%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU715^2 : 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 : n004.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 08:33:05 AM UTC 2026
% Result : Theorem 2.95s 0.74s
% Output : Refutation 2.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU715^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:13:52 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.24 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
% 2.95/0.74 % (1348659)Will run a generic schedule for satisfiability detection.
% 2.95/0.74 % (1348667)dis+10_1_sil=32000:sp=arity:random_seed=1060997696:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.95/0.74 % (1348668)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3838412044:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.95/0.74 % (1348668)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.95/0.74 % (1348665)% WARNING: option uhcvi not known.
% 2.95/0.74 % (1348664)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2004624464_2999 on theBenchmark for (2999ds/0Mi)
% 2.95/0.74 % (1348665)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=607875158:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.95/0.74 % (1348665)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.95/0.74 % (1348666)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2571280174:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.95/0.74 % Exception at run slice level
% 2.95/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.95/0.74 % (1348665)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.95/0.74 % (1348669)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=906685766:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.95/0.74 % (1348670)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2600036542:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.95/0.74 % (1348667)Instruction limit reached!
% 2.95/0.74 % (1348667)------------------------------
% 2.95/0.74 % (1348667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.74 % (1348667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.74 % (1348667)CaDiCaL version: 2.1.3
% 2.95/0.74 % (1348667)Termination reason: Instruction limit
% 2.95/0.74 % (1348667)Termination phase: Saturation
% 2.95/0.74 % (1348667)Time elapsed: 0.050 s
% 2.95/0.74 % (1348667)Peak memory usage: 12 MB
% 2.95/0.74 % (1348667)Instructions burned: 104 (million)
% 2.95/0.74 % (1348677)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=83330527:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.95/0.74 % Exception at run slice level
% 2.95/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.95/0.74 % (1348668)Instruction limit reached!
% 2.95/0.74 % (1348668)------------------------------
% 2.95/0.74 % (1348668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.74 % (1348668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.74 % (1348668)CaDiCaL version: 2.1.3
% 2.95/0.74 % (1348668)Termination reason: Instruction limit
% 2.95/0.74 % (1348668)Termination phase: Saturation
% 2.95/0.74 % (1348668)Time elapsed: 0.064 s
% 2.95/0.74 % (1348668)Peak memory usage: 12 MB
% 2.95/0.74 % (1348668)Instructions burned: 116 (million)
% 2.95/0.74 % (1348679)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1025806604:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.95/0.74 % (1348681)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=1478837977:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.95/0.74 % (1348681)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.95/0.74 % (1348681)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.95/0.74 % (1348682)ott-21_1_sil=16000:fs=off:random_seed=552150455:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.95/0.74 % (1348669)Instruction limit reached!
% 2.95/0.74 % (1348669)------------------------------
% 2.95/0.74 % (1348669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.74 % (1348669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.74 % (1348669)CaDiCaL version: 2.1.3
% 2.95/0.74 % (1348669)Termination reason: Instruction limit
% 2.95/0.74 % (1348669)Termination phase: Saturation
% 2.95/0.74 % (1348669)Time elapsed: 0.111 s
% 2.95/0.74 % (1348669)Peak memory usage: 12 MB
% 2.95/0.74 % (1348669)Instructions burned: 131 (million)
% 2.95/0.74 % (1348679)Instruction limit reached!
% 2.95/0.74 % (1348679)------------------------------
% 2.95/0.74 % (1348679)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.74 % (1348679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.74 % (1348679)CaDiCaL version: 2.1.3
% 2.95/0.74 % (1348679)Termination reason: Instruction limit
% 2.95/0.74 % (1348679)Termination phase: Saturation
% 2.95/0.74 % (1348679)Time elapsed: 0.070 s
% 2.95/0.74 % (1348679)Peak memory usage: 12 MB
% 2.95/0.74 % (1348679)Instructions burned: 131 (million)
% 2.95/0.74 % (1348686)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3405037778:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.95/0.74 % (1348670)Instruction limit reached!
% 2.95/0.74 % (1348670)------------------------------
% 2.95/0.74 % (1348670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.74 % (1348670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.74 % (1348670)CaDiCaL version: 2.1.3
% 2.95/0.74 % (1348670)Termination reason: Instruction limit
% 2.95/0.74 % (1348670)Termination phase: Saturation
% 2.95/0.74 % (1348670)Time elapsed: 0.155 s
% 2.95/0.74 % (1348670)Peak memory usage: 12 MB
% 2.95/0.74 % (1348670)Instructions burned: 159 (million)
% 2.95/0.74 % (1348687)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4280432305:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.95/0.74 % Exception at run slice level
% 2.95/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.95/0.74 % (1348689)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=797864934:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.95/0.74 % (1348691)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3903608243:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.95/0.74 % Exception at run slice level
% 2.95/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.95/0.74 % (1348694)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=128990989: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)
% 2.95/0.74 % (1348694)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.95/0.74 % (1348682)Instruction limit reached!
