%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU875^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:34:19 AM UTC 2026
% Result : Theorem 1.85s 0.55s
% Output : Refutation 1.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU875^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:45:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 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
% 1.85/0.55 % (3616394)Will run a generic schedule for satisfiability detection.
% 1.85/0.55 % (3616402)dis+10_1_sil=32000:sp=arity:random_seed=3908205745:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.85/0.55 % (3616400)% WARNING: option uhcvi not known.
% 1.85/0.55 % (3616400)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3640809255:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.85/0.55 % (3616401)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=529270503:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.85/0.55 % (3616399)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3400261073_2999 on theBenchmark for (2999ds/0Mi)
% 1.85/0.55 % (3616400)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.55 % (3616400)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.85/0.55 % Exception at run slice level
% 1.85/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.55 % (3616403)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2515405067:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.85/0.55 % (3616403)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.55 % (3616404)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1166963596:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.85/0.55 % (3616405)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=97229806:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.85/0.55 % (3616410)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2238167569:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.85/0.55 % (3616402)Instruction limit reached!
% 1.85/0.55 % (3616402)------------------------------
% 1.85/0.55 % (3616402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.55 % (3616402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.55 % (3616402)CaDiCaL version: 2.1.3
% 1.85/0.55 % (3616402)Termination reason: Instruction limit
% 1.85/0.55 % (3616402)Termination phase: Saturation
% 1.85/0.55 % (3616402)Time elapsed: 0.036 s
% 1.85/0.55 % (3616402)Peak memory usage: 12 MB
% 1.85/0.55 % (3616402)Instructions burned: 107 (million)
% 1.85/0.55 % Exception at run slice level
% 1.85/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.55 % (3616415)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2793066659:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.85/0.55 % (3616416)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=240335441:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.85/0.55 % (3616416)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.55 % (3616416)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.85/0.55 % (3616415)Instruction limit reached!
% 1.85/0.55 % (3616415)------------------------------
% 1.85/0.55 % (3616415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.55 % (3616415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.55 % (3616415)CaDiCaL version: 2.1.3
% 1.85/0.55 % (3616415)Termination reason: Instruction limit
% 1.85/0.55 % (3616415)Termination phase: Saturation
% 1.85/0.55 % (3616415)Time elapsed: 0.037 s
% 1.85/0.55 % (3616415)Peak memory usage: 12 MB
% 1.85/0.55 % (3616415)Instructions burned: 131 (million)
% 1.85/0.55 % (3616404)Instruction limit reached!
% 1.85/0.55 % (3616404)------------------------------
% 1.85/0.55 % (3616404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.55 % (3616404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.55 % (3616404)CaDiCaL version: 2.1.3
% 1.85/0.55 % (3616404)Termination reason: Instruction limit
% 1.85/0.55 % (3616404)Termination phase: Saturation
% 1.85/0.55 % (3616404)Time elapsed: 0.067 s
% 1.85/0.55 % (3616404)Peak memory usage: 13 MB
% 1.85/0.55 % (3616404)Instructions burned: 132 (million)
% 1.85/0.55 % (3616419)ott-21_1_sil=16000:fs=off:random_seed=2898128067:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.85/0.55 % (3616420)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3316189628:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.85/0.55 % (3616403)Instruction limit reached!
% 1.85/0.55 % (3616403)------------------------------
% 1.85/0.55 % (3616403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.55 % (3616403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.55 % (3616403)CaDiCaL version: 2.1.3
% 1.85/0.55 % (3616403)Termination reason: Instruction limit
% 1.85/0.55 % (3616403)Termination phase: Saturation
% 1.85/0.55 % (3616403)Time elapsed: 0.103 s
% 1.85/0.55 % (3616403)Peak memory usage: 12 MB
% 1.85/0.55 % (3616403)Instructions burned: 116 (million)
% 1.85/0.55 % (3616419)Instruction limit reached!
% 1.85/0.55 % (3616419)------------------------------
% 1.85/0.55 % (3616419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.55 % (3616419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.55 % (3616419)CaDiCaL version: 2.1.3
% 1.85/0.55 % (3616419)Termination reason: Instruction limit
% 1.85/0.55 % (3616419)Termination phase: Saturation
% 1.85/0.55 % (3616419)Time elapsed: 0.046 s
% 1.85/0.55 % (3616419)Peak memory usage: 13 MB
% 1.85/0.55 % (3616419)Instructions burned: 184 (million)
% 1.85/0.55 % (3616423)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1725476637:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.85/0.55 % Exception at run slice level
% 1.85/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.55 % (3616425)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=949249756:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.85/0.55 % (3616426)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3296807778:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.85/0.55 % Exception at run slice level
% 1.85/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.55 % (3616405)Instruction limit reached!
% 1.85/0.55 % (3616405)------------------------------
% 1.85/0.55 % (3616405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.55 % (3616405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.55 % (3616405)CaDiCaL version: 2.1.3
% 1.85/0.55 % (3616405)Termination reason: Instruction limit
% 1.85/0.55 % (3616405)Termination phase: Saturation
% 1.85/0.55 % (3616405)Time elapsed: 0.143 s
% 1.85/0.55 % (3616405)Peak memory usage: 13 MB
% 1.85/0.55 % (3616405)Instructions burned: 159 (million)
% 1.85/0.55 % (3616429)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=101812813: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)
% 1.85/0.55 % (3616429)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.55 % (3616430)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2561348564:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 1.85/0.55 % (3616430)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.55 % (3616420) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3616394-3616420"...
