%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MSC020^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 08:15:37 AM UTC 2026
% Result : Theorem 3.93s 0.96s
% Output : Refutation 3.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MSC020^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 % Computer : n017.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 11:16:52 UTC 2026
% 0.08/0.24 % CPUTime :
% 0.08/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.24/0.29 Running first-order model finding
% 0.24/0.29 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.93/0.96 % (212585)Will run a generic schedule for satisfiability detection.
% 3.93/0.96 % (212595)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=449805160:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 3.93/0.96 % (212596)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3668586104:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 3.93/0.96 % (212591)% WARNING: option uhcvi not known.
% 3.93/0.96 % (212590)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3055371090_3000 on theBenchmark for (3000ds/0Mi)
% 3.93/0.96 % (212591)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=812539055:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 3.93/0.96 % (212592)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=977321624:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 3.93/0.96 % (212594)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2960380745:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 3.93/0.96 % (212593)dis+10_1_sil=32000:sp=arity:random_seed=1099091482:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 3.93/0.96 % (212591)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.93/0.96 % (212594)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.93/0.96 % Exception at run slice level
% 3.93/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs% (212591)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.93/0.96
% 3.93/0.96 % (212604)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3000583763:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.93/0.96 % Exception at run slice level
% 3.93/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.93/0.96 % (212595)Instruction limit reached!
% 3.93/0.96 % (212595)------------------------------
% 3.93/0.96 % (212595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.96 % (212595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.96 % (212595)CaDiCaL version: 2.1.3
% 3.93/0.96 % (212595)Termination reason: Instruction limit
% 3.93/0.96 % (212595)Termination phase: Saturation
% 3.93/0.96 % (212595)Time elapsed: 0.059 s
% 3.93/0.96 % (212595)Peak memory usage: 12 MB
% 3.93/0.96 % (212595)Instructions burned: 132 (million)
% 3.93/0.96 % (212607)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=2370441721:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.93/0.96 % (212607)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.93/0.96 % (212607)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.93/0.96 % (212606)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=200937024:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.93/0.96 % (212593)Instruction limit reached!
% 3.93/0.96 % (212593)------------------------------
% 3.93/0.96 % (212593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.96 % (212593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.96 % (212593)CaDiCaL version: 2.1.3
% 3.93/0.96 % (212593)Termination reason: Instruction limit
% 3.93/0.96 % (212593)Termination phase: Saturation
% 3.93/0.96 % (212593)Time elapsed: 0.089 s
% 3.93/0.96 % (212593)Peak memory usage: 12 MB
% 3.93/0.96 % (212593)Instructions burned: 103 (million)
% 3.93/0.96 % (212594)Instruction limit reached!
% 3.93/0.96 % (212594)------------------------------
% 3.93/0.96 % (212594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.96 % (212594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.96 % (212594)CaDiCaL version: 2.1.3
% 3.93/0.96 % (212594)Termination reason: Instruction limit
% 3.93/0.96 % (212594)Termination phase: Saturation
% 3.93/0.96 % (212594)Time elapsed: 0.098 s
% 3.93/0.96 % (212594)Peak memory usage: 12 MB
% 3.93/0.96 % (212594)Instructions burned: 117 (million)
% 3.93/0.96 % (212596)Instruction limit reached!
% 3.93/0.96 % (212596)------------------------------
% 3.93/0.96 % (212596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.96 % (212596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.96 % (212596)CaDiCaL version: 2.1.3
% 3.93/0.96 % (212596)Termination reason: Instruction limit
% 3.93/0.96 % (212596)Termination phase: Saturation
% 3.93/0.96 % (212596)Time elapsed: 0.124 s
% 3.93/0.96 % (212596)Peak memory usage: 12 MB
% 3.93/0.96 % (212596)Instructions burned: 160 (million)
% 3.93/0.96 % (212611)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2416494360:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.93/0.96 % (212610)ott-21_1_sil=16000:fs=off:random_seed=1899409836:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.93/0.96 % (212612)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2426554487:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.93/0.96 % Exception at run slice level
% 3.93/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.93/0.96 % (212616)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2035734643:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.93/0.96 % (212606)Instruction limit reached!