% 2.95/0.74 % (1348682)------------------------------
% 2.95/0.74 % (1348682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.74 % (1348682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.74 % (1348682)CaDiCaL version: 2.1.3
% 2.95/0.74 % (1348682)Termination reason: Instruction limit
% 2.95/0.74 % (1348682)Termination phase: Saturation
% 2.95/0.74 % (1348682)Time elapsed: 0.145 s
% 2.95/0.74 % (1348682)Peak memory usage: 12 MB
% 2.95/0.74 % (1348682)Instructions burned: 180 (million)
% 2.95/0.74 % (1348696)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=522751012:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.95/0.74 % (1348696)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.95/0.74 % (1348681)Instruction limit reached!
% 2.95/0.74 % (1348681)------------------------------
% 2.95/0.74 % (1348681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.74 % (1348681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.74 % (1348681)CaDiCaL version: 2.1.3
% 2.95/0.74 % (1348681)Termination reason: Instruction limit
% 2.95/0.74 % (1348681)Termination phase: Saturation
% 2.95/0.74 % (1348681)Time elapsed: 0.289 s
% 2.95/0.74 % (1348681)Peak memory usage: 14 MB
% 2.95/0.74 % (1348681)Instructions burned: 687 (million)
% 2.95/0.74 % (1348698)fmb+10_1_sil=64000:random_seed=3773386161:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 2.95/0.74 % (1348698)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.95/0.74 % Exception at run slice level
% 2.95/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.95/0.74 % (1348686)Instruction limit reached!
% 2.95/0.74 % (1348686)------------------------------
% 2.95/0.74 % (1348686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.74 % (1348686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.74 % (1348686)CaDiCaL version: 2.1.3
% 2.95/0.74 % (1348686)Termination reason: Instruction limit
% 2.95/0.74 % (1348686)Termination phase: Saturation
% 2.95/0.74 % (1348686)Time elapsed: 0.240 s
% 2.95/0.74 % (1348686)Peak memory usage: 13 MB
% 2.95/0.74 % (1348686)Instructions burned: 477 (million)
% 2.95/0.74 % (1348700)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3070497096:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 2.95/0.74 % Exception at run slice level
% 2.95/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.95/0.74 % (1348701)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=250689406:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 2.95/0.74 % (1348703)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=424952229:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 2.95/0.74 % (1348703)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.95/0.74 % Exception at run slice level
% 2.95/0.74 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.95/0.74 % (1348706)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3147586262:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 2.95/0.74 % (1348706)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.95/0.74 % (1348706)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.95/0.74 % (1348694) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1348659-1348694"...
% 2.95/0.74 % (1348694)...printing done.
% 2.95/0.74 % (1348694)Refutation found. Thanks to Tanya!
% 2.95/0.74 % SZS status Theorem for theBenchmark
% 2.95/0.74 % SZS output start Proof for theBenchmark
% 2.95/0.74 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 2.95/0.74 thf(func_def_0, type, in: ($i > $i > $o)).
% 2.95/0.74 thf(func_def_1, type, powerset: ($i > $i)).
% 2.95/0.74 thf(func_def_2, type, setext: $o).
% 2.95/0.74 thf(func_def_4, type, powersetE: $o).
% 2.95/0.74 thf(func_def_5, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.95/0.74 thf(func_def_6, type, vIMP: ($o > $o > $o)).
% 2.95/0.74 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 2.95/0.75 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 2.95/0.75 thf(func_def_9, type, db2: !>[X0: $tType]:(X0)).
% 2.95/0.75 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.95/0.75 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.95/0.75 thf(func_def_17, type, vNOT: ($o > $o)).
% 2.95/0.75 thf(func_def_18, type, sK3: ($i > $i > $i)).
% 2.95/0.75 thf(func_def_19, type, sK4: ($i > $i > $i)).
% 2.95/0.75 thf(f1,axiom,(
% 2.95/0.75 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))))),
% 2.95/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext)).
% 2.95/0.75 thf(f2,axiom,(
% 2.95/0.75 (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 2.95/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE)).
% 2.95/0.75 thf(f3,conjecture,(
% 2.95/0.75 setext => (powersetE => ! [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))) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ X1))) => (X1 = X2))))))),
% 2.95/0.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextT)).
% 2.95/0.75 thf(f4,negated_conjecture,(
% 2.95/0.75 ~(setext => (powersetE => ! [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))) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ X1))) => (X1 = X2)))))))),
% 2.95/0.75 inference(negated_conjecture,[status(cth)],[f3])).
% 2.95/0.75 thf(f5,plain,(
% 2.95/0.75 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))))),
% 2.95/0.75 inference(rectify,[],[f1])).
% 2.95/0.75 thf(f6,plain,(
% 2.95/0.75 (setext = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))))),
% 2.95/0.75 inference(fool_elimination,[],[f5])).
% 2.95/0.75 thf(f7,plain,(
% 2.95/0.75 (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 2.95/0.75 inference(rectify,[],[f2])).