% 1.85/0.55 % (3616420)...printing done.
% 1.85/0.55 % (3616420)Refutation found. Thanks to Tanya!
% 1.85/0.55 % SZS status Theorem for theBenchmark
% 1.85/0.55 % SZS output start Proof for theBenchmark
% 1.85/0.55 thf(type_def_5, type, a: $tType).
% 1.85/0.55 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 1.85/0.55 thf(func_def_0, type, t: a).
% 1.85/0.55 thf(func_def_1, type, cA: ((a > $o) > $o)).
% 1.85/0.55 thf(func_def_5, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.85/0.55 thf(func_def_6, type, vOR: ($o > $o > $o)).
% 1.85/0.55 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 1.85/0.55 thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.85/0.55 thf(func_def_9, type, sP0: ((a > $o) > $o)).
% 1.85/0.55 thf(func_def_10, type, sP1: $o).
% 1.85/0.55 thf(func_def_11, type, sK2: (a > $o)).
% 1.85/0.55 thf(func_def_12, type, sK3: ((a > $o) > a > $o)).
% 1.85/0.55 thf(func_def_13, type, sK4: ((a > $o) > a)).
% 1.85/0.55 thf(func_def_14, type, sK5: ((a > $o) > (a > $o) > $o)).
% 1.85/0.55 thf(func_def_15, type, sK6: (a > $o)).
% 1.85/0.55 thf(func_def_16, type, vNOT: ($o > $o)).
% 1.85/0.55 thf(func_def_18, type, db1: !>[X0: $tType]:(X0)).
% 1.85/0.55 thf(func_def_19, type, sK8: ((a > $o) > a)).
% 1.85/0.55 thf(f1,conjecture,(
% 1.85/0.55 ! [X0 : (a > $o)] : (((X0 @ t) & (cA @ X0)) => ? [X1 : (a > $o)] : (! [X3 : (a > $o)] : ((! [X4 : a] : ((X1 @ X4) => (X3 @ X4)) & (cA @ X3)) => ((X3 @ t) & (cA @ X3))) & ! [X4 : a] : ((X1 @ X4) => (X0 @ X4)) & ! [X2 : ((a > $o) > $o)] : ((! [X4 : (a > $o)] : ((X2 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X2 @ (^[X6 : a] : ((X5 = X6) | (X4 @ X6)))))) & (X2 @ (^[X3 : a] : ($false)))) => (X2 @ X1)))) & ! [X0 : (a > $o)] : (((X0 @ t) & (cA @ X0)) => (cA @ X0))),
% 1.85/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cDOMLEMMA5_pme)).
% 1.85/0.55 thf(f2,negated_conjecture,(
% 1.85/0.55 ~(! [X0 : (a > $o)] : (((X0 @ t) & (cA @ X0)) => ? [X1 : (a > $o)] : (! [X3 : (a > $o)] : ((! [X4 : a] : ((X1 @ X4) => (X3 @ X4)) & (cA @ X3)) => ((X3 @ t) & (cA @ X3))) & ! [X4 : a] : ((X1 @ X4) => (X0 @ X4)) & ! [X2 : ((a > $o) > $o)] : ((! [X4 : (a > $o)] : ((X2 @ X4) => ! [X5 : a] : ((X1 @ X5) => (X2 @ (^[X6 : a] : ((X5 = X6) | (X4 @ X6)))))) & (X2 @ (^[X3 : a] : ($false)))) => (X2 @ X1)))) & ! [X0 : (a > $o)] : (((X0 @ t) & (cA @ X0)) => (cA @ X0)))),
% 1.85/0.55 inference(negated_conjecture,[status(cth)],[f1])).
% 1.85/0.55 thf(f3,plain,(
% 1.85/0.55 ~(! [X0 : (a > $o)] : (((X0 @ t) & (cA @ X0)) => ? [X1 : (a > $o)] : (! [X2 : (a > $o)] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & (cA @ X2)) => ((X2 @ t) & (cA @ X2))) & ! [X4 : a] : ((X1 @ X4) => (X0 @ X4)) & ! [X5 : ((a > $o) > $o)] : ((! [X6 : (a > $o)] : ((X5 @ X6) => ! [X7 : a] : ((X1 @ X7) => (X5 @ (^[X8 : a] : ((X7 = X8) | (X6 @ X8)))))) & (X5 @ (^[X9 : a] : ($false)))) => (X5 @ X1)))) & ! [X10 : (a > $o)] : (((X10 @ t) & (cA @ X10)) => (cA @ X10)))),
% 1.85/0.55 inference(rectify,[],[f2])).
% 1.85/0.55 thf(f4,plain,(
% 1.85/0.55 ~(! [X0 : (a > $o)] : (((((X0 @ t)) = $true) & (((cA @ X0)) = $true)) => ? [X1 : (a > $o)] : (! [X2 : (a > $o)] : ((! [X3 : a] : ((((X1 @ X3)) = $true) => (((X2 @ X3)) = $true)) & (((cA @ X2)) = $true)) => ((((X2 @ t)) = $true) & (((cA @ X2)) = $true))) & ! [X4 : a] : ((((X1 @ X4)) = $true) => (((X0 @ X4)) = $true)) & ! [X5 : ((a > $o) > $o)] : ((! [X6 : (a > $o)] : ((((X5 @ X6)) = $true) => ! [X7 : a] : ((((X1 @ X7)) = $true) => ($true = ((X5 @ (^[Y0 : a]: ((X6 @ Y0) | (X7 = Y0)))))))) & ($true = ((X5 @ (^[Y0 : a]: ($false)))))) => (((X5 @ X1)) = $true)))) & ! [X10 : (a > $o)] : (((((X10 @ t)) = $true) & (((cA @ X10)) = $true)) => (((cA @ X10)) = $true)))),
% 1.85/0.55 inference(fool_elimination,[],[f3])).
