%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU734^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:33:10 AM UTC 2026
% Result : Theorem 1.43s 0.47s
% Output : Refutation 1.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU734^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n002.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:21:23 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.23 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
% 1.43/0.47 % (1358154)Will run a generic schedule for satisfiability detection.
% 1.43/0.47 % (1358160)% WARNING: option uhcvi not known.
% 1.43/0.47 % (1358159)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=234814032_3000 on theBenchmark for (3000ds/0Mi)
% 1.43/0.47 % (1358162)dis+10_1_sil=32000:sp=arity:random_seed=2767744961:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 1.43/0.47 % (1358164)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=655094590:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 1.43/0.47 % (1358161)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=8904422:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 1.43/0.47 % (1358163)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1812335871:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 1.43/0.47 % (1358165)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2497067025:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 1.43/0.47 % (1358163)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.43/0.47 % Exception at run slice level
% 1.43/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.43/0.47 % (1358160)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2162988757:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 1.43/0.47 % (1358160)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.43/0.47 % (1358174)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2432316247:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.43/0.47 % (1358160)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.43/0.47 % Exception at run slice level
% 1.43/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.43/0.47 % (1358178)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2397797861:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.43/0.47 % (1358178)Instruction limit reached!
% 1.43/0.47 % (1358178)------------------------------
% 1.43/0.47 % (1358178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.47 % (1358178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.47 % (1358178)CaDiCaL version: 2.1.3
% 1.43/0.47 % (1358178)Termination reason: Instruction limit
% 1.43/0.47 % (1358178)Termination phase: Saturation
% 1.43/0.47 % (1358178)Time elapsed: 0.048 s
% 1.43/0.47 % (1358178)Peak memory usage: 12 MB
% 1.43/0.47 % (1358178)Instructions burned: 132 (million)
% 1.43/0.47 % (1358162)Instruction limit reached!
% 1.43/0.47 % (1358162)------------------------------
% 1.43/0.47 % (1358162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.47 % (1358162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.47 % (1358162)CaDiCaL version: 2.1.3
% 1.43/0.47 % (1358162)Termination reason: Instruction limit
% 1.43/0.47 % (1358162)Termination phase: Saturation
% 1.43/0.47 % (1358162)Time elapsed: 0.088 s
% 1.43/0.47 % (1358162)Peak memory usage: 12 MB
% 1.43/0.47 % (1358162)Instructions burned: 103 (million)
% 1.43/0.47 % (1358183)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=1823197428:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.43/0.47 % (1358163)Instruction limit reached!
% 1.43/0.47 % (1358163)------------------------------
% 1.43/0.47 % (1358163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.47 % (1358163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.47 % (1358183)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.43/0.47 % (1358163)CaDiCaL version: 2.1.3
% 1.43/0.47 % (1358163)Termination reason: Instruction limit
% 1.43/0.47 % (1358163)Termination phase: Saturation
% 1.43/0.47 % (1358163)Time elapsed: 0.097 s
% 1.43/0.47 % (1358163)Peak memory usage: 12 MB
% 1.43/0.47 % (1358163)Instructions burned: 117 (million)
% 1.43/0.47 % (1358183)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.43/0.47 % (1358164)Instruction limit reached!
% 1.43/0.47 % (1358164)------------------------------
% 1.43/0.47 % (1358164)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.47 % (1358164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.47 % (1358164)CaDiCaL version: 2.1.3
% 1.43/0.47 % (1358164)Termination reason: Instruction limit
% 1.43/0.47 % (1358164)Termination phase: Saturation
% 1.43/0.47 % (1358164)Time elapsed: 0.105 s
% 1.43/0.47 % (1358164)Peak memory usage: 12 MB
% 1.43/0.47 % (1358164)Instructions burned: 131 (million)
% 1.43/0.47 % (1358185)ott-21_1_sil=16000:fs=off:random_seed=3870289813:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.43/0.47 % (1358188)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=208375175:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.43/0.47 % (1358165)Instruction limit reached!
% 1.43/0.47 % (1358165)------------------------------
% 1.43/0.47 % (1358165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.47 % (1358165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.47 % (1358165)CaDiCaL version: 2.1.3
% 1.43/0.47 % (1358165)Termination reason: Instruction limit
% 1.43/0.47 % (1358165)Termination phase: Saturation
% 1.43/0.47 % (1358165)Time elapsed: 0.133 s
% 1.43/0.47 % (1358165)Peak memory usage: 12 MB
% 1.43/0.47 % (1358165)Instructions burned: 160 (million)
% 1.43/0.47 % (1358190)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4215014710:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.43/0.47 % Exception at run slice level
% 1.43/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.43/0.47 % (1358192)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=755141313:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.43/0.47 % (1358185)Instruction limit reached!