% 2.95/0.75 thf(f8,plain,(
% 2.95/0.75 (powersetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (powerset @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2)))))))))))),
% 2.95/0.75 inference(fool_elimination,[],[f7])).
% 2.95/0.75 thf(f9,plain,(
% 2.95/0.75 ~(setext => (powersetE => ! [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))) => (! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ X2) => (in @ X4 @ X1))) => (X1 = X2)))))))),
% 2.95/0.75 inference(rectify,[],[f4])).
% 2.95/0.75 thf(f10,plain,(
% 2.95/0.75 ~((setext = $true) => ((powersetE = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ((((in @ X3 @ X1)) = $true) => (((in @ X3 @ X2)) = $true))) => (! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => ((((in @ X4 @ X2)) = $true) => (((in @ X4 @ X1)) = $true))) => (X1 = X2)))))))),
% 2.95/0.75 inference(fool_elimination,[],[f9])).
% 2.95/0.75 thf(f11,plain,(
% 2.95/0.75 (? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((X1 != X2) & ! [X4 : $i] : (((((in @ X4 @ X1)) = $true) | (((in @ X4 @ X2)) != $true)) | (((in @ X4 @ X0)) != $true))) & ! [X3 : $i] : (((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X1)) != $true)) | (((in @ X3 @ X0)) != $true))) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (powersetE = $true)) & (setext = $true)),
% 2.95/0.75 inference(ennf_transformation,[],[f10])).
% 2.95/0.75 thf(f12,plain,(
% 2.95/0.75 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((X1 != X2) & ! [X4 : $i] : ((((in @ X4 @ X1)) = $true) | (((in @ X4 @ X2)) != $true) | (((in @ X4 @ X0)) != $true)) & ! [X3 : $i] : ((((in @ X3 @ X2)) = $true) | (((in @ X3 @ X1)) != $true) | (((in @ X3 @ X0)) != $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (powersetE = $true) & (setext = $true)),
% 2.95/0.75 inference(flattening,[],[f11])).
% 2.95/0.75 thf(f13,plain,(
% 2.95/0.75 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((X1 != X2) & ! [X3 : $i] : ((((in @ X3 @ X1)) = $true) | (((in @ X3 @ X2)) != $true) | (((in @ X3 @ X0)) != $true)) & ! [X4 : $i] : ((((in @ X4 @ X2)) = $true) | (((in @ X4 @ X1)) != $true) | (((in @ X4 @ X0)) != $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (powersetE = $true) & (setext = $true)),
% 2.95/0.75 inference(rectify,[],[f12])).
% 2.95/0.75 thf(f14,plain,(
% 2.95/0.75 (((sK1 != sK2) & ! [X3 : $i] : (($true = ((in @ X3 @ sK1))) | ($true != ((in @ X3 @ sK2))) | ($true != ((in @ X3 @ sK0)))) & ! [X4 : $i] : (($true = ((in @ X4 @ sK2))) | ($true != ((in @ X4 @ sK1))) | ($true != ((in @ X4 @ sK0)))) & ($true = ((in @ sK2 @ (powerset @ sK0))))) & ($true = ((in @ sK1 @ (powerset @ sK0))))) & (powersetE = $true) & (setext = $true)),
% 2.95/0.75 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13])).
% 2.95/0.75 thf(f15,plain,(
% 2.95/0.75 (setext = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))))),
% 2.95/0.75 inference(cnf_transformation,[],[f6])).
% 2.95/0.75 thf(f16,plain,(
% 2.95/0.75 (powersetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (powerset @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2)))))))))))),
% 2.95/0.75 inference(cnf_transformation,[],[f8])).
% 2.95/0.75 thf(f17,plain,(
% 2.95/0.75 (setext = $true)),
% 2.95/0.75 inference(cnf_transformation,[],[f14])).
% 2.95/0.75 thf(f18,plain,(
% 2.95/0.75 (powersetE = $true)),
% 2.95/0.75 inference(cnf_transformation,[],[f14])).
% 2.95/0.75 thf(f19,plain,(
% 2.95/0.75 ($true = ((in @ sK1 @ (powerset @ sK0))))),
% 2.95/0.75 inference(cnf_transformation,[],[f14])).
% 2.95/0.75 thf(f20,plain,(
% 2.95/0.75 ($true = ((in @ sK2 @ (powerset @ sK0))))),
% 2.95/0.75 inference(cnf_transformation,[],[f14])).
% 2.95/0.75 thf(f21,plain,(
% 2.95/0.75 ( ! [X4 : $i] : (($true != ((in @ X4 @ sK1))) | ($true = ((in @ X4 @ sK2))) | ($true != ((in @ X4 @ sK0)))) )),
% 2.95/0.75 inference(cnf_transformation,[],[f14])).
% 2.95/0.75 thf(f22,plain,(
% 2.95/0.75 ( ! [X3 : $i] : (($true != ((in @ X3 @ sK2))) | ($true = ((in @ X3 @ sK1))) | ($true != ((in @ X3 @ sK0)))) )),
% 2.95/0.75 inference(cnf_transformation,[],[f14])).
