI2 = $true)),
% 1.56/0.47 inference(ennf_transformation,[],[f19])).
% 1.56/0.47 thf(f21,plain,(
% 1.56/0.47 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X0 @ X1))) != $true) & (((in @ X3 @ X1)) = $true)) & (((in @ X2 @ X0)) = $true)) & (upairset2E = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (subsetE = $true) & (subsetI2 = $true)),
% 1.56/0.47 inference(flattening,[],[f20])).
% 1.56/0.47 thf(f22,plain,(
% 1.56/0.47 ((($true != ((subset @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ (binunion @ sK0 @ sK1)))) & ($true = ((in @ sK3 @ sK1)))) & ($true = ((in @ sK2 @ sK0)))) & (upairset2E = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (subsetE = $true) & (subsetI2 = $true)),
% 1.56/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f21])).
% 1.56/0.47 thf(f23,plain,(
% 1.56/0.47 (subsetI2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))))),
% 1.56/0.47 inference(cnf_transformation,[],[f9])).
% 1.56/0.47 thf(f24,plain,(
% 1.56/0.47 (subsetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))))))),
% 1.56/0.47 inference(cnf_transformation,[],[f11])).
% 1.56/0.47 thf(f25,plain,(
% 1.56/0.47 (binunionLsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0))))))))),
% 1.56/0.47 inference(cnf_transformation,[],[f13])).
% 1.56/0.47 thf(f26,plain,(
% 1.56/0.47 (binunionRsub = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0))))))))),
% 1.56/0.47 inference(cnf_transformation,[],[f15])).
% 1.56/0.47 thf(f27,plain,(
% 1.56/0.47 (upairset2E = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0)))))))))))),
% 1.56/0.47 inference(cnf_transformation,[],[f17])).
% 1.56/0.47 thf(f28,plain,(
% 1.56/0.47 (subsetI2 = $true)),
% 1.56/0.47 inference(cnf_transformation,[],[f22])).
% 1.56/0.47 thf(f29,plain,(
% 1.56/0.47 (subsetE = $true)),
% 1.56/0.47 inference(cnf_transformation,[],[f22])).
% 1.56/0.47 thf(f30,plain,(
% 1.56/0.47 (binunionLsub = $true)),
% 1.56/0.47 inference(cnf_transformation,[],[f22])).
% 1.56/0.47 thf(f31,plain,(
% 1.56/0.47 (binunionRsub = $true)),
% 1.56/0.47 inference(cnf_transformation,[],[f22])).
% 1.56/0.47 thf(f32,plain,(
% 1.56/0.47 (upairset2E = $true)),
% 1.56/0.47 inference(cnf_transformation,[],[f22])).
% 1.56/0.47 thf(f33,plain,(
% 1.56/0.47 ($true = ((in @ sK2 @ sK0)))),
% 1.56/0.47 inference(cnf_transformation,[],[f22])).
% 1.56/0.47 thf(f34,plain,(
% 1.56/0.47 ($true = ((in @ sK3 @ sK1)))),
% 1.56/0.47 inference(cnf_transformation,[],[f22])).
% 1.56/0.47 thf(f35,plain,(
% 1.56/0.47 ($true != ((subset @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ (binunion @ sK0 @ sK1))))),
% 1.56/0.47 inference(cnf_transformation,[],[f22])).
% 1.56/0.47 thf(f37,definition,(
% 1.56/0.47 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.56/0.47 introduced(theory,[fool_exhaustiveness_axiom])).
% 1.56/0.47 thf(f38,plain,(
% 1.56/0.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))))) = $true)),
% 1.56/0.47 inference(definition_unfolding,[],[f23,f28])).
% 1.56/0.47 thf(f39,plain,(
% 1.56/0.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))))) = $true)),
% 1.56/0.47 inference(definition_unfolding,[],[f24,f29])).
