%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV034^5 : 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 : n007.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 08:38:53 AM UTC 2026
% Result : Theorem 6.45s 1.38s
% Output : Refutation 6.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV034^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.28 % Computer : n007.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8046.5625MB
% 0.10/0.28 % OS : Linux 6.8.0-71-generic
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Tue Sep 29 15:02:16 UTC 2026
% 0.10/0.28 % CPUTime :
% 0.10/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.29/0.33 Running first-order model finding
% 0.29/0.33 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
% 6.45/1.38 % (3473904)Will run a generic schedule for satisfiability detection.
% 6.45/1.38 % (3473910)% WARNING: option uhcvi not known.
% 6.45/1.38 % (3473910)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1770137163:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.45/1.38 % (3473910)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.45/1.38 % (3473910)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.45/1.38 % (3473909)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=841787541_2999 on theBenchmark for (2999ds/0Mi)
% 6.45/1.38 % (3473911)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3733462947:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.45/1.38 % (3473912)dis+10_1_sil=32000:sp=arity:random_seed=3385811855:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.45/1.38 % (3473913)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=581999284:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.45/1.38 % (3473915)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3900435778:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.45/1.38 % (3473914)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=905459637:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.45/1.38 % (3473913)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.45/1.38 % Exception at run slice level
% 6.45/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.45/1.38 % (3473923)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2486574929:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.45/1.38 % Exception at run slice level
% 6.45/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.45/1.38 % (3473925)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4044673896:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.45/1.38 % (3473912)Instruction limit reached!
% 6.45/1.38 % (3473912)------------------------------
% 6.45/1.38 % (3473912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.38 % (3473912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.38 % (3473912)CaDiCaL version: 2.1.3
% 6.45/1.38 % (3473912)Termination reason: Instruction limit
% 6.45/1.38 % (3473912)Termination phase: Saturation
% 6.45/1.38 % (3473912)Time elapsed: 0.090 s
% 6.45/1.38 % (3473912)Peak memory usage: 12 MB
% 6.45/1.38 % (3473912)Instructions burned: 103 (million)
% 6.45/1.38 % (3473913)Instruction limit reached!
% 6.45/1.38 % (3473913)------------------------------
% 6.45/1.38 % (3473913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.38 % (3473913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.38 % (3473913)CaDiCaL version: 2.1.3
% 6.45/1.38 % (3473913)Termination reason: Instruction limit
% 6.45/1.38 % (3473913)Termination phase: Saturation
% 6.45/1.38 % (3473913)Time elapsed: 0.097 s
% 6.45/1.38 % (3473913)Peak memory usage: 12 MB
% 6.45/1.38 % (3473913)Instructions burned: 116 (million)
% 6.45/1.38 % (3473914)Instruction limit reached!
% 6.45/1.38 % (3473914)------------------------------
% 6.45/1.38 % (3473914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.38 % (3473914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.38 % (3473914)CaDiCaL version: 2.1.3
% 6.45/1.38 % (3473914)Termination reason: Instruction limit
% 6.45/1.38 % (3473914)Termination phase: Saturation
% 6.45/1.38 % (3473914)Time elapsed: 0.114 s
% 6.45/1.38 % (3473914)Peak memory usage: 12 MB
% 6.45/1.38 % (3473914)Instructions burned: 132 (million)
% 6.45/1.38 % (3473927)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=2598379259:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.45/1.38 % (3473927)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.45/1.38 % (3473927)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.45/1.38 % (3473928)ott-21_1_sil=16000:fs=off:random_seed=1151789760:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.45/1.38 % (3473915)Instruction limit reached!
% 6.45/1.38 % (3473915)------------------------------
% 6.45/1.38 % (3473915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.38 % (3473915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.38 % (3473915)CaDiCaL version: 2.1.3
% 6.45/1.38 % (3473915)Termination reason: Instruction limit
% 6.45/1.38 % (3473915)Termination phase: Saturation
% 6.45/1.38 % (3473915)Time elapsed: 0.132 s
% 6.45/1.38 % (3473915)Peak memory usage: 12 MB
% 6.45/1.38 % (3473915)Instructions burned: 159 (million)
% 6.45/1.38 % (3473929)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2257029686:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.45/1.38 % (3473932)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1286096492:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.45/1.38 % Exception at run slice level
% 6.45/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.45/1.38 % (3473925)Instruction limit reached!