% 2.95/0.75 thf(f23,plain,(
% 2.95/0.75 (sK1 != sK2)),
% 2.95/0.75 inference(cnf_transformation,[],[f14])).
% 2.95/0.75 thf(f25,definition,(
% 2.95/0.75 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 2.95/0.75 introduced(theory,[fool_exhaustiveness_axiom])).
% 2.95/0.75 thf(f26,plain,(
% 2.95/0.75 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))))) = $true)),
% 2.95/0.75 inference(definition_unfolding,[],[f15,f17])).
% 2.95/0.75 thf(f27,plain,(
% 2.95/0.75 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (powerset @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2)))))))))) = $true)),
% 2.95/0.75 inference(definition_unfolding,[],[f16,f18])).
% 2.95/0.75 thf(f28,plain,(
% 2.95/0.75 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (powerset @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2)))))))) @ X1)))) )),
% 2.95/0.75 inference(pi_proxy_clausification,[],[f27])).
% 2.95/0.75 thf(f29,plain,(
% 2.95/0.75 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => ((in @ X1 @ Y0) => (in @ X1 @ Y1)))))))))) )),
% 2.95/0.75 inference(beta-eta_normalization,[],[f28])).
% 2.95/0.75 thf(f30,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => ((in @ X1 @ Y0) => (in @ X1 @ Y1)))))) @ X2)))) )),
% 2.95/0.75 inference(pi_proxy_clausification,[],[f29])).
% 2.95/0.75 thf(f31,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (powerset @ Y0)) => ((in @ X1 @ X2) => (in @ X1 @ Y0)))))))) )),
% 2.95/0.75 inference(beta-eta_normalization,[],[f30])).
% 2.95/0.75 thf(f32,plain,(
% 2.95/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X2 @ (powerset @ Y0)) => ((in @ X1 @ X2) => (in @ X1 @ Y0)))) @ X3)))) )),
% 2.95/0.75 inference(pi_proxy_clausification,[],[f31])).
% 2.95/0.75 thf(f33,plain,(
% 2.95/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X2 @ (powerset @ X3)) => ((in @ X1 @ X2) => (in @ X1 @ X3)))))) )),
% 2.95/0.75 inference(beta-eta_normalization,[],[f32])).
% 2.95/0.75 thf(f34,plain,(
% 2.95/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X2 @ (powerset @ X3)))) | ($true = (((in @ X1 @ X2) => (in @ X1 @ X3))))) )),
% 2.95/0.75 inference(imp_proxy_clausification,[],[f33])).
% 2.95/0.75 thf(f35,plain,(
% 2.95/0.75 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X2 @ (powerset @ X3)))) | ($false = ((in @ X1 @ X2))) | ($true = ((in @ X1 @ X3)))) )),
% 2.95/0.75 inference(imp_proxy_clausification,[],[f34])).
% 2.95/0.75 thf(f36,plain,(
% 2.95/0.75 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) @ X1)))) )),
% 2.95/0.75 inference(pi_proxy_clausification,[],[f26])).
% 2.95/0.75 thf(f37,plain,(
% 2.95/0.75 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1)))))))) )),
% 2.95/0.75 inference(beta-eta_normalization,[],[f36])).
% 2.95/0.75 thf(f38,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (Y0 = X1)))) @ X2)))) )),
% 2.95/0.75 inference(pi_proxy_clausification,[],[f37])).
% 2.95/0.75 thf(f39,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1)))))) )),
% 2.95/0.75 inference(beta-eta_normalization,[],[f38])).
% 2.95/0.75 thf(f40,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))))) )),
% 2.95/0.75 inference(imp_proxy_clausification,[],[f39])).
% 2.95/0.75 thf(f41,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK3 @ X1 @ X2)))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (X2 = X1))))) )),
% 2.95/0.75 inference(sigma_proxy_clausification,[],[f40])).
% 2.95/0.75 thf(f42,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK3 @ X1 @ X2)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))))) | ($true = ((X2 = X1)))) )),
% 2.95/0.75 inference(imp_proxy_clausification,[],[f41])).
% 2.95/0.75 thf(f43,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK3 @ X1 @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK4 @ X1 @ X2)))) | ($true = ((X2 = X1)))) )),
% 2.95/0.75 inference(sigma_proxy_clausification,[],[f42])).
% 2.95/0.75 thf(f44,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK3 @ X1 @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK4 @ X1 @ X2)))) | (X1 = X2)) )),
% 2.95/0.75 inference(equality_proxy_clausification,[],[f43])).
% 2.95/0.75 thf(f45,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($false = (((in @ (sK3 @ X1 @ X2) @ X2) => (in @ (sK3 @ X1 @ X2) @ X1)))) | ($false = (((in @ (sK4 @ X1 @ X2) @ X1) => (in @ (sK4 @ X1 @ X2) @ X2)))) | (X1 = X2)) )),
% 2.95/0.75 inference(beta-eta_normalization,[],[f44])).