% 1.85/0.55 thf(f5,plain,(
% 1.85/0.55 ~(! [X0 : (a > $o)] : (((((X0 @ t)) = $true) & (((cA @ X0)) = $true)) => ? [X1 : (a > $o)] : (! [X2 : (a > $o)] : ((! [X3 : a] : ((((X1 @ X3)) = $true) => (((X2 @ X3)) = $true)) & (((cA @ X2)) = $true)) => ((((X2 @ t)) = $true) & (((cA @ X2)) = $true))) & ! [X4 : a] : ((((X1 @ X4)) = $true) => (((X0 @ X4)) = $true)) & ! [X5 : ((a > $o) > $o)] : ((! [X6 : (a > $o)] : ((((X5 @ X6)) = $true) => ! [X7 : a] : ((((X1 @ X7)) = $true) => ($true = ((X5 @ (^[Y0 : a]: ((X6 @ Y0) | (X7 = Y0)))))))) & ($true = ((X5 @ (^[Y0 : a]: ($false)))))) => (((X5 @ X1)) = $true)))) & ! [X8 : (a > $o)] : ((($true = ((X8 @ t))) & ($true = ((cA @ X8)))) => ($true = ((cA @ X8)))))),
% 1.85/0.55 inference(rectify,[],[f4])).
% 1.85/0.55 thf(f6,plain,(
% 1.85/0.55 ? [X0 : (a > $o)] : (! [X1 : (a > $o)] : (? [X2 : (a > $o)] : (((((X2 @ t)) != $true) | (((cA @ X2)) != $true)) & (! [X3 : a] : ((((X2 @ X3)) = $true) | (((X1 @ X3)) != $true)) & (((cA @ X2)) = $true))) | ? [X4 : a] : ((((X0 @ X4)) != $true) & (((X1 @ X4)) = $true)) | ? [X5 : ((a > $o) > $o)] : ((((X5 @ X1)) != $true) & (! [X6 : (a > $o)] : (! [X7 : a] : (($true = ((X5 @ (^[Y0 : a]: ((X6 @ Y0) | (X7 = Y0)))))) | (((X1 @ X7)) != $true)) | (((X5 @ X6)) != $true)) & ($true = ((X5 @ (^[Y0 : a]: ($false)))))))) & ((((X0 @ t)) = $true) & (((cA @ X0)) = $true))) | ? [X8 : (a > $o)] : (($true != ((cA @ X8))) & (($true = ((X8 @ t))) & ($true = ((cA @ X8)))))),
% 1.85/0.55 inference(ennf_transformation,[],[f5])).
% 1.85/0.55 thf(f7,plain,(
% 1.85/0.55 ? [X0 : (a > $o)] : (! [X1 : (a > $o)] : (? [X2 : (a > $o)] : (((((X2 @ t)) != $true) | (((cA @ X2)) != $true)) & ! [X3 : a] : ((((X2 @ X3)) = $true) | (((X1 @ X3)) != $true)) & (((cA @ X2)) = $true)) | ? [X4 : a] : ((((X0 @ X4)) != $true) & (((X1 @ X4)) = $true)) | ? [X5 : ((a > $o) > $o)] : ((((X5 @ X1)) != $true) & ! [X6 : (a > $o)] : (! [X7 : a] : (($true = ((X5 @ (^[Y0 : a]: ((X6 @ Y0) | (X7 = Y0)))))) | (((X1 @ X7)) != $true)) | (((X5 @ X6)) != $true)) & ($true = ((X5 @ (^[Y0 : a]: ($false))))))) & (((X0 @ t)) = $true) & (((cA @ X0)) = $true)) | ? [X8 : (a > $o)] : (($true != ((cA @ X8))) & ($true = ((X8 @ t))) & ($true = ((cA @ X8))))),
% 1.85/0.55 inference(flattening,[],[f6])).
% 1.85/0.55 thf(f8,definition,(
% 1.85/0.55 ! [X1 : (a > $o)] : (? [X5 : ((a > $o) > $o)] : ((((X5 @ X1)) != $true) & ! [X6 : (a > $o)] : (! [X7 : a] : (($true = ((X5 @ (^[Y0 : a]: ((X6 @ Y0) | (X7 = Y0)))))) | (((X1 @ X7)) != $true)) | (((X5 @ X6)) != $true)) & ($true = ((X5 @ (^[Y0 : a]: ($false)))))) | ~ ($true = ((sP0 @ X1))))),
% 1.85/0.55 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.85/0.55 thf(f9,definition,(
% 1.85/0.55 ? [X0 : (a > $o)] : (! [X1 : (a > $o)] : (? [X2 : (a > $o)] : (((((X2 @ t)) != $true) | (((cA @ X2)) != $true)) & ! [X3 : a] : ((((X2 @ X3)) = $true) | (((X1 @ X3)) != $true)) & (((cA @ X2)) = $true)) | ? [X4 : a] : ((((X0 @ X4)) != $true) & (((X1 @ X4)) = $true)) | ($true = ((sP0 @ X1)))) & (((X0 @ t)) = $true) & (((cA @ X0)) = $true)) | ~ ($true = sP1)),
% 1.85/0.55 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 1.85/0.55 thf(f10,plain,(
% 1.85/0.55 ($true = sP1) | ? [X8 : (a > $o)] : (($true != ((cA @ X8))) & ($true = ((X8 @ t))) & ($true = ((cA @ X8))))),
% 1.85/0.55 inference(definition_folding,[],[f7,f9,f8])).