% 6.45/1.38 % (3473925)------------------------------
% 6.45/1.38 % (3473925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.38 % (3473925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.38 % (3473925)CaDiCaL version: 2.1.3
% 6.45/1.38 % (3473925)Termination reason: Instruction limit
% 6.45/1.38 % (3473925)Termination phase: Saturation
% 6.45/1.38 % (3473925)Time elapsed: 0.125 s
% 6.45/1.38 % (3473925)Peak memory usage: 12 MB
% 6.45/1.38 % (3473925)Instructions burned: 131 (million)
% 6.45/1.38 % (3473935)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1189835776:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 6.45/1.38 % (3473936)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=781518400:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 6.45/1.38 % Exception at run slice level
% 6.45/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.45/1.38 % (3473939)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=3517809570: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)
% 6.45/1.38 % (3473939)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.45/1.38 % (3473928)Instruction limit reached!
% 6.45/1.38 % (3473928)------------------------------
% 6.45/1.38 % (3473928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.38 % (3473928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.38 % (3473928)CaDiCaL version: 2.1.3
% 6.45/1.38 % (3473928)Termination reason: Instruction limit
% 6.45/1.38 % (3473928)Termination phase: Saturation
% 6.45/1.38 % (3473928)Time elapsed: 0.147 s
% 6.45/1.38 % (3473928)Peak memory usage: 12 MB
% 6.45/1.38 % (3473928)Instructions burned: 180 (million)
% 6.45/1.38 % (3473941)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3072985250:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 6.45/1.38 % (3473941)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.45/1.38 % (3473929)Instruction limit reached!
% 6.45/1.38 % (3473929)------------------------------
% 6.45/1.38 % (3473929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.38 % (3473929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.38 % (3473929)CaDiCaL version: 2.1.3
% 6.45/1.38 % (3473929)Termination reason: Instruction limit
% 6.45/1.38 % (3473929)Termination phase: Saturation
% 6.45/1.38 % (3473929)Time elapsed: 0.417 s
% 6.45/1.38 % (3473929)Peak memory usage: 12 MB
% 6.45/1.38 % (3473929)Instructions burned: 478 (million)
% 6.45/1.38 % (3473943)fmb+10_1_sil=64000:random_seed=2687749984:i=22061:nm=2:gsp=on_2993 on theBenchmark for (2993ds/22061Mi)
% 6.45/1.38 % (3473943)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.45/1.38 % Exception at run slice level
% 6.45/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.45/1.38 % (3473945)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=488587377:i=9515:nm=5_2993 on theBenchmark for (2993ds/9515Mi)
% 6.45/1.38 % Exception at run slice level
% 6.45/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.45/1.38 % (3473927)Instruction limit reached!
% 6.45/1.38 % (3473927)------------------------------
% 6.45/1.38 % (3473927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.38 % (3473927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.38 % (3473927)CaDiCaL version: 2.1.3
% 6.45/1.38 % (3473927)Termination reason: Instruction limit
% 6.45/1.38 % (3473927)Termination phase: Saturation
% 6.45/1.38 % (3473927)Time elapsed: 0.533 s
% 6.45/1.38 % (3473927)Peak memory usage: 13 MB
% 6.45/1.38 % (3473927)Instructions burned: 684 (million)
% 6.45/1.38 % (3473947)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3808022411:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 6.45/1.38 % Exception at run slice level
% 6.45/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.45/1.38 % (3473948)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1229873220:i=5131_2992 on theBenchmark for (2992ds/5131Mi)
% 6.45/1.38 % (3473948)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.45/1.38 % (3473950)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=299409616:i=1472:ins=7:fdi=8:gsp=on_2992 on theBenchmark for (2992ds/1472Mi)
% 6.45/1.38 % (3473950)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.45/1.38 % (3473950)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.45/1.38 % (3473939)Instruction limit reached!
% 6.45/1.38 % (3473939)------------------------------
% 6.45/1.38 % (3473939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.38 % (3473939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.38 % (3473939)CaDiCaL version: 2.1.3
% 6.45/1.38 % (3473939)Termination reason: Instruction limit
% 6.45/1.38 % (3473939)Termination phase: Saturation
% 6.45/1.38 % (3473939)Time elapsed: 0.586 s
% 6.45/1.38 % (3473939)Peak memory usage: 15 MB
% 6.45/1.38 % (3473939)Instructions burned: 693 (million)
% 6.45/1.38 % (3473953)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=4027770728:i=6324_2991 on theBenchmark for (2991ds/6324Mi)
% 6.45/1.38 % Exception at run slice level
% 6.45/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.45/1.38 % (3473955)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2642027641:fmbsr=2.30978:i=2174_2990 on theBenchmark for (2990ds/2174Mi)
% 6.45/1.38 % Exception at run slice level
% 6.45/1.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.45/1.38 % (3473957)ott-2_1_sil=16000:newcnf=on:random_seed=82141046:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2990 on theBenchmark for (2990ds/869Mi)
% 6.45/1.38 % (3473957)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.45/1.38 % (3473910) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3473904-3473910"...