% 3.93/0.96 % (212606)------------------------------
% 3.93/0.96 % (212606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.96 % (212606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.96 % (212606)CaDiCaL version: 2.1.3
% 3.93/0.96 % (212606)Termination reason: Instruction limit
% 3.93/0.96 % (212606)Termination phase: Saturation
% 3.93/0.96 % (212606)Time elapsed: 0.117 s
% 3.93/0.96 % (212606)Peak memory usage: 13 MB
% 3.93/0.96 % (212606)Instructions burned: 132 (million)
% 3.93/0.96 % (212618)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1654482243:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 3.93/0.96 % Exception at run slice level
% 3.93/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.93/0.96 % (212620)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=1853705427: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)
% 3.93/0.96 % (212620)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.93/0.96 % (212610)Instruction limit reached!
% 3.93/0.96 % (212610)------------------------------
% 3.93/0.96 % (212610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.96 % (212610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.96 % (212610)CaDiCaL version: 2.1.3
% 3.93/0.96 % (212610)Termination reason: Instruction limit
% 3.93/0.96 % (212610)Termination phase: Saturation
% 3.93/0.96 % (212610)Time elapsed: 0.152 s
% 3.93/0.96 % (212610)Peak memory usage: 12 MB
% 3.93/0.96 % (212610)Instructions burned: 181 (million)
% 3.93/0.96 % (212611)Instruction limit reached!
% 3.93/0.96 % (212611)------------------------------
% 3.93/0.96 % (212611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.96 % (212611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.96 % (212611)CaDiCaL version: 2.1.3
% 3.93/0.96 % (212611)Termination reason: Instruction limit
% 3.93/0.96 % (212611)Termination phase: Saturation
% 3.93/0.96 % (212611)Time elapsed: 0.189 s
% 3.93/0.96 % (212611)Peak memory usage: 13 MB
% 3.93/0.96 % (212611)Instructions burned: 480 (million)
% 3.93/0.96 % (212623)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4174811785:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 3.93/0.96 % (212623)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.93/0.96 % (212624)fmb+10_1_sil=64000:random_seed=254564025:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 3.93/0.96 % (212624)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.93/0.96 % Exception at run slice level
% 3.93/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.93/0.96 % (212627)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=35503702:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 3.93/0.96 % Exception at run slice level
% 3.93/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.93/0.96 % (212629)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1776932572:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 3.93/0.96 % Exception at run slice level
% 3.93/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.93/0.96 % (212631)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=77761151:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 3.93/0.96 % (212631)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.93/0.96 % (212607)Instruction limit reached!
% 3.93/0.96 % (212607)------------------------------
% 3.93/0.96 % (212607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.96 % (212607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.96 % (212607)CaDiCaL version: 2.1.3
% 3.93/0.96 % (212607)Termination reason: Instruction limit
% 3.93/0.96 % (212607)Termination phase: Saturation
% 3.93/0.96 % (212607)Time elapsed: 0.538 s
% 3.93/0.96 % (212607)Peak memory usage: 14 MB
% 3.93/0.96 % (212607)Instructions burned: 684 (million)
% 3.93/0.96 % (212631) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-212585-212631"...
% 3.93/0.96 % (212631)...printing done.
% 3.93/0.96 % (212631)Refutation found. Thanks to Tanya!
% 3.93/0.96 % SZS status Theorem for theBenchmark
% 3.93/0.96 % SZS output start Proof for theBenchmark
% 3.93/0.96 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 3.93/0.96 thf(func_def_0, type, cHALF: ($i > $i > $o)).
% 3.93/0.96 thf(func_def_1, type, cDOUBLE: ($i > $i > $o)).
% 3.93/0.96 thf(func_def_2, type, cS: ($i > $i)).
% 3.93/0.96 thf(func_def_9, type, sK2: (($i > $i > $o) > $i)).
% 3.93/0.96 thf(func_def_10, type, sK3: (($i > $i > $o) > $i)).
% 3.93/0.96 thf(func_def_11, type, vNOT: ($o > $o)).