% 1.43/0.47 % (1358185)------------------------------
% 1.43/0.47 % (1358185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.47 % (1358185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.47 % (1358185)CaDiCaL version: 2.1.3
% 1.43/0.47 % (1358185)Termination reason: Instruction limit
% 1.43/0.47 % (1358185)Termination phase: Saturation
% 1.43/0.47 % (1358185)Time elapsed: 0.075 s
% 1.43/0.47 % (1358185)Peak memory usage: 13 MB
% 1.43/0.47 % (1358185)Instructions burned: 180 (million)
% 1.43/0.47 % (1358160) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1358154-1358160"...
% 1.43/0.47 % (1358160)...printing done.
% 1.43/0.47 % (1358198)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=2065617741:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 1.43/0.47 % (1358194)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4089203982:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.43/0.47 % (1358160)Refutation found. Thanks to Tanya!
% 1.43/0.47 % SZS status Theorem for theBenchmark
% 1.43/0.47 % SZS output start Proof for theBenchmark
% 1.43/0.47 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 1.43/0.47 thf(func_def_0, type, in: ($i > $i > $o)).
% 1.43/0.47 thf(func_def_1, type, powerset: ($i > $i)).
% 1.43/0.47 thf(func_def_2, type, subset: ($i > $i > $o)).
% 1.43/0.47 thf(func_def_3, type, binintersect: ($i > $i > $i)).
% 1.43/0.47 thf(func_def_4, type, setminus: ($i > $i > $i)).
% 1.43/0.47 thf(func_def_5, type, binintersectT_lem: $o).
% 1.43/0.47 thf(func_def_7, type, complementT_lem: $o).
% 1.43/0.47 thf(func_def_8, type, subsetTI: $o).
% 1.43/0.47 thf(func_def_9, type, complementImpComplementIntersect: $o).
% 1.43/0.47 thf(func_def_10, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.43/0.47 thf(func_def_11, type, vIMP: ($o > $o > $o)).
% 1.43/0.47 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 1.43/0.47 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 1.43/0.47 thf(func_def_14, type, db2: !>[X0: $tType]:(X0)).
% 1.43/0.47 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.43/0.47 thf(func_def_16, type, db3: !>[X0: $tType]:(X0)).
% 1.43/0.47 thf(func_def_22, type, vNOT: ($o > $o)).
% 1.43/0.47 thf(func_def_23, type, sK3: ($i > $i > $i > $i)).
% 1.43/0.47 thf(f1,axiom,(
% 1.43/0.47 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 1.43/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem)).
% 1.43/0.47 thf(f2,axiom,(
% 1.43/0.47 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 1.43/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem)).
% 1.43/0.47 thf(f3,axiom,(
% 1.43/0.47 (subsetTI = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (subset @ X1 @ X2)))))),
% 1.43/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI)).
% 1.43/0.47 thf(f4,axiom,(
% 1.43/0.47 (complementImpComplementIntersect = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))))),
% 1.43/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementImpComplementIntersect)).
% 1.43/0.47 thf(f5,conjecture,(
% 1.43/0.47 binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))))),
% 1.43/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementSubsetComplementIntersect)).
% 1.43/0.47 thf(f6,negated_conjecture,(
% 1.43/0.47 ~(binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))))))),
% 1.43/0.47 inference(negated_conjecture,[status(cth)],[f5])).
% 1.43/0.47 thf(f7,plain,(
% 1.43/0.47 (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 1.43/0.47 inference(rectify,[],[f1])).
% 1.43/0.47 thf(f8,plain,(
% 1.43/0.47 (binintersectT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binintersect @ Y0 @ Y2) @ (powerset @ Y1))))))))))))),
% 1.43/0.47 inference(fool_elimination,[],[f7])).
% 1.43/0.47 thf(f9,plain,(
% 1.43/0.47 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 1.43/0.47 inference(rectify,[],[f2])).
% 1.43/0.47 thf(f10,plain,(
% 1.43/0.47 (complementT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))))),
% 1.43/0.47 inference(fool_elimination,[],[f9])).