% 1.56/0.47 thf(f40,plain,(
% 1.56/0.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0))))))) = $true)),
% 1.56/0.47 inference(definition_unfolding,[],[f25,f30])).
% 1.56/0.47 thf(f41,plain,(
% 1.56/0.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0))))))) = $true)),
% 1.56/0.47 inference(definition_unfolding,[],[f26,f31])).
% 1.56/0.47 thf(f42,plain,(
% 1.56/0.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0)))))))))) = $true)),
% 1.56/0.47 inference(definition_unfolding,[],[f27,f32])).
% 1.56/0.47 thf(f43,plain,(
% 1.56/0.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0)))))))) @ X1)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f42])).
% 1.56/0.47 thf(f44,plain,(
% 1.56/0.47 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y1 = X1) | (Y0 = X1)))))))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f43])).
% 1.56/0.47 thf(f45,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y1 = X1) | (Y0 = X1)))))) @ X2)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f44])).
% 1.56/0.47 thf(f46,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ X2 @ emptyset))) => ((Y0 = X1) | (X2 = X1)))))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f45])).
% 1.56/0.47 thf(f47,plain,(
% 1.56/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ X2 @ emptyset))) => ((Y0 = X1) | (X2 = X1)))) @ X3)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f46])).
% 1.56/0.47 thf(f48,plain,(
% 1.56/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))) => ((X3 = X1) | (X2 = X1)))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f47])).
% 1.56/0.47 thf(f49,plain,(
% 1.56/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))))) | ($true = (((X3 = X1) | (X2 = X1))))) )),
% 1.56/0.47 inference(imp_proxy_clausification,[],[f48])).
% 1.56/0.47 thf(f50,plain,(
% 1.56/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))))) | ($true = ((X2 = X1))) | ($true = ((X3 = X1)))) )),
% 1.56/0.47 inference(or_proxy_clausification,[],[f49])).
% 1.56/0.47 thf(f51,plain,(
% 1.56/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))))) | (X1 = X2) | ($true = ((X3 = X1)))) )),
% 1.56/0.47 inference(equality_proxy_clausification,[],[f50])).
% 1.56/0.47 thf(f52,plain,(
% 1.56/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))))) | (X1 = X2) | (X1 = X3)) )),
% 1.56/0.47 inference(equality_proxy_clausification,[],[f51])).
% 1.56/0.47 thf(f53,plain,(
% 1.56/0.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0))))) @ X1)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f41])).
% 1.56/0.47 thf(f54,plain,(
% 1.56/0.47 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (subset @ X1 @ (binunion @ Y0 @ X1))))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f53])).
% 1.56/0.47 thf(f55,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (subset @ X1 @ (binunion @ Y0 @ X1))) @ X2)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f54])).
% 1.56/0.47 thf(f56,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($true = ((subset @ X1 @ (binunion @ X2 @ X1))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f55])).
% 1.56/0.47 thf(f57,plain,(
% 1.56/0.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0))))) @ X1)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f40])).
% 1.56/0.47 thf(f58,plain,(
% 1.56/0.47 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (binunion @ Y0 @ X1))))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f57])).
% 1.56/0.47 thf(f59,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (subset @ Y0 @ (binunion @ Y0 @ X1))) @ X2)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f58])).
% 1.56/0.47 thf(f60,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($true = ((subset @ X2 @ (binunion @ X2 @ X1))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f59])).
% 1.56/0.47 thf(f61,plain,(
% 1.56/0.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1)))))))) @ X1)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f39])).
% 1.56/0.47 thf(f62,plain,(
% 1.56/0.47 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((in @ X1 @ Y1) => (in @ X1 @ Y0)))))))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f61])).
% 1.56/0.47 thf(f63,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((in @ X1 @ Y1) => (in @ X1 @ Y0)))))) @ X2)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f62])).
% 1.56/0.47 thf(f64,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ X2) => ((in @ X1 @ Y0) => (in @ X1 @ X2)))))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f63])).