% 1.85/0.55 thf(f11,plain,(
% 1.85/0.55 ? [X0 : (a > $o)] : (! [X1 : (a > $o)] : (? [X2 : (a > $o)] : (((((X2 @ t)) != $true) | (((cA @ X2)) != $true)) & ! [X3 : a] : ((((X2 @ X3)) = $true) | (((X1 @ X3)) != $true)) & (((cA @ X2)) = $true)) | ? [X4 : a] : ((((X0 @ X4)) != $true) & (((X1 @ X4)) = $true)) | ($true = ((sP0 @ X1)))) & (((X0 @ t)) = $true) & (((cA @ X0)) = $true)) | ($true != sP1)),
% 1.85/0.55 inference(nnf_transformation,[],[f9])).
% 1.85/0.55 thf(f12,plain,(
% 1.85/0.55 (! [X1 : (a > $o)] : (((($true != ((sK3 @ X1 @ t))) | ($true != ((cA @ (sK3 @ X1))))) & ! [X3 : a] : (($true = ((sK3 @ X1 @ X3))) | (((X1 @ X3)) != $true)) & ($true = ((cA @ (sK3 @ X1))))) | (($true != ((sK2 @ (sK4 @ X1)))) & ($true = ((X1 @ (sK4 @ X1))))) | ($true = ((sP0 @ X1)))) & ($true = ((sK2 @ t))) & ($true = ((cA @ sK2)))) | ($true != sP1)),
% 1.85/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,vAPP,vAPP]),skolemize(X0,sK2),skolemize(X4,sK4 @ X1),skolemize(X4,sK4 @ X1)],[f11])).
% 1.85/0.55 thf(f13,plain,(
% 1.85/0.55 ! [X1 : (a > $o)] : (? [X5 : ((a > $o) > $o)] : ((((X5 @ X1)) != $true) & ! [X6 : (a > $o)] : (! [X7 : a] : (($true = ((X5 @ (^[Y0 : a]: ((X6 @ Y0) | (X7 = Y0)))))) | (((X1 @ X7)) != $true)) | (((X5 @ X6)) != $true)) & ($true = ((X5 @ (^[Y0 : a]: ($false)))))) | ($true != ((sP0 @ X1))))),
% 1.85/0.55 inference(nnf_transformation,[],[f8])).
% 1.85/0.55 thf(f14,plain,(
% 1.85/0.55 ! [X0 : (a > $o)] : (? [X1 : ((a > $o) > $o)] : (($true != ((X1 @ X0))) & ! [X2 : (a > $o)] : (! [X3 : a] : (($true = ((X1 @ (^[Y0 : a]: ((X2 @ Y0) | (X3 = Y0)))))) | ($true != ((X0 @ X3)))) | ($true != ((X1 @ X2)))) & ($true = ((X1 @ (^[Y0 : a]: ($false)))))) | ($true != ((sP0 @ X0))))),
% 1.85/0.55 inference(rectify,[],[f13])).
% 1.85/0.55 thf(f15,plain,(
% 1.85/0.55 ! [X0 : (a > $o)] : ((($true != ((sK5 @ X0 @ X0))) & ! [X2 : (a > $o)] : (! [X3 : a] : (($true = ((sK5 @ X0 @ (^[Y0 : a]: ((X2 @ Y0) | (X3 = Y0)))))) | ($true != ((X0 @ X3)))) | ($true != ((sK5 @ X0 @ X2)))) & ($true = ((sK5 @ X0 @ (^[Y0 : a]: ($false)))))) | ($true != ((sP0 @ X0))))),
% 1.85/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK4 @ X1)],[f14])).
% 1.85/0.55 thf(f16,plain,(
% 1.85/0.55 ($true = sP1) | ? [X0 : (a > $o)] : ((((cA @ X0)) != $true) & (((X0 @ t)) = $true) & (((cA @ X0)) = $true))),
% 1.85/0.55 inference(rectify,[],[f10])).
% 1.85/0.55 thf(f17,plain,(
% 1.85/0.55 ($true = sP1) | (($true != ((cA @ sK6))) & ($true = ((sK6 @ t))) & ($true = ((cA @ sK6))))),
% 1.85/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f16])).
% 1.85/0.55 thf(f19,plain,(
% 1.85/0.55 ($true = ((sK2 @ t))) | ($true != sP1)),
% 1.85/0.55 inference(cnf_transformation,[],[f12])).
% 1.85/0.55 thf(f20,plain,(
% 1.85/0.55 ( ! [X1 : (a > $o)] : (($true = ((cA @ (sK3 @ X1)))) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))) | ($true != sP1)) )),
% 1.85/0.55 inference(cnf_transformation,[],[f12])).
% 1.85/0.55 thf(f21,plain,(
% 1.85/0.55 ( ! [X1 : (a > $o)] : (($true = ((cA @ (sK3 @ X1)))) | ($true != ((sK2 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))) | ($true != sP1)) )),
% 1.85/0.55 inference(cnf_transformation,[],[f12])).
% 1.85/0.55 thf(f22,plain,(
% 1.85/0.55 ( ! [X3 : a,X1 : (a > $o)] : (($true = ((sK3 @ X1 @ X3))) | (((X1 @ X3)) != $true) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))) | ($true != sP1)) )),
% 1.85/0.55 inference(cnf_transformation,[],[f12])).