% 1.43/0.47 thf(f11,plain,(
% 1.43/0.47 (subsetTI = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (subset @ X1 @ X2)))))),
% 1.43/0.47 inference(rectify,[],[f3])).
% 1.43/0.47 thf(f12,plain,(
% 1.43/0.47 (subsetTI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ Y0) => (in @ Y3 @ Y2))))) => (subset @ Y0 @ Y2))))))))))))),
% 1.43/0.47 inference(fool_elimination,[],[f11])).
% 1.43/0.47 thf(f13,plain,(
% 1.43/0.47 (complementImpComplementIntersect = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))))),
% 1.43/0.47 inference(rectify,[],[f4])).
% 1.43/0.47 thf(f14,plain,(
% 1.43/0.47 (complementImpComplementIntersect = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((in @ Y3 @ (setminus @ Y1 @ Y0)) => (in @ Y3 @ (setminus @ Y1 @ (binintersect @ Y0 @ Y2)))))))))))))))))),
% 1.43/0.47 inference(fool_elimination,[],[f13])).
% 1.43/0.47 thf(f15,plain,(
% 1.43/0.47 ~(binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))))))),
% 1.43/0.47 inference(rectify,[],[f6])).
% 1.43/0.47 thf(f16,plain,(
% 1.43/0.47 ~((binintersectT_lem = $true) => ((complementT_lem = $true) => ((subsetTI = $true) => ((complementImpComplementIntersect = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true)))))))),
% 1.43/0.47 inference(fool_elimination,[],[f15])).
% 1.43/0.47 thf(f17,plain,(
% 1.43/0.47 (((? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (complementImpComplementIntersect = $true)) & (subsetTI = $true)) & (complementT_lem = $true)) & (binintersectT_lem = $true)),
% 1.43/0.47 inference(ennf_transformation,[],[f16])).
% 1.43/0.47 thf(f18,plain,(
% 1.43/0.47 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (complementImpComplementIntersect = $true) & (subsetTI = $true) & (complementT_lem = $true) & (binintersectT_lem = $true)),
% 1.43/0.47 inference(flattening,[],[f17])).
% 1.43/0.47 thf(f19,plain,(
% 1.43/0.47 ((($true != ((subset @ (setminus @ sK0 @ sK1) @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2))))) & ($true = ((in @ sK2 @ (powerset @ sK0))))) & ($true = ((in @ sK1 @ (powerset @ sK0))))) & (complementImpComplementIntersect = $true) & (subsetTI = $true) & (complementT_lem = $true) & (binintersectT_lem = $true)),
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% 1.43/0.47 inference(cnf_transformation,[],[f8])).
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% 1.43/0.47 (complementT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))))),
% 1.43/0.47 inference(cnf_transformation,[],[f10])).
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% 1.43/0.47 inference(cnf_transformation,[],[f12])).
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% 1.43/0.47 inference(cnf_transformation,[],[f14])).
% 1.43/0.47 thf(f24,plain,(
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% 1.43/0.47 inference(cnf_transformation,[],[f19])).
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% 1.43/0.47 thf(f27,plain,(
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% 1.43/0.47 inference(cnf_transformation,[],[f19])).
% 1.43/0.47 thf(f28,plain,(
% 1.43/0.47 ($true = ((in @ sK1 @ (powerset @ sK0))))),
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% 1.43/0.47 inference(cnf_transformation,[],[f19])).
% 1.43/0.47 thf(f32,definition,(
% 1.43/0.47 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.43/0.47 introduced(theory,[fool_exhaustiveness_axiom])).
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% 1.43/0.47 inference(definition_unfolding,[],[f20,f24])).
% 1.43/0.47 thf(f34,plain,(
% 1.43/0.47 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))) = $true)),
% 1.43/0.47 inference(definition_unfolding,[],[f21,f25])).
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% 1.43/0.47 inference(definition_unfolding,[],[f22,f26])).
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% 1.43/0.47 inference(definition_unfolding,[],[f23,f27])).
% 1.43/0.47 thf(f37,plain,(
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% 1.43/0.47 thf(f40,plain,(
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% 1.43/0.47 inference(beta-eta_normalization,[],[f39])).
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% 1.43/0.47 inference(pi_proxy_clausification,[],[f44])).
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% 1.43/0.47 inference(beta-eta_normalization,[],[f45])).