% 1.56/0.47 thf(f65,plain,(
% 1.56/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((subset @ Y0 @ X2) => ((in @ X1 @ Y0) => (in @ X1 @ X2)))) @ X3)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f64])).
% 1.56/0.47 thf(f66,plain,(
% 1.56/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((subset @ X3 @ X2) => ((in @ X1 @ X3) => (in @ X1 @ X2)))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f65])).
% 1.56/0.47 thf(f67,plain,(
% 1.56/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((subset @ X3 @ X2))) | ($true = (((in @ X1 @ X3) => (in @ X1 @ X2))))) )),
% 1.56/0.47 inference(imp_proxy_clausification,[],[f66])).
% 1.56/0.47 thf(f68,plain,(
% 1.56/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((subset @ X3 @ X2))) | ($false = ((in @ X1 @ X3))) | ($true = ((in @ X1 @ X2)))) )),
% 1.56/0.47 inference(imp_proxy_clausification,[],[f67])).
% 1.56/0.47 thf(f69,plain,(
% 1.56/0.47 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0))))) @ X1)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f38])).
% 1.56/0.47 thf(f70,plain,(
% 1.56/0.47 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f69])).
% 1.56/0.47 thf(f71,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (subset @ Y0 @ X1))) @ X2)))) )),
% 1.56/0.47 inference(pi_proxy_clausification,[],[f70])).
% 1.56/0.47 thf(f72,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => (subset @ X2 @ X1))))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f71])).
% 1.56/0.47 thf(f73,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))))) | ($true = ((subset @ X2 @ X1)))) )),
% 1.56/0.47 inference(imp_proxy_clausification,[],[f72])).
% 1.56/0.47 thf(f74,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK4 @ X1 @ X2)))) | ($true = ((subset @ X2 @ X1)))) )),
% 1.56/0.47 inference(sigma_proxy_clausification,[],[f73])).
% 1.56/0.47 thf(f75,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($false = (((in @ (sK4 @ X1 @ X2) @ X2) => (in @ (sK4 @ X1 @ X2) @ X1)))) | ($true = ((subset @ X2 @ X1)))) )),
% 1.56/0.47 inference(beta-eta_normalization,[],[f74])).
% 1.56/0.47 thf(f76,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ (sK4 @ X1 @ X2) @ X1))) | ($true = ((subset @ X2 @ X1)))) )),
% 1.56/0.47 inference(imp_proxy_clausification,[],[f75])).
% 1.56/0.47 thf(f77,plain,(
% 1.56/0.47 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK4 @ X1 @ X2) @ X2))) | ($true = ((subset @ X2 @ X1)))) )),
% 1.56/0.47 inference(imp_proxy_clausification,[],[f75])).
% 1.56/0.47 thf(f84,plain,(
% 1.56/0.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | (((in @ X2 @ X0)) = $false) | ($true = ((in @ X2 @ (binunion @ X1 @ X0))))) )),
% 1.56/0.47 inference(constrained_superposition,[],[f56,f68])).
% 1.56/0.47 thf(f85,plain,(
% 1.56/0.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | (((in @ X2 @ X0)) = $false) | ($true = ((in @ X2 @ (binunion @ X0 @ X1))))) )),
% 1.56/0.47 inference(constrained_superposition,[],[f60,f68])).
% 1.56/0.47 thf(f91,plain,(
% 1.56/0.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X2 @ (binunion @ X0 @ X1)))) | (((in @ X2 @ X0)) = $false)) )),
% 1.56/0.47 inference(trivial_inequality_removal,[],[f85])).
% 1.56/0.47 thf(f92,plain,(
% 1.56/0.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X2 @ (binunion @ X1 @ X0)))) | (((in @ X2 @ X0)) = $false)) )),
% 1.56/0.47 inference(trivial_inequality_removal,[],[f84])).