% 3.93/0.96 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 3.93/0.96 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 3.93/0.96 thf(func_def_14, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.93/0.96 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.93/0.96 thf(func_def_16, type, db2: !>[X0: $tType]:(X0)).
% 3.93/0.96 thf(func_def_18, type, db3: !>[X0: $tType]:(X0)).
% 3.93/0.96 thf(func_def_19, type, db4: !>[X0: $tType]:(X0)).
% 3.93/0.96 thf(f1,conjecture,(
% 3.93/0.96 (! [X3 : $i,X4 : $i] : ((cHALF @ X3 @ X4) => (cHALF @ (cS @ (cS @ X3)) @ (cS @ X4))) & (cHALF @ (cS @ c0) @ c0) & (cHALF @ c0 @ c0) & ! [X0 : ($i > $i > $o),X1 : $i,X2 : $i] : ((! [X3 : $i,X4 : $i] : ((X0 @ X3 @ X4) => (X0 @ (cS @ X3) @ (cS @ (cS @ X4)))) & (X0 @ c0 @ c0) & (cDOUBLE @ X1 @ X2)) => (X0 @ X1 @ X2))) => ! [X1 : $i,X2 : $i] : ((cDOUBLE @ X1 @ X2) => (cHALF @ X2 @ X1))),
% 3.93/0.96 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM301)).
% 3.93/0.96 thf(f2,negated_conjecture,(
% 3.93/0.96 ~((! [X3 : $i,X4 : $i] : ((cHALF @ X3 @ X4) => (cHALF @ (cS @ (cS @ X3)) @ (cS @ X4))) & (cHALF @ (cS @ c0) @ c0) & (cHALF @ c0 @ c0) & ! [X0 : ($i > $i > $o),X1 : $i,X2 : $i] : ((! [X3 : $i,X4 : $i] : ((X0 @ X3 @ X4) => (X0 @ (cS @ X3) @ (cS @ (cS @ X4)))) & (X0 @ c0 @ c0) & (cDOUBLE @ X1 @ X2)) => (X0 @ X1 @ X2))) => ! [X1 : $i,X2 : $i] : ((cDOUBLE @ X1 @ X2) => (cHALF @ X2 @ X1)))),
% 3.93/0.96 inference(negated_conjecture,[status(cth)],[f1])).
% 3.93/0.96 thf(f3,plain,(
% 3.93/0.96 ~((! [X0 : $i,X1 : $i] : ((cHALF @ X0 @ X1) => (cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) & (cHALF @ (cS @ c0) @ c0) & (cHALF @ c0 @ c0) & ! [X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((! [X5 : $i,X6 : $i] : ((X2 @ X5 @ X6) => (X2 @ (cS @ X5) @ (cS @ (cS @ X6)))) & (X2 @ c0 @ c0) & (cDOUBLE @ X3 @ X4)) => (X2 @ X3 @ X4))) => ! [X7 : $i,X8 : $i] : ((cDOUBLE @ X7 @ X8) => (cHALF @ X8 @ X7)))),
% 3.93/0.96 inference(rectify,[],[f2])).
% 3.93/0.96 thf(f4,plain,(
% 3.93/0.96 ~((! [X0 : $i,X1 : $i] : ((((cHALF @ X0 @ X1)) = $true) => (((cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) = $true)) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((! [X5 : $i,X6 : $i] : ((((X2 @ X5 @ X6)) = $true) => (((X2 @ (cS @ X5) @ (cS @ (cS @ X6)))) = $true)) & (((X2 @ c0 @ c0)) = $true) & (((cDOUBLE @ X3 @ X4)) = $true)) => (((X2 @ X3 @ X4)) = $true))) => ! [X7 : $i,X8 : $i] : ((((cDOUBLE @ X7 @ X8)) = $true) => (((cHALF @ X8 @ X7)) = $true)))),
% 3.93/0.96 inference(fool_elimination,[],[f3])).