% 2.95/0.75 thf(f46,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ (sK3 @ X1 @ X2) @ X1))) | ($false = (((in @ (sK4 @ X1 @ X2) @ X1) => (in @ (sK4 @ X1 @ X2) @ X2)))) | (X1 = X2)) )),
% 2.95/0.75 inference(imp_proxy_clausification,[],[f45])).
% 2.95/0.75 thf(f47,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X2) @ X2))) | ($false = (((in @ (sK4 @ X1 @ X2) @ X1) => (in @ (sK4 @ X1 @ X2) @ X2)))) | (X1 = X2)) )),
% 2.95/0.75 inference(imp_proxy_clausification,[],[f45])).
% 2.95/0.75 thf(f48,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ (sK4 @ X1 @ X2) @ X2))) | ($true = ((in @ (sK3 @ X1 @ X2) @ X2))) | (X1 = X2)) )),
% 2.95/0.75 inference(imp_proxy_clausification,[],[f47])).
% 2.95/0.75 thf(f49,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X2) @ X2))) | ($true = ((in @ (sK4 @ X1 @ X2) @ X1))) | (X1 = X2)) )),
% 2.95/0.75 inference(imp_proxy_clausification,[],[f47])).
% 2.95/0.75 thf(f50,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ (sK3 @ X1 @ X2) @ X1))) | ($false = ((in @ (sK4 @ X1 @ X2) @ X2))) | (X1 = X2)) )),
% 2.95/0.75 inference(imp_proxy_clausification,[],[f46])).
% 2.95/0.75 thf(f51,plain,(
% 2.95/0.75 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (sK4 @ X1 @ X2) @ X1))) | ($false = ((in @ (sK3 @ X1 @ X2) @ X1))) | (X1 = X2)) )),
% 2.95/0.75 inference(imp_proxy_clausification,[],[f46])).
% 2.95/0.75 thf(f54,plain,(
% 2.95/0.75 ( ! [X0 : $i] : (($true != $true) | ($true = ((in @ X0 @ sK2))) | ($true != ((in @ X0 @ sK0))) | ($false = ((in @ X0 @ sK1)))) )),
% 2.95/0.75 inference(constrained_superposition,[],[f21,f25])).
% 2.95/0.75 thf(f58,plain,(
% 2.95/0.75 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK0))) | ($true = ((in @ X0 @ sK2))) | ($false = ((in @ X0 @ sK1)))) )),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f54])).
% 2.95/0.75 thf(f89,plain,(
% 2.95/0.75 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ X0 @ sK1))) | ($true = ((in @ X0 @ sK0)))) )),
% 2.95/0.75 inference(constrained_superposition,[],[f19,f35])).
% 2.95/0.75 thf(f90,plain,(
% 2.95/0.75 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ X0 @ sK2))) | ($true = ((in @ X0 @ sK0)))) )),
% 2.95/0.75 inference(constrained_superposition,[],[f20,f35])).
% 2.95/0.75 thf(f112,plain,(
% 2.95/0.75 ( ! [X0 : $i] : (($false = ((in @ X0 @ sK2))) | ($true = ((in @ X0 @ sK0)))) )),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f90])).
% 2.95/0.75 thf(f113,plain,(
% 2.95/0.75 ( ! [X0 : $i] : (($false = ((in @ X0 @ sK1))) | ($true = ((in @ X0 @ sK0)))) )),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f89])).
% 2.95/0.75 thf(f1033,plain,(
% 2.95/0.75 ( ! [X0 : $i] : (($true = $false) | ($true = ((in @ (sK4 @ sK1 @ X0) @ sK0))) | ($true = ((in @ (sK3 @ sK1 @ X0) @ X0))) | (sK1 = X0)) )),
% 2.95/0.75 inference(constrained_superposition,[],[f113,f49])).
% 2.95/0.75 thf(f1042,plain,(
% 2.95/0.75 ( ! [X0 : $i] : (($true = ((in @ (sK4 @ sK1 @ X0) @ sK0))) | ($true = ((in @ (sK3 @ sK1 @ X0) @ X0))) | (sK1 = X0)) )),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f1033])).
% 2.95/0.75 thf(f2349,definition,(
% 2.95/0.75 spl5_67 <=> ($true = ((in @ (sK4 @ sK1 @ sK2) @ sK0)))),
% 2.95/0.75 introduced(definition,[new_symbols(definition,[spl5_67])],[avatar_definition])).
% 2.95/0.75 thf(f2350,plain,(
% 2.95/0.75 ($true != ((in @ (sK4 @ sK1 @ sK2) @ sK0))) | spl5_67),
% 2.95/0.75 inference(avatar_component_clause,[],[f2349])).
% 2.95/0.75 thf(f2351,plain,(
% 2.95/0.75 ($true = ((in @ (sK4 @ sK1 @ sK2) @ sK0))) | ~spl5_67),
% 2.95/0.75 inference(avatar_component_clause,[],[f2349])).