% 6.45/1.38 % (3473910)...printing done.
% 6.45/1.38 % (3473910)Refutation found. Thanks to Tanya!
% 6.45/1.38 % SZS status Theorem for theBenchmark
% 6.45/1.38 % SZS output start Proof for theBenchmark
% 6.45/1.38 thf(type_def_5, type, a: $tType).
% 6.45/1.38 thf(type_def_6, type, b: $tType).
% 6.45/1.38 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 6.45/1.38 thf(func_def_3, type, sK0: (a > a > $o)).
% 6.45/1.38 thf(func_def_4, type, sK1: (a > b > b > $o)).
% 6.45/1.38 thf(func_def_5, type, sK2: (a > b)).
% 6.45/1.38 thf(func_def_6, type, sK3: (a > b)).
% 6.45/1.38 thf(func_def_7, type, sK4: a).
% 6.45/1.38 thf(func_def_8, type, sK5: a).
% 6.45/1.38 thf(f1,conjecture,(
% 6.45/1.38 ! [X0 : (a > a > $o),X1 : (a > b > b > $o),X2 : (a > b),X3 : (a > b)] : (! [X4 : a] : ((X0 @ X4 @ X4) => (X1 @ X4 @ (X2 @ X4) @ (X3 @ X4))) => (! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X1 @ X4 @ (X2 @ X4) @ (X2 @ X5))) => (((X0 = X0) & ! [X4 : a,X5 : a,X6 : a] : (((X0 @ X5 @ X6) & (X0 @ X4 @ X5)) => (X0 @ X4 @ X6)) & ! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X0 @ X5 @ X4))) => (! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => ((((X1 @ X4)) = ((X1 @ X5))) & ! [X7 : b,X8 : b,X6 : b] : (((X1 @ X4 @ X8 @ X6) & (X1 @ X4 @ X7 @ X8)) => (X1 @ X4 @ X7 @ X6)) & ! [X7 : b,X8 : b] : ((X1 @ X4 @ X7 @ X8) => (X1 @ X4 @ X8 @ X7)))) => ! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X1 @ X4 @ (X2 @ X4) @ (X3 @ X5)))))))),
% 6.45/1.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM518_pme)).
% 6.45/1.38 thf(f2,negated_conjecture,(
% 6.45/1.38 ~ ! [X0 : (a > a > $o),X1 : (a > b > b > $o),X2 : (a > b),X3 : (a > b)] : (! [X4 : a] : ((X0 @ X4 @ X4) => (X1 @ X4 @ (X2 @ X4) @ (X3 @ X4))) => (! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X1 @ X4 @ (X2 @ X4) @ (X2 @ X5))) => (((X0 = X0) & ! [X4 : a,X5 : a,X6 : a] : (((X0 @ X5 @ X6) & (X0 @ X4 @ X5)) => (X0 @ X4 @ X6)) & ! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X0 @ X5 @ X4))) => (! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => ((((X1 @ X4)) = ((X1 @ X5))) & ! [X7 : b,X8 : b,X6 : b] : (((X1 @ X4 @ X8 @ X6) & (X1 @ X4 @ X7 @ X8)) => (X1 @ X4 @ X7 @ X6)) & ! [X7 : b,X8 : b] : ((X1 @ X4 @ X7 @ X8) => (X1 @ X4 @ X8 @ X7)))) => ! [X4 : a,X5 : a] : ((X0 @ X4 @ X5) => (X1 @ X4 @ (X2 @ X4) @ (X3 @ X5)))))))),
% 6.45/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 6.45/1.38 thf(f3,plain,(
% 6.45/1.38 ~ ! [X0 : (a > a > $o),X1 : (a > b > b > $o),X2 : (a > b),X3 : (a > b)] : (! [X4 : a] : ((X0 @ X4 @ X4) => (X1 @ X4 @ (X2 @ X4) @ (X3 @ X4))) => (! [X5 : a,X6 : a] : ((X0 @ X5 @ X6) => (X1 @ X5 @ (X2 @ X5) @ (X2 @ X6))) => (((X0 = X0) & ! [X7 : a,X8 : a,X9 : a] : (((X0 @ X8 @ X9) & (X0 @ X7 @ X8)) => (X0 @ X7 @ X9)) & ! [X10 : a,X11 : a] : ((X0 @ X10 @ X11) => (X0 @ X11 @ X10))) => (! [X12 : a,X13 : a] : ((X0 @ X12 @ X13) => ((((X1 @ X12)) = ((X1 @ X13))) & ! [X14 : b,X15 : b,X16 : b] : (((X1 @ X12 @ X15 @ X16) & (X1 @ X12 @ X14 @ X15)) => (X1 @ X12 @ X14 @ X16)) & ! [X17 : b,X18 : b] : ((X1 @ X12 @ X17 @ X18) => (X1 @ X12 @ X18 @ X17)))) => ! [X19 : a,X20 : a] : ((X0 @ X19 @ X20) => (X1 @ X19 @ (X2 @ X19) @ (X3 @ X20)))))))),
% 6.45/1.38 inference(rectify,[],[f2])).