% 3.93/0.96 thf(f5,plain,(
% 3.93/0.96 ? [X7 : $i,X8 : $i] : ((((cHALF @ X8 @ X7)) != $true) & (((cDOUBLE @ X7 @ X8)) = $true)) & (! [X0 : $i,X1 : $i] : ((((cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) = $true) | (((cHALF @ X0 @ X1)) != $true)) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((((X2 @ X3 @ X4)) = $true) | (? [X5 : $i,X6 : $i] : ((((X2 @ (cS @ X5) @ (cS @ (cS @ X6)))) != $true) & (((X2 @ X5 @ X6)) = $true)) | (((X2 @ c0 @ c0)) != $true) | (((cDOUBLE @ X3 @ X4)) != $true))))),
% 3.93/0.96 inference(ennf_transformation,[],[f4])).
% 3.93/0.96 thf(f6,plain,(
% 3.93/0.96 ? [X7 : $i,X8 : $i] : ((((cHALF @ X8 @ X7)) != $true) & (((cDOUBLE @ X7 @ X8)) = $true)) & ! [X0 : $i,X1 : $i] : ((((cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) = $true) | (((cHALF @ X0 @ X1)) != $true)) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X2 : ($i > $i > $o),X3 : $i,X4 : $i] : ((((X2 @ X3 @ X4)) = $true) | ? [X5 : $i,X6 : $i] : ((((X2 @ (cS @ X5) @ (cS @ (cS @ X6)))) != $true) & (((X2 @ X5 @ X6)) = $true)) | (((X2 @ c0 @ c0)) != $true) | (((cDOUBLE @ X3 @ X4)) != $true))),
% 3.93/0.96 inference(flattening,[],[f5])).
% 3.93/0.96 thf(f7,plain,(
% 3.93/0.96 ? [X0 : $i,X1 : $i] : (($true != ((cHALF @ X1 @ X0))) & ($true = ((cDOUBLE @ X0 @ X1)))) & ! [X2 : $i,X3 : $i] : (($true = ((cHALF @ (cS @ (cS @ X2)) @ (cS @ X3)))) | ($true != ((cHALF @ X2 @ X3)))) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X4 : ($i > $i > $o),X5 : $i,X6 : $i] : (($true = ((X4 @ X5 @ X6))) | ? [X7 : $i,X8 : $i] : (($true != ((X4 @ (cS @ X7) @ (cS @ (cS @ X8))))) & ($true = ((X4 @ X7 @ X8)))) | ($true != ((X4 @ c0 @ c0))) | ($true != ((cDOUBLE @ X5 @ X6))))),
% 3.93/0.96 inference(rectify,[],[f6])).
% 3.93/0.96 thf(f8,plain,(
% 3.93/0.96 (($true != ((cHALF @ sK1 @ sK0))) & ($true = ((cDOUBLE @ sK0 @ sK1)))) & ! [X2 : $i,X3 : $i] : (($true = ((cHALF @ (cS @ (cS @ X2)) @ (cS @ X3)))) | ($true != ((cHALF @ X2 @ X3)))) & (((cHALF @ (cS @ c0) @ c0)) = $true) & (((cHALF @ c0 @ c0)) = $true) & ! [X4 : ($i > $i > $o),X5 : $i,X6 : $i] : (($true = ((X4 @ X5 @ X6))) | (($true != ((X4 @ (cS @ (sK2 @ X4)) @ (cS @ (cS @ (sK3 @ X4)))))) & ($true = ((X4 @ (sK2 @ X4) @ (sK3 @ X4))))) | ($true != ((X4 @ c0 @ c0))) | ($true != ((cDOUBLE @ X5 @ X6))))),
% 3.93/0.96 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X8,sK3 @ X4),skolemize(X8,sK3 @ X4)],[f7])).
% 3.93/0.96 thf(f9,plain,(
% 3.93/0.96 ( ! [X6 : $i,X4 : ($i > $i > $o),X5 : $i] : (($true != ((X4 @ c0 @ c0))) | ($true = ((X4 @ (sK2 @ X4) @ (sK3 @ X4)))) | ($true = ((X4 @ X5 @ X6))) | ($true != ((cDOUBLE @ X5 @ X6)))) )),
% 3.93/0.96 inference(cnf_transformation,[],[f8])).