% 2.95/0.75 thf(f2364,definition,(
% 2.95/0.75 spl5_70 <=> ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK0)))),
% 2.95/0.75 introduced(definition,[new_symbols(definition,[spl5_70])],[avatar_definition])).
% 2.95/0.75 thf(f2478,plain,(
% 2.95/0.75 ($true != $true) | ($true = ((in @ (sK4 @ sK1 @ sK2) @ sK2))) | ($false = ((in @ (sK4 @ sK1 @ sK2) @ sK1))) | ~spl5_67),
% 2.95/0.75 inference(constrained_superposition,[],[f58,f2351])).
% 2.95/0.75 thf(f2481,plain,(
% 2.95/0.75 ($true = ((in @ (sK4 @ sK1 @ sK2) @ sK2))) | ($false = ((in @ (sK4 @ sK1 @ sK2) @ sK1))) | ~spl5_67),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2478])).
% 2.95/0.75 thf(f2485,definition,(
% 2.95/0.75 spl5_75 <=> ($false = ((in @ (sK4 @ sK1 @ sK2) @ sK2)))),
% 2.95/0.75 introduced(definition,[new_symbols(definition,[spl5_75])],[avatar_definition])).
% 2.95/0.75 thf(f2486,plain,(
% 2.95/0.75 ($false != ((in @ (sK4 @ sK1 @ sK2) @ sK2))) | spl5_75),
% 2.95/0.75 inference(avatar_component_clause,[],[f2485])).
% 2.95/0.75 thf(f2487,plain,(
% 2.95/0.75 ($false = ((in @ (sK4 @ sK1 @ sK2) @ sK2))) | ~spl5_75),
% 2.95/0.75 inference(avatar_component_clause,[],[f2485])).
% 2.95/0.75 thf(f2494,definition,(
% 2.95/0.75 spl5_77 <=> ($false = ((in @ (sK4 @ sK1 @ sK2) @ sK1)))),
% 2.95/0.75 introduced(definition,[new_symbols(definition,[spl5_77])],[avatar_definition])).
% 2.95/0.75 thf(f2495,plain,(
% 2.95/0.75 ($false != ((in @ (sK4 @ sK1 @ sK2) @ sK1))) | spl5_77),
% 2.95/0.75 inference(avatar_component_clause,[],[f2494])).
% 2.95/0.75 thf(f2496,plain,(
% 2.95/0.75 ($false = ((in @ (sK4 @ sK1 @ sK2) @ sK1))) | ~spl5_77),
% 2.95/0.75 inference(avatar_component_clause,[],[f2494])).
% 2.95/0.75 thf(f2498,definition,(
% 2.95/0.75 spl5_78 <=> ($true = ((in @ (sK4 @ sK1 @ sK2) @ sK2)))),
% 2.95/0.75 introduced(definition,[new_symbols(definition,[spl5_78])],[avatar_definition])).
% 2.95/0.75 thf(f2500,plain,(
% 2.95/0.75 ($true = ((in @ (sK4 @ sK1 @ sK2) @ sK2))) | ~spl5_78),
% 2.95/0.75 inference(avatar_component_clause,[],[f2498])).
% 2.95/0.75 thf(f2501,plain,(
% 2.95/0.75 spl5_77 | spl5_78 | ~spl5_67),
% 2.95/0.75 inference(avatar_split_clause,[],[f2481,f2349,f2498,f2494])).
% 2.95/0.75 thf(f2502,plain,(
% 2.95/0.75 ($true = $false) | (~spl5_75 | ~spl5_78)),
% 2.95/0.75 inference(forward_demodulation,[],[f2500,f2487])).
% 2.95/0.75 thf(f2503,plain,(
% 2.95/0.75 $false | (~spl5_75 | ~spl5_78)),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2502])).
% 2.95/0.75 thf(f2504,plain,(
% 2.95/0.75 ~spl5_75 | ~spl5_78),
% 2.95/0.75 inference(avatar_contradiction_clause,[],[f2503])).
% 2.95/0.75 thf(f2545,plain,(
% 2.95/0.75 ($true = $false) | ($false = ((in @ (sK3 @ sK1 @ sK2) @ sK1))) | (sK1 = sK2) | ~spl5_77),
% 2.95/0.75 inference(constrained_superposition,[],[f51,f2496])).
% 2.95/0.75 thf(f2546,plain,(
% 2.95/0.75 ($true = $false) | ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK2))) | (sK1 = sK2) | ~spl5_77),
% 2.95/0.75 inference(constrained_superposition,[],[f49,f2496])).
% 2.95/0.75 thf(f2550,plain,(
% 2.95/0.75 ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK2))) | (sK1 = sK2) | ~spl5_77),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2546])).
% 2.95/0.75 thf(f2551,plain,(
% 2.95/0.75 ($false = ((in @ (sK3 @ sK1 @ sK2) @ sK1))) | (sK1 = sK2) | ~spl5_77),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2545])).