% 6.45/1.38 thf(f4,plain,(
% 6.45/1.38 ~ ! [X0 : (a > a > $o),X1 : (a > b > b > $o),X2 : (a > b),X3 : (a > b)] : (! [X4 : a] : ((((X0 @ X4 @ X4)) = $true) => (((X1 @ X4 @ (X2 @ X4) @ (X3 @ X4))) = $true)) => (! [X5 : a,X6 : a] : ((((X0 @ X5 @ X6)) = $true) => (((X1 @ X5 @ (X2 @ X5) @ (X2 @ X6))) = $true)) => (((X0 = X0) & ! [X7 : a,X8 : a,X9 : a] : (((((X0 @ X8 @ X9)) = $true) & (((X0 @ X7 @ X8)) = $true)) => (((X0 @ X7 @ X9)) = $true)) & ! [X10 : a,X11 : a] : ((((X0 @ X10 @ X11)) = $true) => (((X0 @ X11 @ X10)) = $true))) => (! [X12 : a,X13 : a] : ((((X0 @ X12 @ X13)) = $true) => ((((X1 @ X12)) = ((X1 @ X13))) & ! [X14 : b,X15 : b,X16 : b] : (((((X1 @ X12 @ X15 @ X16)) = $true) & (((X1 @ X12 @ X14 @ X15)) = $true)) => (((X1 @ X12 @ X14 @ X16)) = $true)) & ! [X17 : b,X18 : b] : ((((X1 @ X12 @ X17 @ X18)) = $true) => (((X1 @ X12 @ X18 @ X17)) = $true)))) => ! [X19 : a,X20 : a] : ((((X0 @ X19 @ X20)) = $true) => (((X1 @ X19 @ (X2 @ X19) @ (X3 @ X20))) = $true))))))),
% 6.45/1.38 inference(fool_elimination,[],[f3])).
% 6.45/1.38 thf(f5,plain,(
% 6.45/1.38 ? [X0 : (a > a > $o),X1 : (a > b > b > $o),X2 : (a > b),X3 : (a > b)] : ((((? [X19 : a,X20 : a] : ((((X1 @ X19 @ (X2 @ X19) @ (X3 @ X20))) != $true) & (((X0 @ X19 @ X20)) = $true)) & ! [X12 : a,X13 : a] : (((((X1 @ X12)) = ((X1 @ X13))) & ! [X14 : b,X15 : b,X16 : b] : ((((X1 @ X12 @ X14 @ X16)) = $true) | ((((X1 @ X12 @ X15 @ X16)) != $true) | (((X1 @ X12 @ X14 @ X15)) != $true))) & ! [X17 : b,X18 : b] : ((((X1 @ X12 @ X18 @ X17)) = $true) | (((X1 @ X12 @ X17 @ X18)) != $true))) | (((X0 @ X12 @ X13)) != $true))) & ((X0 = X0) & ! [X7 : a,X8 : a,X9 : a] : ((((X0 @ X7 @ X9)) = $true) | ((((X0 @ X8 @ X9)) != $true) | (((X0 @ X7 @ X8)) != $true))) & ! [X10 : a,X11 : a] : ((((X0 @ X11 @ X10)) = $true) | (((X0 @ X10 @ X11)) != $true)))) & ! [X5 : a,X6 : a] : ((((X1 @ X5 @ (X2 @ X5) @ (X2 @ X6))) = $true) | (((X0 @ X5 @ X6)) != $true))) & ! [X4 : a] : ((((X1 @ X4 @ (X2 @ X4) @ (X3 @ X4))) = $true) | (((X0 @ X4 @ X4)) != $true)))),
% 6.45/1.38 inference(ennf_transformation,[],[f4])).