% 3.93/0.96 thf(f10,plain,(
% 3.93/0.96 ( ! [X6 : $i,X4 : ($i > $i > $o),X5 : $i] : (($true != ((X4 @ c0 @ c0))) | ($true != ((X4 @ (cS @ (sK2 @ X4)) @ (cS @ (cS @ (sK3 @ X4)))))) | ($true = ((X4 @ X5 @ X6))) | ($true != ((cDOUBLE @ X5 @ X6)))) )),
% 3.93/0.96 inference(cnf_transformation,[],[f8])).
% 3.93/0.96 thf(f11,plain,(
% 3.93/0.96 (((cHALF @ c0 @ c0)) = $true)),
% 3.93/0.96 inference(cnf_transformation,[],[f8])).
% 3.93/0.96 thf(f13,plain,(
% 3.93/0.96 ( ! [X2 : $i,X3 : $i] : (($true != ((cHALF @ X2 @ X3))) | ($true = ((cHALF @ (cS @ (cS @ X2)) @ (cS @ X3))))) )),
% 3.93/0.96 inference(cnf_transformation,[],[f8])).
% 3.93/0.96 thf(f14,plain,(
% 3.93/0.96 ($true = ((cDOUBLE @ sK0 @ sK1)))),
% 3.93/0.96 inference(cnf_transformation,[],[f8])).
% 3.93/0.96 thf(f15,plain,(
% 3.93/0.96 ($true != ((cHALF @ sK1 @ sK0)))),
% 3.93/0.96 inference(cnf_transformation,[],[f8])).
% 3.93/0.96 thf(f17,definition,(
% 3.93/0.96 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.93/0.96 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.93/0.96 thf(f26,plain,(
% 3.93/0.96 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) = $true) | (((cHALF @ X0 @ X1)) = $false)) )),
% 3.93/0.96 inference(constrained_superposition,[],[f13,f17])).
% 3.93/0.96 thf(f30,plain,(
% 3.93/0.96 ( ! [X0 : $i,X1 : $i] : ((((cHALF @ (cS @ (cS @ X0)) @ (cS @ X1))) = $true) | (((cHALF @ X0 @ X1)) = $false)) )),
% 3.93/0.96 inference(trivial_inequality_removal,[],[f26])).
% 3.93/0.96 thf(f44,plain,(
% 3.93/0.96 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : (($true != $true) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X1 @ X2))) | (((cDOUBLE @ X1 @ X2)) != $true) | (c0 != ((X0 @ c0 @ c0)))) )),
% 3.93/0.96 inference(constrained_superposition,[],[f9,f11])).
% 3.93/0.96 thf(f76,plain,(
% 3.93/0.96 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : (($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X1 @ X2))) | (((cDOUBLE @ X1 @ X2)) != $true) | (c0 != ((X0 @ c0 @ c0)))) )),
% 3.93/0.96 inference(trivial_inequality_removal,[],[f44])).
% 3.93/0.96 thf(f77,plain,(
% 3.93/0.96 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : ((c0 != ((X0 @ c0 @ c0))) | ($true = ((cHALF @ (X0 @ X1 @ X2) @ X1))) | (((cDOUBLE @ X1 @ X2)) != $true) | ($true = ((cHALF @ (X0 @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0))))))))) )),
% 3.93/0.96 inference(beta-eta_normalization,[],[f76])).
% 3.93/0.96 thf(f108,plain,(
% 3.93/0.96 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : (($true != $true) | ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ (cS @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))) @ (cS @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))))))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X1 @ X2))) | (((cDOUBLE @ X1 @ X2)) != $true) | (c0 != ((X0 @ c0 @ c0)))) )),
% 3.93/0.96 inference(constrained_superposition,[],[f10,f11])).
% 3.93/0.96 thf(f141,plain,(
% 3.93/0.96 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : (($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ (cS @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))) @ (cS @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))))))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X1 @ X2))) | (((cDOUBLE @ X1 @ X2)) != $true) | (c0 != ((X0 @ c0 @ c0)))) )),
% 3.93/0.96 inference(trivial_inequality_removal,[],[f108])).