% 1.85/0.55 thf(f23,plain,(
% 1.85/0.55 ( ! [X3 : a,X1 : (a > $o)] : (($true = ((sK3 @ X1 @ X3))) | (((X1 @ X3)) != $true) | ($true != ((sK2 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))) | ($true != sP1)) )),
% 1.85/0.55 inference(cnf_transformation,[],[f12])).
% 1.85/0.55 thf(f24,plain,(
% 1.85/0.55 ( ! [X1 : (a > $o)] : (($true != ((sK3 @ X1 @ t))) | ($true != ((cA @ (sK3 @ X1)))) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))) | ($true != sP1)) )),
% 1.85/0.55 inference(cnf_transformation,[],[f12])).
% 1.85/0.55 thf(f25,plain,(
% 1.85/0.55 ( ! [X1 : (a > $o)] : (($true != ((sK3 @ X1 @ t))) | ($true != ((cA @ (sK3 @ X1)))) | ($true != ((sK2 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1))) | ($true != sP1)) )),
% 1.85/0.55 inference(cnf_transformation,[],[f12])).
% 1.85/0.55 thf(f26,plain,(
% 1.85/0.55 ( ! [X0 : (a > $o)] : (($true != ((sP0 @ X0))) | ($true = ((sK5 @ X0 @ (^[Y0 : a]: ($false)))))) )),
% 1.85/0.55 inference(cnf_transformation,[],[f15])).
% 1.85/0.55 thf(f27,plain,(
% 1.85/0.55 ( ! [X2 : (a > $o),X3 : a,X0 : (a > $o)] : (($true != ((sK5 @ X0 @ X2))) | ($true != ((X0 @ X3))) | ($true = ((sK5 @ X0 @ (^[Y0 : a]: ((X2 @ Y0) | (X3 = Y0)))))) | ($true != ((sP0 @ X0)))) )),
% 1.85/0.55 inference(cnf_transformation,[],[f15])).
% 1.85/0.55 thf(f28,plain,(
% 1.85/0.55 ( ! [X0 : (a > $o)] : (($true != ((sK5 @ X0 @ X0))) | ($true != ((sP0 @ X0)))) )),
% 1.85/0.55 inference(cnf_transformation,[],[f15])).
% 1.85/0.55 thf(f29,plain,(
% 1.85/0.55 ($true = sP1) | ($true = ((cA @ sK6)))),
% 1.85/0.55 inference(cnf_transformation,[],[f17])).
% 1.85/0.55 thf(f31,plain,(
% 1.85/0.55 ($true = sP1) | ($true != ((cA @ sK6)))),
% 1.85/0.55 inference(cnf_transformation,[],[f17])).
% 1.85/0.55 thf(f33,definition,(
% 1.85/0.55 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.85/0.55 introduced(theory,[fool_exhaustiveness_axiom])).
% 1.85/0.55 thf(f39,definition,(
% 1.85/0.55 spl7_2 <=> ($true = sP1)),
% 1.85/0.55 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 1.85/0.55 thf(f40,plain,(
% 1.85/0.55 ($true != sP1) | spl7_2),
% 1.85/0.55 inference(avatar_component_clause,[],[f39])).
% 1.85/0.55 thf(f41,plain,(
% 1.85/0.55 ($true = sP1) | ~spl7_2),
% 1.85/0.55 inference(avatar_component_clause,[],[f39])).
% 1.85/0.55 thf(f392,plain,(
% 1.85/0.55 ($true != $true) | ($false = sP1) | spl7_2),
% 1.85/0.55 inference(constrained_superposition,[],[f40,f33])).
% 1.85/0.55 thf(f393,plain,(
% 1.85/0.55 ($false = sP1) | spl7_2),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f392])).
% 1.85/0.55 thf(f397,plain,(
% 1.85/0.55 ($true = $false) | ($true = ((cA @ sK6))) | spl7_2),
% 1.85/0.55 inference(forward_demodulation,[],[f29,f393])).
% 1.85/0.55 thf(f398,plain,(
% 1.85/0.55 ($true = ((cA @ sK6))) | spl7_2),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f397])).
% 1.85/0.55 thf(f399,plain,(
% 1.85/0.55 ($true = sP1) | spl7_2),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f31,f398])).
% 1.85/0.55 thf(f400,plain,(
% 1.85/0.55 ($true = $false) | spl7_2),
% 1.85/0.55 inference(forward_demodulation,[],[f399,f393])).
% 1.85/0.55 thf(f401,plain,(
% 1.85/0.55 $false | spl7_2),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f400])).
% 1.85/0.55 thf(f402,plain,(
% 1.85/0.55 spl7_2),
% 1.85/0.55 inference(avatar_contradiction_clause,[],[f401])).
% 1.85/0.55 thf(f499,plain,(
% 1.85/0.55 ($true = ((sK2 @ t))) | ~spl7_2),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f19,f41])).
% 1.85/0.55 thf(f554,plain,(
% 1.85/0.55 ( ! [X3 : a,X1 : (a > $o)] : (($true != ((sK2 @ (sK4 @ X1)))) | (((X1 @ X3)) != $true) | ($true = ((sK3 @ X1 @ X3))) | ($true = ((sP0 @ X1)))) ) | ~spl7_2),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f23,f41])).