% 6.45/1.38 thf(f6,plain,(
% 6.45/1.38 ? [X0 : (a > a > $o),X1 : (a > b > b > $o),X2 : (a > b),X3 : (a > b)] : (? [X19 : a,X20 : a] : ((((X1 @ X19 @ (X2 @ X19) @ (X3 @ X20))) != $true) & (((X0 @ X19 @ X20)) = $true)) & ! [X12 : a,X13 : a] : (((((X1 @ X12)) = ((X1 @ X13))) & ! [X14 : b,X15 : b,X16 : b] : ((((X1 @ X12 @ X14 @ X16)) = $true) | (((X1 @ X12 @ X15 @ X16)) != $true) | (((X1 @ X12 @ X14 @ X15)) != $true)) & ! [X17 : b,X18 : b] : ((((X1 @ X12 @ X18 @ X17)) = $true) | (((X1 @ X12 @ X17 @ X18)) != $true))) | (((X0 @ X12 @ X13)) != $true)) & (X0 = X0) & ! [X7 : a,X8 : a,X9 : a] : ((((X0 @ X7 @ X9)) = $true) | (((X0 @ X8 @ X9)) != $true) | (((X0 @ X7 @ X8)) != $true)) & ! [X10 : a,X11 : a] : ((((X0 @ X11 @ X10)) = $true) | (((X0 @ X10 @ X11)) != $true)) & ! [X5 : a,X6 : a] : ((((X1 @ X5 @ (X2 @ X5) @ (X2 @ X6))) = $true) | (((X0 @ X5 @ X6)) != $true)) & ! [X4 : a] : ((((X1 @ X4 @ (X2 @ X4) @ (X3 @ X4))) = $true) | (((X0 @ X4 @ X4)) != $true)))),
% 6.45/1.38 inference(flattening,[],[f5])).
% 6.45/1.38 thf(f7,plain,(
% 6.45/1.38 ? [X0 : (a > a > $o),X1 : (a > b > b > $o),X2 : (a > b),X3 : (a > b)] : (? [X4 : a,X5 : a] : ((((X1 @ X4 @ (X2 @ X4) @ (X3 @ X5))) != $true) & (((X0 @ X4 @ X5)) = $true)) & ! [X6 : a,X7 : a] : (((((X1 @ X6)) = ((X1 @ X7))) & ! [X8 : b,X9 : b,X10 : b] : (($true = ((X1 @ X6 @ X8 @ X10))) | ($true != ((X1 @ X6 @ X9 @ X10))) | ($true != ((X1 @ X6 @ X8 @ X9)))) & ! [X11 : b,X12 : b] : (($true = ((X1 @ X6 @ X12 @ X11))) | ($true != ((X1 @ X6 @ X11 @ X12))))) | ($true != ((X0 @ X6 @ X7)))) & (X0 = X0) & ! [X13 : a,X14 : a,X15 : a] : (($true = ((X0 @ X13 @ X15))) | ($true != ((X0 @ X14 @ X15))) | ($true != ((X0 @ X13 @ X14)))) & ! [X16 : a,X17 : a] : (($true = ((X0 @ X17 @ X16))) | ($true != ((X0 @ X16 @ X17)))) & ! [X18 : a,X19 : a] : (($true = ((X1 @ X18 @ (X2 @ X18) @ (X2 @ X19)))) | ($true != ((X0 @ X18 @ X19)))) & ! [X20 : a] : (($true = ((X1 @ X20 @ (X2 @ X20) @ (X3 @ X20)))) | ($true != ((X0 @ X20 @ X20)))))),
% 6.45/1.38 inference(rectify,[],[f6])).
% 6.45/1.38 thf(f8,plain,(
% 6.45/1.38 (($true != ((sK1 @ sK4 @ (sK2 @ sK4) @ (sK3 @ sK5)))) & ($true = ((sK0 @ sK4 @ sK5)))) & ! [X6 : a,X7 : a] : (((((sK1 @ X6)) = ((sK1 @ X7))) & ! [X8 : b,X9 : b,X10 : b] : (($true = ((sK1 @ X6 @ X8 @ X10))) | ($true != ((sK1 @ X6 @ X9 @ X10))) | ($true != ((sK1 @ X6 @ X8 @ X9)))) & ! [X11 : b,X12 : b] : (($true = ((sK1 @ X6 @ X12 @ X11))) | ($true != ((sK1 @ X6 @ X11 @ X12))))) | ($true != ((sK0 @ X6 @ X7)))) & (sK0 = sK0) & ! [X13 : a,X14 : a,X15 : a] : (($true = ((sK0 @ X13 @ X15))) | ($true != ((sK0 @ X14 @ X15))) | ($true != ((sK0 @ X13 @ X14)))) & ! [X16 : a,X17 : a] : (($true = ((sK0 @ X17 @ X16))) | ($true != ((sK0 @ X16 @ X17)))) & ! [X18 : a,X19 : a] : (($true = ((sK1 @ X18 @ (sK2 @ X18) @ (sK2 @ X19)))) | ($true != ((sK0 @ X18 @ X19)))) & ! [X20 : a] : (($true = ((sK1 @ X20 @ (sK2 @ X20) @ (sK3 @ X20)))) | ($true != ((sK0 @ X20 @ X20))))),
% 6.45/1.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f7])).