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% 1.43/0.47 inference(imp_proxy_clausification,[],[f46])).
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% 1.43/0.47 inference(imp_proxy_clausification,[],[f47])).
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% 1.43/0.47 thf(f50,plain,(
% 1.43/0.47 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ X1) => (in @ Y2 @ Y1))))) => (subset @ X1 @ Y1))))))))))) )),
% 1.43/0.47 inference(beta-eta_normalization,[],[f49])).
% 1.43/0.47 thf(f51,plain,(
% 1.43/0.47 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ X1) => (in @ Y2 @ Y1))))) => (subset @ X1 @ Y1))))))) @ X2)))) )),
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% 1.43/0.47 inference(pi_proxy_clausification,[],[f53])).
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% 1.43/0.47 inference(imp_proxy_clausification,[],[f56])).
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% 1.43/0.47 inference(sigma_proxy_clausification,[],[f57])).
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% 1.43/0.47 thf(f60,plain,(
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% 1.43/0.47 inference(beta-eta_normalization,[],[f64])).
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% 1.43/0.47 inference(beta-eta_normalization,[],[f66])).
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% 1.43/0.47 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (setminus @ X2 @ X1) @ (powerset @ X2)))) | ($false = ((in @ X1 @ (powerset @ X2))))) )),
% 1.43/0.47 inference(imp_proxy_clausification,[],[f67])).
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% 1.43/0.47 inference(pi_proxy_clausification,[],[f33])).
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% 1.43/0.47 inference(beta-eta_normalization,[],[f69])).
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% 1.43/0.47 inference(pi_proxy_clausification,[],[f70])).
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% 1.43/0.47 thf(f73,plain,(
% 1.43/0.47 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (in @ (binintersect @ X1 @ Y0) @ (powerset @ X2)))))))) )),
% 1.43/0.47 inference(imp_proxy_clausification,[],[f72])).
% 1.43/0.47 thf(f74,plain,(
% 1.43/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (in @ (binintersect @ X1 @ Y0) @ (powerset @ X2)))) @ X3)))) )),
% 1.43/0.47 inference(pi_proxy_clausification,[],[f73])).
% 1.43/0.47 thf(f75,plain,(
% 1.43/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((in @ X3 @ (powerset @ X2)) => (in @ (binintersect @ X1 @ X3) @ (powerset @ X2)))))) )),
% 1.43/0.47 inference(beta-eta_normalization,[],[f74])).
% 1.43/0.47 thf(f76,plain,(
% 1.43/0.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ (binintersect @ X1 @ X3) @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X1 @ (powerset @ X2))))) )),
% 1.43/0.47 inference(imp_proxy_clausification,[],[f75])).
% 1.43/0.47 thf(f79,plain,(
% 1.43/0.47 ($true != $true) | (((subset @ (setminus @ sK0 @ sK1) @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)))) = $false)),
% 1.43/0.47 inference(constrained_superposition,[],[f30,f32])).
% 1.43/0.47 thf(f81,plain,(
% 1.43/0.47 (((subset @ (setminus @ sK0 @ sK1) @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)))) = $false)),
% 1.43/0.47 inference(trivial_inequality_removal,[],[f79])).
% 1.43/0.47 thf(f92,plain,(
% 1.43/0.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true = $false) | (((in @ X2 @ (powerset @ X0))) = $false) | ($false = ((in @ (sK3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ X0))) | ($false = ((in @ (sK3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ X1)))) | (((in @ X1 @ (powerset @ X0))) = $false) | ($false = ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X4)))) | ($false = ((in @ X3 @ (powerset @ X4)))) | ($true = ((subset @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))) )),
% 1.43/0.47 inference(constrained_superposition,[],[f48,f62])).
% 1.43/0.47 thf(f96,plain,(
% 1.43/0.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($false = ((in @ (sK3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ X1)))) | ($false = ((in @ (sK3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ X0))) | (((in @ X2 @ (powerset @ X0))) = $false) | (((in @ X1 @ (powerset @ X0))) = $false) | ($false = ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X4)))) | ($false = ((in @ X3 @ (powerset @ X4)))) | ($true = ((subset @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))) )),
% 1.43/0.47 inference(trivial_inequality_removal,[],[f92])).