% 2.95/0.75 thf(f2557,plain,(
% 2.95/0.75 ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK2))) | ~spl5_77),
% 2.95/0.75 inference(forward_subsumption_resolution,[],[f2550,f23])).
% 2.95/0.75 thf(f2558,plain,(
% 2.95/0.75 ($false = ((in @ (sK3 @ sK1 @ sK2) @ sK1))) | ~spl5_77),
% 2.95/0.75 inference(forward_subsumption_resolution,[],[f2551,f23])).
% 2.95/0.75 thf(f2574,plain,(
% 2.95/0.75 ($true = $false) | ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | ~spl5_77),
% 2.95/0.75 inference(constrained_superposition,[],[f112,f2557])).
% 2.95/0.75 thf(f2576,plain,(
% 2.95/0.75 ($true != $true) | ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK1))) | ($true != ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | ~spl5_77),
% 2.95/0.75 inference(constrained_superposition,[],[f22,f2557])).
% 2.95/0.75 thf(f2577,plain,(
% 2.95/0.75 ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK1))) | ($true != ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | ~spl5_77),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2576])).
% 2.95/0.75 thf(f2579,plain,(
% 2.95/0.75 ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | ~spl5_77),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2574])).
% 2.95/0.75 thf(f2592,plain,(
% 2.95/0.75 ($true = $false) | ($true != ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | ~spl5_77),
% 2.95/0.75 inference(forward_demodulation,[],[f2577,f2558])).
% 2.95/0.75 thf(f2593,plain,(
% 2.95/0.75 ($true != ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | ~spl5_77),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2592])).
% 2.95/0.75 thf(f2596,plain,(
% 2.95/0.75 spl5_70 | ~spl5_77),
% 2.95/0.75 inference(avatar_split_clause,[],[f2579,f2494,f2364])).
% 2.95/0.75 thf(f2606,plain,(
% 2.95/0.75 ~spl5_70 | ~spl5_77),
% 2.95/0.75 inference(avatar_split_clause,[],[f2593,f2494,f2364])).
% 2.95/0.75 thf(f2615,plain,(
% 2.95/0.75 ($false != $false) | ($false = ((in @ (sK3 @ sK1 @ sK2) @ sK1))) | (sK1 = sK2) | spl5_75),
% 2.95/0.75 inference(constrained_superposition,[],[f2486,f50])).
% 2.95/0.75 thf(f2616,plain,(
% 2.95/0.75 ($false != $false) | ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK2))) | (sK1 = sK2) | spl5_75),
% 2.95/0.75 inference(constrained_superposition,[],[f2486,f48])).
% 2.95/0.75 thf(f2625,plain,(
% 2.95/0.75 ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK2))) | (sK1 = sK2) | spl5_75),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2616])).
% 2.95/0.75 thf(f2626,plain,(
% 2.95/0.75 ($false = ((in @ (sK3 @ sK1 @ sK2) @ sK1))) | (sK1 = sK2) | spl5_75),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2615])).
% 2.95/0.75 thf(f2631,plain,(
% 2.95/0.75 ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK2))) | spl5_75),
% 2.95/0.75 inference(forward_subsumption_resolution,[],[f2625,f23])).
% 2.95/0.75 thf(f2632,plain,(
% 2.95/0.75 ($false = ((in @ (sK3 @ sK1 @ sK2) @ sK1))) | spl5_75),
% 2.95/0.75 inference(forward_subsumption_resolution,[],[f2626,f23])).
% 2.95/0.75 thf(f2706,plain,(
% 2.95/0.75 ($true = $false) | ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | spl5_75),
% 2.95/0.75 inference(constrained_superposition,[],[f112,f2631])).
% 2.95/0.75 thf(f2708,plain,(
% 2.95/0.75 ($true != $true) | ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK1))) | ($true != ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | spl5_75),
% 2.95/0.75 inference(constrained_superposition,[],[f22,f2631])).
% 2.95/0.75 thf(f2709,plain,(
% 2.95/0.75 ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK1))) | ($true != ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | spl5_75),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2708])).
% 2.95/0.75 thf(f2711,plain,(
% 2.95/0.75 ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | spl5_75),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2706])).
% 2.95/0.75 thf(f2724,plain,(
% 2.95/0.75 ($true = $false) | ($true != ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | spl5_75),
% 2.95/0.75 inference(forward_demodulation,[],[f2709,f2632])).
% 2.95/0.75 thf(f2725,plain,(
% 2.95/0.75 ($true != ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | spl5_75),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2724])).
% 2.95/0.75 thf(f2728,plain,(
% 2.95/0.75 spl5_70 | spl5_75),
% 2.95/0.75 inference(avatar_split_clause,[],[f2711,f2485,f2364])).
% 2.95/0.75 thf(f2738,plain,(
% 2.95/0.75 ~spl5_70 | spl5_75),
% 2.95/0.75 inference(avatar_split_clause,[],[f2725,f2485,f2364])).