% 6.45/1.38 thf(f9,plain,(
% 6.45/1.38 ( ! [X20 : a] : (($true != ((sK0 @ X20 @ X20))) | ($true = ((sK1 @ X20 @ (sK2 @ X20) @ (sK3 @ X20))))) )),
% 6.45/1.38 inference(cnf_transformation,[],[f8])).
% 6.45/1.38 thf(f10,plain,(
% 6.45/1.38 ( ! [X18 : a,X19 : a] : (($true != ((sK0 @ X18 @ X19))) | ($true = ((sK1 @ X18 @ (sK2 @ X18) @ (sK2 @ X19))))) )),
% 6.45/1.38 inference(cnf_transformation,[],[f8])).
% 6.45/1.38 thf(f11,plain,(
% 6.45/1.38 ( ! [X16 : a,X17 : a] : (($true != ((sK0 @ X16 @ X17))) | ($true = ((sK0 @ X17 @ X16)))) )),
% 6.45/1.38 inference(cnf_transformation,[],[f8])).
% 6.45/1.38 thf(f12,plain,(
% 6.45/1.38 ( ! [X14 : a,X15 : a,X13 : a] : (($true != ((sK0 @ X14 @ X15))) | ($true = ((sK0 @ X13 @ X15))) | ($true != ((sK0 @ X13 @ X14)))) )),
% 6.45/1.38 inference(cnf_transformation,[],[f8])).
% 6.45/1.38 thf(f14,plain,(
% 6.45/1.38 ( ! [X11 : b,X6 : a,X7 : a,X12 : b] : (($true != ((sK1 @ X6 @ X11 @ X12))) | ($true = ((sK1 @ X6 @ X12 @ X11))) | ($true != ((sK0 @ X6 @ X7)))) )),
% 6.45/1.38 inference(cnf_transformation,[],[f8])).
% 6.45/1.38 thf(f15,plain,(
% 6.45/1.38 ( ! [X10 : b,X8 : b,X6 : a,X9 : b,X7 : a] : (($true != ((sK1 @ X6 @ X9 @ X10))) | ($true = ((sK1 @ X6 @ X8 @ X10))) | ($true != ((sK1 @ X6 @ X8 @ X9))) | ($true != ((sK0 @ X6 @ X7)))) )),
% 6.45/1.38 inference(cnf_transformation,[],[f8])).
% 6.45/1.38 thf(f16,plain,(
% 6.45/1.38 ( ! [X6 : a,X7 : a] : (($true != ((sK0 @ X6 @ X7))) | (((sK1 @ X6)) = ((sK1 @ X7)))) )),
% 6.45/1.38 inference(cnf_transformation,[],[f8])).
% 6.45/1.38 thf(f17,plain,(
% 6.45/1.38 ($true = ((sK0 @ sK4 @ sK5)))),
% 6.45/1.38 inference(cnf_transformation,[],[f8])).
% 6.45/1.38 thf(f18,plain,(
% 6.45/1.38 ($true != ((sK1 @ sK4 @ (sK2 @ sK4) @ (sK3 @ sK5))))),
% 6.45/1.38 inference(cnf_transformation,[],[f8])).
% 6.45/1.38 thf(f20,definition,(
% 6.45/1.38 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 6.45/1.38 introduced(theory,[fool_exhaustiveness_axiom])).
% 6.45/1.38 thf(f21,plain,(
% 6.45/1.38 ($true != $true) | ($true = ((sK0 @ sK5 @ sK4)))),
% 6.45/1.38 inference(constrained_superposition,[],[f11,f17])).
% 6.45/1.38 thf(f22,plain,(
% 6.45/1.38 ($true = ((sK0 @ sK5 @ sK4)))),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f21])).