% 3.93/0.96 thf(f142,plain,(
% 3.93/0.96 ( ! [X2 : $i,X0 : ($i > $i > $i),X1 : $i] : ((c0 != ((X0 @ c0 @ c0))) | ($true = ((cHALF @ (X0 @ X1 @ X2) @ X1))) | (((cDOUBLE @ X1 @ X2)) != $true) | ($true != ((cHALF @ (X0 @ (cS @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))) @ (cS @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))))) @ (cS @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ (X0 @ Y0 @ Y1) @ Y0)))))))))) )),
% 3.93/0.96 inference(beta-eta_normalization,[],[f141])).
% 3.93/0.96 thf(f511,plain,(
% 3.93/0.96 ( ! [X0 : $i,X1 : $i] : (($true = ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ X0 @ X1) @ X0))) | ($true != ((cDOUBLE @ X0 @ X1))) | ($true = ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0))))) @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0)))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0))))))))) )),
% 3.93/0.96 inference(equality_resolution,[],[f77])).
% 3.93/0.96 thf(f514,plain,(
% 3.93/0.96 ( ! [X0 : $i,X1 : $i] : (($true = ((cHALF @ X1 @ X0))) | ($true != ((cDOUBLE @ X0 @ X1))) | ($true = ((cHALF @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))))) )),
% 3.93/0.96 inference(beta-eta_normalization,[],[f511])).
% 3.93/0.96 thf(f567,plain,(
% 3.93/0.96 ( ! [X0 : $i,X1 : $i] : (($true = ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ X0 @ X1) @ X0))) | ($true != ((cDOUBLE @ X0 @ X1))) | ($true != ((cHALF @ ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1)))) @ (cS @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0)))))) @ (cS @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0)))))))) @ (cS @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ Y0)))))))))) )),
% 3.93/0.96 inference(equality_resolution,[],[f142])).
% 3.93/0.96 thf(f570,plain,(
% 3.93/0.96 ( ! [X0 : $i,X1 : $i] : (($true = ((cHALF @ X1 @ X0))) | ($true != ((cDOUBLE @ X0 @ X1))) | ($true != ((cHALF @ (cS @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))) @ (cS @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))))) )),
% 3.93/0.96 inference(beta-eta_normalization,[],[f567])).
% 3.93/0.96 thf(f2014,definition,(
% 3.93/0.96 spl4_33 <=> ($true = ((cHALF @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))))),
% 3.93/0.96 introduced(definition,[new_symbols(definition,[spl4_33])],[avatar_definition])).
% 3.93/0.96 thf(f2016,plain,(
% 3.93/0.96 ($true = ((cHALF @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))) | ~spl4_33),
% 3.93/0.96 inference(avatar_component_clause,[],[f2014])).
% 3.93/0.96 thf(f2018,definition,(
% 3.93/0.96 spl4_34 <=> ! [X0 : $i,X1 : $i] : (($true = ((cHALF @ X1 @ X0))) | ($true != ((cDOUBLE @ X0 @ X1))))),
% 3.93/0.96 introduced(definition,[new_symbols(definition,[spl4_34])],[avatar_definition])).
% 3.93/0.96 thf(f2019,plain,(
% 3.93/0.96 ( ! [X0 : $i,X1 : $i] : (($true != ((cDOUBLE @ X0 @ X1))) | ($true = ((cHALF @ X1 @ X0)))) ) | ~spl4_34),
% 3.93/0.96 inference(avatar_component_clause,[],[f2018])).
% 3.93/0.96 thf(f2020,plain,(
% 3.93/0.96 spl4_33 | spl4_34),
% 3.93/0.96 inference(avatar_split_clause,[],[f514,f2018,f2014])).
% 3.93/0.96 thf(f2700,definition,(
% 3.93/0.96 spl4_40 <=> ($true = ((cHALF @ (cS @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))) @ (cS @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))))),
% 3.93/0.96 introduced(definition,[new_symbols(definition,[spl4_40])],[avatar_definition])).