% 1.85/0.55 thf(f555,plain,(
% 1.85/0.55 ( ! [X3 : a,X1 : (a > $o)] : ((((X1 @ X3)) != $true) | ($true = ((sK3 @ X1 @ X3))) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_2),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f22,f41])).
% 1.85/0.55 thf(f556,plain,(
% 1.85/0.55 ( ! [X1 : (a > $o)] : (($true != ((sK3 @ X1 @ t))) | ($true != ((cA @ (sK3 @ X1)))) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_2),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f24,f41])).
% 1.85/0.55 thf(f574,plain,(
% 1.85/0.55 ( ! [X1 : (a > $o)] : (($true != ((sK2 @ (sK4 @ X1)))) | ($true = ((cA @ (sK3 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_2),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f21,f41])).
% 1.85/0.55 thf(f575,plain,(
% 1.85/0.55 ( ! [X1 : (a > $o)] : (($true = ((cA @ (sK3 @ X1)))) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_2),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f20,f41])).
% 1.85/0.55 thf(f721,plain,(
% 1.85/0.55 ( ! [X1 : (a > $o)] : (($true != ((sK3 @ X1 @ t))) | ($true = ((X1 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_2),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f556,f575])).
% 1.85/0.55 thf(f797,plain,(
% 1.85/0.55 ( ! [X0 : (a > $o),X1 : a] : (($true != $true) | ($true = ((sK3 @ X0 @ X1))) | ($true = ((X0 @ (sK4 @ X0)))) | ($true = ((sP0 @ X0))) | ($false = ((X0 @ X1)))) ) | ~spl7_2),
% 1.85/0.55 inference(constrained_superposition,[],[f555,f33])).
% 1.85/0.55 thf(f840,plain,(
% 1.85/0.55 ( ! [X0 : (a > $o),X1 : a] : (($true = ((sK3 @ X0 @ X1))) | ($true = ((X0 @ (sK4 @ X0)))) | ($true = ((sP0 @ X0))) | ($false = ((X0 @ X1)))) ) | ~spl7_2),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f797])).
% 1.85/0.55 thf(f1377,plain,(
% 1.85/0.55 ( ! [X1 : (a > $o)] : (($true != ((sK3 @ X1 @ t))) | ($true != ((cA @ (sK3 @ X1)))) | ($true != ((sK2 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_2),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f25,f41])).
% 1.85/0.55 thf(f1588,definition,(
% 1.85/0.55 spl7_36 <=> ($true = ((sP0 @ (= @ t))))),
% 1.85/0.55 introduced(definition,[new_symbols(definition,[spl7_36])],[avatar_definition])).
% 1.85/0.55 thf(f1589,plain,(
% 1.85/0.55 ($true != ((sP0 @ (= @ t)))) | spl7_36),
% 1.85/0.55 inference(avatar_component_clause,[],[f1588])).
% 1.85/0.55 thf(f1590,plain,(
% 1.85/0.55 ($true = ((sP0 @ (= @ t)))) | ~spl7_36),
% 1.85/0.55 inference(avatar_component_clause,[],[f1588])).
% 1.85/0.55 thf(f1592,definition,(
% 1.85/0.55 spl7_37 <=> (t = ((sK4 @ (= @ t))))),
% 1.85/0.55 introduced(definition,[new_symbols(definition,[spl7_37])],[avatar_definition])).
% 1.85/0.55 thf(f1593,plain,(
% 1.85/0.55 (t != ((sK4 @ (= @ t)))) | spl7_37),
% 1.85/0.55 inference(avatar_component_clause,[],[f1592])).
% 1.85/0.55 thf(f1594,plain,(
% 1.85/0.55 (t = ((sK4 @ (= @ t)))) | ~spl7_37),
% 1.85/0.55 inference(avatar_component_clause,[],[f1592])).
% 1.85/0.55 thf(f2229,plain,(
% 1.85/0.55 ($true != $true) | ($false = ((sP0 @ (= @ t)))) | spl7_36),
% 1.85/0.55 inference(constrained_superposition,[],[f1589,f33])).
% 1.85/0.55 thf(f2230,plain,(
% 1.85/0.55 ($false = ((sP0 @ (= @ t)))) | spl7_36),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f2229])).
% 1.85/0.55 thf(f2267,plain,(
% 1.85/0.55 ( ! [X0 : a] : (($true != ((sK2 @ t))) | ($true != ((t = X0))) | ($true = ((sK3 @ (= @ t) @ X0))) | ($true = ((sP0 @ (= @ t))))) ) | (~spl7_2 | ~spl7_37)),
% 1.85/0.55 inference(constrained_superposition,[],[f554,f1594])).
% 1.85/0.55 thf(f2270,plain,(
% 1.85/0.55 ( ! [X0 : a] : (($true != ((sK2 @ t))) | (t != X0) | ($true = ((sK3 @ (= @ t) @ X0))) | ($true = ((sP0 @ (= @ t))))) ) | (~spl7_2 | ~spl7_37)),
% 1.85/0.55 inference(equality_proxy_clausification,[],[f2267])).
% 1.85/0.55 thf(f2271,plain,(
% 1.85/0.55 ( ! [X0 : a] : ((t != X0) | ($true = ((sK3 @ (= @ t) @ X0))) | ($true = ((sP0 @ (= @ t))))) ) | (~spl7_2 | ~spl7_37)),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f2270,f499])).
% 1.85/0.55 thf(f2272,plain,(
% 1.85/0.55 ( ! [X0 : a] : (($true = $false) | (t != X0) | ($true = ((sK3 @ (= @ t) @ X0)))) ) | (~spl7_2 | spl7_36 | ~spl7_37)),
% 1.85/0.55 inference(forward_demodulation,[],[f2271,f2230])).