% 6.45/1.38 thf(f25,plain,(
% 6.45/1.38 ($true != $true) | (((sK1 @ sK4)) = ((sK1 @ sK5)))),
% 6.45/1.38 inference(constrained_superposition,[],[f16,f17])).
% 6.45/1.38 thf(f28,plain,(
% 6.45/1.38 (((sK1 @ sK4)) = ((sK1 @ sK5)))),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f25])).
% 6.45/1.38 thf(f29,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true != $true) | ($true = ((sK0 @ X0 @ sK5))) | ($true != ((sK0 @ X0 @ sK4)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f12,f17])).
% 6.45/1.38 thf(f30,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true != $true) | ($true = ((sK0 @ X0 @ sK4))) | ($true != ((sK0 @ X0 @ sK5)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f12,f22])).
% 6.45/1.38 thf(f31,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true != ((sK0 @ X0 @ sK5))) | ($true = ((sK0 @ X0 @ sK4)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f30])).
% 6.45/1.38 thf(f32,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true != ((sK0 @ X0 @ sK4))) | ($true = ((sK0 @ X0 @ sK5)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f29])).
% 6.45/1.38 thf(f33,plain,(
% 6.45/1.38 ( ! [X1 : b] : ((((sK1 @ sK4 @ X1)) = ((sK1 @ sK5 @ X1)))) )),
% 6.45/1.38 inference(argument_congruence,[],[f28])).
% 6.45/1.38 thf(f35,plain,(
% 6.45/1.38 ($true != $true) | ($true = ((sK1 @ sK5 @ (sK2 @ sK5) @ (sK2 @ sK4))))),
% 6.45/1.38 inference(constrained_superposition,[],[f10,f22])).
% 6.45/1.38 thf(f36,plain,(
% 6.45/1.38 ($true = ((sK1 @ sK5 @ (sK2 @ sK5) @ (sK2 @ sK4))))),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f35])).
% 6.45/1.38 thf(f41,plain,(
% 6.45/1.38 ( ! [X2 : a,X0 : a,X1 : a] : (($true != $true) | ($true = ((sK0 @ X2 @ X1))) | ($true != ((sK0 @ X2 @ X0))) | ($false = ((sK0 @ X0 @ X1)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f12,f20])).
% 6.45/1.38 thf(f43,plain,(
% 6.45/1.38 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = ((sK0 @ X1 @ X0))) | ($false = ((sK0 @ X0 @ X1)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f11,f20])).
% 6.45/1.38 thf(f44,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true != $true) | ($true = ((sK1 @ X0 @ (sK2 @ X0) @ (sK3 @ X0)))) | ($false = ((sK0 @ X0 @ X0)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f9,f20])).
% 6.45/1.38 thf(f46,plain,(
% 6.45/1.38 ( ! [X2 : b,X3 : a,X0 : a,X1 : b] : (($true != $true) | ($true = ((sK1 @ X0 @ X2 @ X1))) | ($true != ((sK0 @ X0 @ X3))) | ($false = ((sK1 @ X0 @ X1 @ X2)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f14,f20])).
% 6.45/1.38 thf(f48,plain,(
% 6.45/1.38 ( ! [X2 : b,X3 : a,X0 : a,X1 : b] : (($true != ((sK0 @ X0 @ X3))) | ($true = ((sK1 @ X0 @ X2 @ X1))) | ($false = ((sK1 @ X0 @ X1 @ X2)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f46])).
% 6.45/1.38 thf(f50,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = ((sK1 @ X0 @ (sK2 @ X0) @ (sK3 @ X0)))) | ($false = ((sK0 @ X0 @ X0)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f44])).
% 6.45/1.38 thf(f51,plain,(
% 6.45/1.38 ( ! [X0 : a,X1 : a] : (($true = ((sK0 @ X1 @ X0))) | ($false = ((sK0 @ X0 @ X1)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f43])).
% 6.45/1.38 thf(f53,plain,(
% 6.45/1.38 ( ! [X2 : a,X0 : a,X1 : a] : (($true != ((sK0 @ X2 @ X0))) | ($true = ((sK0 @ X2 @ X1))) | ($false = ((sK0 @ X0 @ X1)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f41])).
% 6.45/1.38 thf(f61,plain,(
% 6.45/1.38 ($true != $true) | ($true = ((sK0 @ sK5 @ sK5)))),
% 6.45/1.38 inference(constrained_superposition,[],[f32,f22])).
% 6.45/1.38 thf(f62,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true != $true) | ($true = ((sK0 @ X0 @ sK5))) | ($false = ((sK0 @ X0 @ sK4)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f32,f20])).