% 2.95/0.75 thf(f2837,plain,(
% 2.95/0.75 ($true != $true) | ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK2))) | (sK1 = sK2) | spl5_67),
% 2.95/0.75 inference(constrained_superposition,[],[f2350,f1042])).
% 2.95/0.75 thf(f2840,plain,(
% 2.95/0.75 ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK2))) | (sK1 = sK2) | spl5_67),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f2837])).
% 2.95/0.75 thf(f2844,plain,(
% 2.95/0.75 ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK2))) | spl5_67),
% 2.95/0.75 inference(forward_subsumption_resolution,[],[f2840,f23])).
% 2.95/0.75 thf(f3172,plain,(
% 2.95/0.75 ($true = $false) | ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | spl5_67),
% 2.95/0.75 inference(constrained_superposition,[],[f112,f2844])).
% 2.95/0.75 thf(f3177,plain,(
% 2.95/0.75 ($true = ((in @ (sK3 @ sK1 @ sK2) @ sK0))) | spl5_67),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f3172])).
% 2.95/0.75 thf(f3196,plain,(
% 2.95/0.75 spl5_70 | spl5_67),
% 2.95/0.75 inference(avatar_split_clause,[],[f3177,f2349,f2364])).
% 2.95/0.75 thf(f3489,plain,(
% 2.95/0.75 ($false != $false) | ($true = ((in @ (sK4 @ sK1 @ sK2) @ sK0))) | spl5_77),
% 2.95/0.75 inference(constrained_superposition,[],[f2495,f113])).
% 2.95/0.75 thf(f3491,plain,(
% 2.95/0.75 ($true = ((in @ (sK4 @ sK1 @ sK2) @ sK0))) | spl5_77),
% 2.95/0.75 inference(trivial_inequality_removal,[],[f3489])).
% 2.95/0.75 thf(f3495,plain,(
% 2.95/0.75 $false | (spl5_67 | spl5_77)),
% 2.95/0.75 inference(forward_subsumption_resolution,[],[f3491,f2350])).
% 2.95/0.75 thf(f3496,plain,(
% 2.95/0.75 spl5_67 | spl5_77),
% 2.95/0.75 inference(avatar_contradiction_clause,[],[f3495])).
% 2.95/0.75 cnf(s119, plain, ~spl5_67 | spl5_77 | spl5_78, inference(sat_conversion,[],[f2501])).
% 2.95/0.75 cnf(s120, plain, ~spl5_75 | ~spl5_78, inference(sat_conversion,[],[f2504])).
% 2.95/0.75 cnf(s121, plain, spl5_70 | ~spl5_77, inference(sat_conversion,[],[f2596])).
% 2.95/0.75 cnf(s125, plain, ~spl5_70 | ~spl5_77, inference(sat_conversion,[],[f2606])).
% 2.95/0.75 cnf(s126, plain, spl5_70 | spl5_75, inference(sat_conversion,[],[f2728])).
% 2.95/0.75 cnf(s130, plain, ~spl5_70 | spl5_75, inference(sat_conversion,[],[f2738])).
% 2.95/0.75 cnf(s161, plain, spl5_67 | spl5_70, inference(sat_conversion,[],[f3196])).
% 2.95/0.75 cnf(s172, plain, spl5_67 | spl5_77, inference(sat_conversion,[],[f3496])).
% 2.95/0.75 cnf(s173, plain, spl5_67, inference(rat,[],[s125,s161,s172])).
% 2.95/0.75 cnf(s174, plain, ~spl5_70, inference(rat,[],[s119,s120,s125,s130,s173])).
% 2.95/0.75 cnf(s175, plain, spl5_75, inference(rat,[],[s126,s174])).
% 2.95/0.75 cnf(s176, plain, ~spl5_77, inference(rat,[],[s121,s174])).
% 2.95/0.75 cnf(s177, plain, ~spl5_78, inference(rat,[],[s120,s175])).
% 2.95/0.75 cnf(s178, plain, $false, inference(rat,[],[s119,s173,s177,s176])).
% 2.95/0.75 thf(f3499,plain,(
% 2.95/0.75 $false),
% 2.95/0.75 inference(avatar_sat_refutation,[],[s178])).
% 2.95/0.75 % SZS output end Proof for theBenchmark
% 2.95/0.75 % (1348694)------------------------------
% 2.95/0.75 % (1348694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.95/0.75 % (1348694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/0.75 % (1348694)CaDiCaL version: 2.1.3
% 2.95/0.75 % (1348694)Termination reason: Refutation
% 2.95/0.75 % (1348694)Time elapsed: 0.217 s
% 2.95/0.75 % (1348694)Peak memory usage: 14 MB
% 2.95/0.75 % (1348694)Instructions burned: 240 (million)
% 2.95/0.75 % (1348659)Success in time 0.496 s
% 2.95/0.75 % Vampire exiting
%------------------------------------------------------------------------------