% 1.85/0.55 thf(f2273,plain,(
% 1.85/0.55 ( ! [X0 : a] : ((t != X0) | ($true = ((sK3 @ (= @ t) @ X0)))) ) | (~spl7_2 | spl7_36 | ~spl7_37)),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f2272])).
% 1.85/0.55 thf(f2277,plain,(
% 1.85/0.55 ($true = ((sK3 @ (= @ t) @ t))) | (~spl7_2 | spl7_36 | ~spl7_37)),
% 1.85/0.55 inference(equality_resolution,[],[f2273])).
% 1.85/0.55 thf(f2593,plain,(
% 1.85/0.55 ( ! [X1 : (a > $o)] : (($true != ((sK3 @ X1 @ t))) | ($true != ((sK2 @ (sK4 @ X1)))) | ($true = ((sP0 @ X1)))) ) | ~spl7_2),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f1377,f574])).
% 1.85/0.55 thf(f2598,plain,(
% 1.85/0.55 ($true != $true) | ($true != ((sK2 @ (sK4 @ (= @ t))))) | ($true = ((sP0 @ (= @ t)))) | (~spl7_2 | spl7_36 | ~spl7_37)),
% 1.85/0.55 inference(constrained_superposition,[],[f2593,f2277])).
% 1.85/0.55 thf(f2601,plain,(
% 1.85/0.55 ($true != ((sK2 @ (sK4 @ (= @ t))))) | ($true = ((sP0 @ (= @ t)))) | (~spl7_2 | spl7_36 | ~spl7_37)),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f2598])).
% 1.85/0.55 thf(f2607,plain,(
% 1.85/0.55 ($true != ((sK2 @ t))) | ($true = ((sP0 @ (= @ t)))) | (~spl7_2 | spl7_36 | ~spl7_37)),
% 1.85/0.55 inference(forward_demodulation,[],[f2601,f1594])).
% 1.85/0.55 thf(f2608,plain,(
% 1.85/0.55 ($true = ((sP0 @ (= @ t)))) | (~spl7_2 | spl7_36 | ~spl7_37)),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f2607,f499])).
% 1.85/0.55 thf(f2609,plain,(
% 1.85/0.55 ($true = $false) | (~spl7_2 | spl7_36 | ~spl7_37)),
% 1.85/0.55 inference(forward_demodulation,[],[f2608,f2230])).
% 1.85/0.55 thf(f2610,plain,(
% 1.85/0.55 $false | (~spl7_2 | spl7_36 | ~spl7_37)),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f2609])).
% 1.85/0.55 thf(f2611,plain,(
% 1.85/0.55 ~spl7_2 | spl7_36 | ~spl7_37),
% 1.85/0.55 inference(avatar_contradiction_clause,[],[f2610])).
% 1.85/0.55 thf(f2640,plain,(
% 1.85/0.55 ($true != $true) | ($true = ((sK5 @ (= @ t) @ (^[Y0 : a]: ($false))))) | ~spl7_36),
% 1.85/0.55 inference(constrained_superposition,[],[f26,f1590])).
% 1.85/0.55 thf(f2644,plain,(
% 1.85/0.55 ($true = ((sK5 @ (= @ t) @ (^[Y0 : a]: ($false))))) | ~spl7_36),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f2640])).
% 1.85/0.55 thf(f2656,plain,(
% 1.85/0.55 ( ! [X0 : a] : (($true != $true) | ($true != ((t = X0))) | ($true = ((sK5 @ (= @ t) @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) | ($true != ((sP0 @ (= @ t))))) ) | ~spl7_36),
% 1.85/0.55 inference(constrained_superposition,[],[f27,f2644])).
% 1.85/0.55 thf(f2660,plain,(
% 1.85/0.55 ( ! [X0 : a] : (($true != $true) | (t != X0) | ($true = ((sK5 @ (= @ t) @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) | ($true != ((sP0 @ (= @ t))))) ) | ~spl7_36),
% 1.85/0.55 inference(equality_proxy_clausification,[],[f2656])).
% 1.85/0.55 thf(f2661,plain,(
% 1.85/0.55 ( ! [X0 : a] : ((t != X0) | ($true = ((sK5 @ (= @ t) @ (^[Y0 : a]: (((^[Y1 : a]: ($false)) @ Y0) | (X0 = Y0)))))) | ($true != ((sP0 @ (= @ t))))) ) | ~spl7_36),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f2660])).
% 1.85/0.55 thf(f2662,plain,(
% 1.85/0.55 ( ! [X0 : a] : ((t != X0) | ($true = ((sK5 @ (= @ t) @ (^[Y0 : a]: ($false | (X0 = Y0)))))) | ($true != ((sP0 @ (= @ t))))) ) | ~spl7_36),
% 1.85/0.55 inference(beta-eta_normalization,[],[f2661])).
% 1.85/0.55 thf(f2663,plain,(
% 1.85/0.55 ( ! [X0 : a] : ((t != X0) | ($true = ((sK5 @ (= @ t) @ (^[Y0 : a]: (X0 = Y0))))) | ($true != ((sP0 @ (= @ t))))) ) | ~spl7_36),
% 1.85/0.55 inference(boolean_simplification,[],[f2662])).
% 1.85/0.55 thf(f2664,plain,(
% 1.85/0.55 ( ! [X0 : a] : ((t != X0) | ($true = ((sK5 @ (= @ t) @ (= @ X0)))) | ($true != ((sP0 @ (= @ t))))) ) | ~spl7_36),
% 1.85/0.55 inference(beta-eta_normalization,[],[f2663])).