% 1.43/0.47 thf(f179,plain,(
% 1.43/0.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | ($false = ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)))) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($false = ((in @ (sK3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (setminus @ X0 @ X1) @ X3) @ X0))) | (((in @ X2 @ (powerset @ X0))) = $false) | (((in @ X1 @ (powerset @ X0))) = $false) | ($false = ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | ($false = ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)))) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true)) )),
% 1.43/0.48 inference(constrained_superposition,[],[f63,f96])).
% 1.43/0.48 thf(f186,plain,(
% 1.43/0.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | ($false = ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)))) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($false = ((in @ (sK3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (setminus @ X0 @ X1) @ X3) @ X0))) | (((in @ X2 @ (powerset @ X0))) = $false) | (((in @ X1 @ (powerset @ X0))) = $false)) )),
% 1.43/0.48 inference(duplicate_literal_removal,[],[f179])).
% 1.43/0.48 thf(f187,plain,(
% 1.43/0.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = ((in @ (sK3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (setminus @ X0 @ X1) @ X3) @ X0))) | ($false = ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)))) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($false = ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ X2 @ (powerset @ X0))) = $false) | (((in @ X1 @ (powerset @ X0))) = $false)) )),
% 1.43/0.48 inference(trivial_inequality_removal,[],[f186])).
% 1.43/0.48 thf(f314,plain,(
% 1.43/0.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)))) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $false) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $false) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($false = ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)))) | (((in @ X2 @ (powerset @ X0))) = $false) | (((in @ X1 @ (powerset @ X0))) = $false)) )),
% 1.43/0.48 inference(constrained_superposition,[],[f61,f187])).
% 1.43/0.48 thf(f317,plain,(
% 1.43/0.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)))) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $false) | (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X2 @ (powerset @ X0))) = $false) | (((in @ X1 @ (powerset @ X0))) = $false)) )),
% 1.43/0.48 inference(duplicate_literal_removal,[],[f314])).
% 1.43/0.48 thf(f318,plain,(
% 1.43/0.48 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $false) | ($false = ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)))) | (((in @ X2 @ (powerset @ X0))) = $false) | (((in @ X1 @ (powerset @ X0))) = $false)) )),
% 1.43/0.48 inference(trivial_inequality_removal,[],[f317])).
% 1.43/0.48 thf(f507,plain,(
% 1.43/0.48 ($true = $false) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)) @ (powerset @ sK0)))) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false)),
% 1.43/0.48 inference(constrained_superposition,[],[f318,f81])).
% 1.43/0.48 thf(f512,plain,(
% 1.43/0.48 ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)) @ (powerset @ sK0)))) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false)),
% 1.43/0.48 inference(trivial_inequality_removal,[],[f507])).
% 1.43/0.48 thf(f517,plain,(
% 1.43/0.48 ($true = $false) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)) @ (powerset @ sK0)))) | (((in @ sK1 @ (powerset @ sK0))) = $false)),
% 1.43/0.48 inference(forward_demodulation,[],[f512,f29])).
% 1.43/0.48 thf(f518,plain,(
% 1.43/0.48 ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)) @ (powerset @ sK0)))) | (((in @ sK1 @ (powerset @ sK0))) = $false)),
% 1.43/0.48 inference(trivial_inequality_removal,[],[f517])).
% 1.43/0.48 thf(f523,plain,(
% 1.43/0.48 ($true = $false) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)) @ (powerset @ sK0))))),
% 1.43/0.48 inference(forward_demodulation,[],[f518,f28])).
% 1.43/0.48 thf(f524,plain,(
% 1.43/0.48 ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)) @ (powerset @ sK0))))),
% 1.43/0.48 inference(trivial_inequality_removal,[],[f523])).
% 1.43/0.48 thf(f526,definition,(
% 1.43/0.48 spl4_4 <=> ($false = ((in @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)) @ (powerset @ sK0))))),
% 1.43/0.48 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 1.43/0.48 thf(f528,plain,(
% 1.43/0.48 ($false = ((in @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)) @ (powerset @ sK0)))) | ~spl4_4),
% 1.43/0.48 inference(avatar_component_clause,[],[f526])).
% 1.43/0.48 thf(f530,definition,(
% 1.43/0.48 spl4_5 <=> ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0))))),
% 1.43/0.48 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 1.43/0.48 thf(f532,plain,(
% 1.43/0.48 ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ~spl4_5),
% 1.43/0.48 inference(avatar_component_clause,[],[f530])).