% 1.56/0.47 thf(f103,plain,(
% 1.56/0.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | (((sK4 @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = X2) | (((sK4 @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = X1) | ($true = ((subset @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ X0)))) )),
% 1.56/0.47 inference(constrained_superposition,[],[f52,f77])).
% 1.56/0.47 thf(f109,plain,(
% 1.56/0.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((subset @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ X0))) | (((sK4 @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = X1) | (((sK4 @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = X2)) )),
% 1.56/0.47 inference(trivial_inequality_removal,[],[f103])).
% 1.56/0.47 thf(f120,plain,(
% 1.56/0.47 ($true != $true) | (((subset @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ (binunion @ sK0 @ sK1))) = $false)),
% 1.56/0.47 inference(constrained_superposition,[],[f35,f37])).
% 1.56/0.47 thf(f122,plain,(
% 1.56/0.47 (((subset @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ (binunion @ sK0 @ sK1))) = $false)),
% 1.56/0.47 inference(trivial_inequality_removal,[],[f120])).
% 1.56/0.47 thf(f134,plain,(
% 1.56/0.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($true = ((subset @ X2 @ (binunion @ X0 @ X1)))) | ($false = ((in @ (sK4 @ (binunion @ X0 @ X1) @ X2) @ X0)))) )),
% 1.56/0.47 inference(constrained_superposition,[],[f76,f91])).
% 1.56/0.47 thf(f135,plain,(
% 1.56/0.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((in @ (sK4 @ (binunion @ X0 @ X1) @ X2) @ X0))) | ($true = ((subset @ X2 @ (binunion @ X0 @ X1))))) )),
% 1.56/0.47 inference(trivial_inequality_removal,[],[f134])).
% 1.56/0.47 thf(f146,plain,(
% 1.56/0.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($true = ((subset @ X2 @ (binunion @ X0 @ X1)))) | ($false = ((in @ (sK4 @ (binunion @ X0 @ X1) @ X2) @ X1)))) )),
% 1.56/0.47 inference(constrained_superposition,[],[f76,f92])).
% 1.56/0.47 thf(f147,plain,(
% 1.56/0.47 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((in @ (sK4 @ (binunion @ X0 @ X1) @ X2) @ X1))) | ($true = ((subset @ X2 @ (binunion @ X0 @ X1))))) )),
% 1.56/0.47 inference(trivial_inequality_removal,[],[f146])).
% 1.56/0.47 thf(f3055,plain,(
% 1.56/0.47 ($true = $false) | (sK2 = ((sK4 @ (binunion @ sK0 @ sK1) @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset))))) | (sK3 = ((sK4 @ (binunion @ sK0 @ sK1) @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)))))),
% 1.56/0.47 inference(constrained_superposition,[],[f109,f122])).
% 1.56/0.47 thf(f3128,plain,(
% 1.56/0.47 (sK2 = ((sK4 @ (binunion @ sK0 @ sK1) @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset))))) | (sK3 = ((sK4 @ (binunion @ sK0 @ sK1) @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)))))),
% 1.56/0.47 inference(trivial_inequality_removal,[],[f3055])).
% 1.56/0.47 thf(f3178,definition,(
% 1.56/0.47 spl5_5 <=> (sK3 = ((sK4 @ (binunion @ sK0 @ sK1) @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)))))),
% 1.56/0.47 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 1.56/0.47 thf(f3180,plain,(
% 1.56/0.47 (sK3 = ((sK4 @ (binunion @ sK0 @ sK1) @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset))))) | ~spl5_5),
% 1.56/0.47 inference(avatar_component_clause,[],[f3178])).
% 1.56/0.47 thf(f3182,definition,(
% 1.56/0.47 spl5_6 <=> (sK2 = ((sK4 @ (binunion @ sK0 @ sK1) @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)))))),
% 1.56/0.47 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 1.56/0.47 thf(f3184,plain,(
% 1.56/0.47 (sK2 = ((sK4 @ (binunion @ sK0 @ sK1) @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset))))) | ~spl5_6),
% 1.56/0.47 inference(avatar_component_clause,[],[f3182])).