% 1.85/0.55 thf(f2665,plain,(
% 1.85/0.55 ( ! [X0 : a] : ((t != X0) | ($true = ((sK5 @ (= @ t) @ (= @ X0))))) ) | ~spl7_36),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f2664,f1590])).
% 1.85/0.55 thf(f2666,plain,(
% 1.85/0.55 ($true = ((sK5 @ (= @ t) @ (= @ t)))) | ~spl7_36),
% 1.85/0.55 inference(equality_resolution,[],[f2665])).
% 1.85/0.55 thf(f2667,plain,(
% 1.85/0.55 ($true != $true) | ($true != ((sP0 @ (= @ t)))) | ~spl7_36),
% 1.85/0.55 inference(constrained_superposition,[],[f28,f2666])).
% 1.85/0.55 thf(f2674,plain,(
% 1.85/0.55 ($true != ((sP0 @ (= @ t)))) | ~spl7_36),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f2667])).
% 1.85/0.55 thf(f2676,plain,(
% 1.85/0.55 $false | ~spl7_36),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f2674,f1590])).
% 1.85/0.55 thf(f2677,plain,(
% 1.85/0.55 ~spl7_36),
% 1.85/0.55 inference(avatar_contradiction_clause,[],[f2676])).
% 1.85/0.55 thf(f2973,plain,(
% 1.85/0.55 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((X0 @ (sK4 @ X0)))) | ($true = ((sP0 @ X0))) | ($true = ((X0 @ (sK4 @ X0)))) | ($true = ((sP0 @ X0))) | (((X0 @ t)) = $false)) ) | ~spl7_2),
% 1.85/0.55 inference(constrained_superposition,[],[f721,f840])).
% 1.85/0.55 thf(f3062,plain,(
% 1.85/0.55 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((X0 @ (sK4 @ X0)))) | ($true = ((sP0 @ X0))) | (((X0 @ t)) = $false)) ) | ~spl7_2),
% 1.85/0.55 inference(duplicate_literal_removal,[],[f2973])).
% 1.85/0.55 thf(f3063,plain,(
% 1.85/0.55 ( ! [X0 : (a > $o)] : (($true = ((X0 @ (sK4 @ X0)))) | ($true = ((sP0 @ X0))) | (((X0 @ t)) = $false)) ) | ~spl7_2),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f3062])).
% 1.85/0.55 thf(f3098,plain,(
% 1.85/0.55 (t = ((sK4 @ (= @ t)))) | ($true = ((sP0 @ (= @ t)))) | ~spl7_2),
% 1.85/0.55 inference(leibniz_equality_elimination,[],[f3063])).
% 1.85/0.55 thf(f3201,plain,(
% 1.85/0.55 ($true = ((sP0 @ (= @ t)))) | (~spl7_2 | spl7_37)),
% 1.85/0.55 inference(forward_subsumption_resolution,[],[f3098,f1593])).
% 1.85/0.55 thf(f3202,plain,(
% 1.85/0.55 ($true = $false) | (~spl7_2 | spl7_36 | spl7_37)),
% 1.85/0.55 inference(forward_demodulation,[],[f3201,f2230])).
% 1.85/0.55 thf(f3203,plain,(
% 1.85/0.55 $false | (~spl7_2 | spl7_36 | spl7_37)),
% 1.85/0.55 inference(trivial_inequality_removal,[],[f3202])).
% 1.85/0.55 thf(f3204,plain,(
% 1.85/0.55 ~spl7_2 | spl7_36 | spl7_37),
% 1.85/0.55 inference(avatar_contradiction_clause,[],[f3203])).
% 1.85/0.55 cnf(s18, plain, spl7_2, inference(sat_conversion,[],[f402])).
% 1.85/0.55 cnf(s98, plain, ~spl7_2 | spl7_36 | ~spl7_37, inference(sat_conversion,[],[f2611])).
% 1.85/0.55 cnf(s102, plain, ~spl7_36, inference(sat_conversion,[],[f2677])).
% 1.85/0.55 cnf(s103, plain, ~spl7_2 | spl7_36 | spl7_37, inference(sat_conversion,[],[f3204])).
% 1.85/0.55 cnf(s104, plain, ~spl7_2 | ~spl7_37, inference(rat,[],[s98,s102])).
% 1.85/0.55 cnf(s112, plain, spl7_37, inference(rat,[],[s103,s102,s18])).
% 1.85/0.55 cnf(s113, plain, $false, inference(rat,[],[s104,s112,s18])).
% 1.85/0.55 thf(f3205,plain,(
% 1.85/0.55 $false),
% 1.85/0.55 inference(avatar_sat_refutation,[],[s113])).
% 1.85/0.55 % SZS output end Proof for theBenchmark
% 1.85/0.55 % (3616420)------------------------------
% 1.85/0.55 % (3616420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.55 % (3616420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.55 % (3616420)CaDiCaL version: 2.1.3
% 1.85/0.55 % (3616420)Termination reason: Refutation
% 1.85/0.55 % (3616420)Time elapsed: 0.172 s
% 1.85/0.55 % (3616420)Peak memory usage: 14 MB
% 1.85/0.55 % (3616420)Instructions burned: 325 (million)
% 1.85/0.55 % (3616394)Success in time 0.313 s
% 1.85/0.55 % Vampire exiting
%------------------------------------------------------------------------------