% 3.93/0.96 thf(f2702,plain,(
% 3.93/0.96 ($true != ((cHALF @ (cS @ (cS @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))) @ (cS @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))))))) | spl4_40),
% 3.93/0.96 inference(avatar_component_clause,[],[f2700])).
% 3.93/0.96 thf(f2703,plain,(
% 3.93/0.96 ~spl4_40 | spl4_34),
% 3.93/0.96 inference(avatar_split_clause,[],[f570,f2018,f2700])).
% 3.93/0.96 thf(f3156,plain,(
% 3.93/0.96 ($true != $true) | ($false = ((cHALF @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))) | spl4_40),
% 3.93/0.96 inference(constrained_superposition,[],[f2702,f30])).
% 3.93/0.96 thf(f3180,plain,(
% 3.93/0.96 ($false = ((cHALF @ (sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))))) | spl4_40),
% 3.93/0.96 inference(trivial_inequality_removal,[],[f3156])).
% 3.93/0.96 thf(f3987,plain,(
% 3.93/0.96 ($true = $false) | (~spl4_33 | spl4_40)),
% 3.93/0.96 inference(constrained_superposition,[],[f3180,f2016])).
% 3.93/0.96 thf(f4065,plain,(
% 3.93/0.96 $false | (~spl4_33 | spl4_40)),
% 3.93/0.96 inference(trivial_inequality_removal,[],[f3987])).
% 3.93/0.96 thf(f4066,plain,(
% 3.93/0.96 ~spl4_33 | spl4_40),
% 3.93/0.96 inference(avatar_contradiction_clause,[],[f4065])).
% 3.93/0.96 thf(f4068,plain,(
% 3.93/0.96 ($true != $true) | ($true = ((cHALF @ sK1 @ sK0))) | ~spl4_34),
% 3.93/0.96 inference(constrained_superposition,[],[f2019,f14])).
% 3.93/0.96 thf(f4085,plain,(
% 3.93/0.96 ($true = ((cHALF @ sK1 @ sK0))) | ~spl4_34),
% 3.93/0.96 inference(trivial_inequality_removal,[],[f4068])).
% 3.93/0.96 thf(f4086,plain,(
% 3.93/0.96 $false | ~spl4_34),
% 3.93/0.96 inference(forward_subsumption_resolution,[],[f4085,f15])).
% 3.93/0.96 thf(f4087,plain,(
% 3.93/0.96 ~spl4_34),
% 3.93/0.96 inference(avatar_contradiction_clause,[],[f4086])).
% 3.93/0.96 cnf(s22, plain, spl4_33 | spl4_34, inference(sat_conversion,[],[f2020])).
% 3.93/0.96 cnf(s26, plain, spl4_34 | ~spl4_40, inference(sat_conversion,[],[f2703])).
% 3.93/0.96 cnf(s31, plain, ~spl4_33 | spl4_40, inference(sat_conversion,[],[f4066])).
% 3.93/0.96 cnf(s32, plain, ~spl4_34, inference(sat_conversion,[],[f4087])).
% 3.93/0.96 cnf(s33, plain, ~spl4_40, inference(rat,[],[s26,s32])).
% 3.93/0.96 cnf(s34, plain, ~spl4_33, inference(rat,[],[s31,s33])).
% 3.93/0.96 cnf(s35, plain, $false, inference(rat,[],[s22,s32,s34])).
% 3.93/0.96 thf(f4088,plain,(
% 3.93/0.96 $false),
% 3.93/0.96 inference(avatar_sat_refutation,[],[s35])).
% 3.93/0.96 % SZS output end Proof for theBenchmark
% 3.93/0.96 % (212631)------------------------------
% 3.93/0.96 % (212631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.93/0.96 % (212631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/0.96 % (212631)CaDiCaL version: 2.1.3
% 3.93/0.96 % (212631)Termination reason: Refutation
% 3.93/0.96 % (212631)Time elapsed: 0.270 s
% 3.93/0.96 % (212631)Peak memory usage: 14 MB
% 3.93/0.96 % (212631)Instructions burned: 852 (million)
% 3.93/0.96 % (212585)Success in time 0.663 s
% 3.93/0.96 % Vampire exiting
%------------------------------------------------------------------------------