% 1.43/0.48 thf(f535,plain,(
% 1.43/0.48 spl4_4 | spl4_5),
% 1.43/0.48 inference(avatar_split_clause,[],[f524,f530,f526])).
% 1.43/0.48 thf(f538,plain,(
% 1.43/0.48 ($true = $false) | ($false = ((in @ (binintersect @ sK1 @ sK2) @ (powerset @ sK0)))) | ~spl4_4),
% 1.43/0.48 inference(constrained_superposition,[],[f68,f528])).
% 1.43/0.48 thf(f539,plain,(
% 1.43/0.48 ($false = ((in @ (binintersect @ sK1 @ sK2) @ (powerset @ sK0)))) | ~spl4_4),
% 1.43/0.48 inference(trivial_inequality_removal,[],[f538])).
% 1.43/0.48 thf(f604,plain,(
% 1.43/0.48 ($true = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_4),
% 1.43/0.48 inference(constrained_superposition,[],[f76,f539])).
% 1.43/0.48 thf(f605,plain,(
% 1.43/0.48 (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_4),
% 1.43/0.48 inference(trivial_inequality_removal,[],[f604])).
% 1.43/0.48 thf(f608,plain,(
% 1.43/0.48 ($true = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | ~spl4_4),
% 1.43/0.48 inference(forward_demodulation,[],[f605,f28])).
% 1.43/0.48 thf(f609,plain,(
% 1.43/0.48 (((in @ sK2 @ (powerset @ sK0))) = $false) | ~spl4_4),
% 1.43/0.48 inference(trivial_inequality_removal,[],[f608])).
% 1.43/0.48 thf(f672,plain,(
% 1.43/0.48 ($true = $false) | ~spl4_4),
% 1.43/0.48 inference(constrained_superposition,[],[f609,f29])).
% 1.43/0.48 thf(f678,plain,(
% 1.43/0.48 $false | ~spl4_4),
% 1.43/0.48 inference(trivial_inequality_removal,[],[f672])).
% 1.43/0.48 thf(f679,plain,(
% 1.43/0.48 ~spl4_4),
% 1.43/0.48 inference(avatar_contradiction_clause,[],[f678])).
% 1.43/0.48 thf(f682,plain,(
% 1.43/0.48 ($true = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_5),
% 1.43/0.48 inference(constrained_superposition,[],[f68,f532])).
% 1.43/0.48 thf(f683,plain,(
% 1.43/0.48 (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_5),
% 1.43/0.48 inference(trivial_inequality_removal,[],[f682])).
% 1.43/0.48 thf(f710,plain,(
% 1.43/0.48 ($true = $false) | ~spl4_5),
% 1.43/0.48 inference(constrained_superposition,[],[f683,f28])).
% 1.43/0.48 thf(f716,plain,(
% 1.43/0.48 $false | ~spl4_5),
% 1.43/0.48 inference(trivial_inequality_removal,[],[f710])).
% 1.43/0.48 thf(f717,plain,(
% 1.43/0.48 ~spl4_5),
% 1.43/0.48 inference(avatar_contradiction_clause,[],[f716])).
% 1.43/0.48 cnf(s7, plain, spl4_4 | spl4_5, inference(sat_conversion,[],[f535])).
% 1.43/0.48 cnf(s9, plain, ~spl4_4, inference(sat_conversion,[],[f679])).
% 1.43/0.48 cnf(s11, plain, ~spl4_5, inference(sat_conversion,[],[f717])).
% 1.43/0.48 cnf(s12, plain, $false, inference(rat,[],[s7,s11,s9])).
% 1.43/0.48 thf(f718,plain,(
% 1.43/0.48 $false),
% 1.43/0.48 inference(avatar_sat_refutation,[],[s12])).
% 1.43/0.48 % SZS output end Proof for theBenchmark
% 1.43/0.48 % (1358160)------------------------------
% 1.43/0.48 % (1358160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.43/0.48 % (1358160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.43/0.48 % (1358160)CaDiCaL version: 2.1.3
% 1.43/0.48 % (1358160)Termination reason: Refutation
% 1.43/0.48 % (1358160)Time elapsed: 0.196 s
% 1.43/0.48 % (1358160)Peak memory usage: 13 MB
% 1.43/0.48 % (1358160)Instructions burned: 205 (million)
% 1.43/0.48 % (1358154)Success in time 0.242 s
% 1.43/0.48 % Vampire exiting
%------------------------------------------------------------------------------