% 1.56/0.47 thf(f3189,plain,(
% 1.56/0.47 spl5_5 | spl5_6),
% 1.56/0.47 inference(avatar_split_clause,[],[f3128,f3182,f3178])).
% 1.56/0.47 thf(f3322,plain,(
% 1.56/0.47 (((in @ sK3 @ sK1)) = $false) | ($true = ((subset @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ (binunion @ sK0 @ sK1)))) | ~spl5_5),
% 1.56/0.47 inference(constrained_superposition,[],[f147,f3180])).
% 1.56/0.47 thf(f3325,plain,(
% 1.56/0.47 (((in @ sK3 @ sK1)) = $false) | ~spl5_5),
% 1.56/0.47 inference(forward_subsumption_resolution,[],[f3322,f35])).
% 1.56/0.47 thf(f3426,plain,(
% 1.56/0.47 ($true = $false) | ~spl5_5),
% 1.56/0.47 inference(constrained_superposition,[],[f3325,f34])).
% 1.56/0.47 thf(f3432,plain,(
% 1.56/0.47 $false | ~spl5_5),
% 1.56/0.47 inference(trivial_inequality_removal,[],[f3426])).
% 1.56/0.47 thf(f3433,plain,(
% 1.56/0.47 ~spl5_5),
% 1.56/0.47 inference(avatar_contradiction_clause,[],[f3432])).
% 1.56/0.47 thf(f3441,plain,(
% 1.56/0.47 (((in @ sK2 @ sK0)) = $false) | ($true = ((subset @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ (binunion @ sK0 @ sK1)))) | ~spl5_6),
% 1.56/0.47 inference(constrained_superposition,[],[f135,f3184])).
% 1.56/0.47 thf(f3443,plain,(
% 1.56/0.47 (((in @ sK2 @ sK0)) = $false) | ~spl5_6),
% 1.56/0.47 inference(forward_subsumption_resolution,[],[f3441,f35])).
% 1.56/0.47 thf(f3542,plain,(
% 1.56/0.47 ($true = $false) | ~spl5_6),
% 1.56/0.47 inference(constrained_superposition,[],[f3443,f33])).
% 1.56/0.47 thf(f3548,plain,(
% 1.56/0.47 $false | ~spl5_6),
% 1.56/0.47 inference(trivial_inequality_removal,[],[f3542])).
% 1.56/0.47 thf(f3549,plain,(
% 1.56/0.47 ~spl5_6),
% 1.56/0.47 inference(avatar_contradiction_clause,[],[f3548])).
% 1.56/0.47 cnf(s7, plain, spl5_5 | spl5_6, inference(sat_conversion,[],[f3189])).
% 1.56/0.47 cnf(s9, plain, ~spl5_5, inference(sat_conversion,[],[f3433])).
% 1.56/0.47 cnf(s11, plain, ~spl5_6, inference(sat_conversion,[],[f3549])).
% 1.56/0.47 cnf(s12, plain, $false, inference(rat,[],[s7,s11,s9])).
% 1.56/0.47 thf(f3550,plain,(
% 1.56/0.47 $false),
% 1.56/0.47 inference(avatar_sat_refutation,[],[s12])).
% 1.56/0.47 % SZS output end Proof for theBenchmark
% 1.56/0.47 % (3569271)------------------------------
% 1.56/0.47 % (3569271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.47 % (3569271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.47 % (3569271)CaDiCaL version: 2.1.3
% 1.56/0.47 % (3569271)Termination reason: Refutation
% 1.56/0.47 % (3569271)Time elapsed: 0.189 s
% 1.56/0.47 % (3569271)Peak memory usage: 13 MB
% 1.56/0.47 % (3569271)Instructions burned: 421 (million)
% 1.56/0.47 % (3569254)Success in time 0.24 s
% 1.56/0.47 % Vampire exiting
%------------------------------------------------------------------------------