% 6.45/1.38 thf(f63,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = ((sK0 @ X0 @ sK5))) | ($false = ((sK0 @ X0 @ sK4)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f62])).
% 6.45/1.38 thf(f64,plain,(
% 6.45/1.38 ($true = ((sK0 @ sK5 @ sK5)))),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f61])).
% 6.45/1.38 thf(f136,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true != $true) | ($true = ((sK0 @ sK5 @ X0))) | ($false = ((sK0 @ sK4 @ X0)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f53,f22])).
% 6.45/1.38 thf(f143,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = ((sK0 @ sK5 @ X0))) | ($false = ((sK0 @ sK4 @ X0)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f136])).
% 6.45/1.38 thf(f152,plain,(
% 6.45/1.38 ( ! [X2 : a,X0 : a,X1 : b] : (($true != $true) | ($true = ((sK1 @ X0 @ X1 @ (sK3 @ X0)))) | ($true != ((sK1 @ X0 @ X1 @ (sK2 @ X0)))) | ($true != ((sK0 @ X0 @ X2))) | ($false = ((sK0 @ X0 @ X0)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f15,f50])).
% 6.45/1.38 thf(f155,plain,(
% 6.45/1.38 ( ! [X2 : a,X0 : a,X1 : b] : (($true != ((sK1 @ X0 @ X1 @ (sK2 @ X0)))) | ($true = ((sK1 @ X0 @ X1 @ (sK3 @ X0)))) | ($true != ((sK0 @ X0 @ X2))) | ($false = ((sK0 @ X0 @ X0)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f152])).
% 6.45/1.38 thf(f156,plain,(
% 6.45/1.38 ($true != $true) | ($true = ((sK0 @ sK4 @ sK4)))),
% 6.45/1.38 inference(constrained_superposition,[],[f31,f17])).
% 6.45/1.38 thf(f165,plain,(
% 6.45/1.38 ($true = ((sK0 @ sK4 @ sK4)))),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f156])).
% 6.45/1.38 thf(f182,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = $false) | ($true = ((sK0 @ sK5 @ X0))) | ($false = ((sK0 @ X0 @ sK4)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f51,f63])).
% 6.45/1.38 thf(f189,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = ((sK0 @ sK5 @ X0))) | ($false = ((sK0 @ X0 @ sK4)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f182])).
% 6.45/1.38 thf(f212,plain,(
% 6.45/1.38 ( ! [X2 : b,X3 : b,X0 : a,X1 : a] : (($true != $true) | ($true = ((sK1 @ X0 @ X2 @ X3))) | ($false = ((sK1 @ X0 @ X3 @ X2))) | ($false = ((sK0 @ X1 @ X0)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f48,f51])).
% 6.45/1.38 thf(f217,plain,(
% 6.45/1.38 ( ! [X2 : b,X3 : b,X0 : a,X1 : a] : (($true = ((sK1 @ X0 @ X2 @ X3))) | ($false = ((sK1 @ X0 @ X3 @ X2))) | ($false = ((sK0 @ X1 @ X0)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f212])).
% 6.45/1.38 thf(f348,definition,(
% 6.45/1.38 spl6_5 <=> ! [X0 : a] : ($false = ((sK0 @ sK4 @ X0)))),
% 6.45/1.38 introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition])).
% 6.45/1.38 thf(f349,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($false = ((sK0 @ sK4 @ X0)))) ) | ~spl6_5),
% 6.45/1.38 inference(avatar_component_clause,[],[f348])).
% 6.45/1.38 thf(f400,definition,(
% 6.45/1.38 spl6_7 <=> ! [X0 : a] : ($true != ((sK0 @ sK5 @ X0)))),
% 6.45/1.38 introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition])).
% 6.45/1.38 thf(f401,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true != ((sK0 @ sK5 @ X0)))) ) | ~spl6_7),
% 6.45/1.38 inference(avatar_component_clause,[],[f400])).
% 6.45/1.38 thf(f403,definition,(
% 6.45/1.38 spl6_8 <=> ($true = ((sK1 @ sK5 @ (sK2 @ sK4) @ (sK2 @ sK5))))),
% 6.45/1.38 introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition])).
% 6.45/1.38 thf(f405,plain,(
% 6.45/1.38 ($true = ((sK1 @ sK5 @ (sK2 @ sK4) @ (sK2 @ sK5)))) | ~spl6_8),
% 6.45/1.38 inference(avatar_component_clause,[],[f403])).
% 6.45/1.38 thf(f429,plain,(
% 6.45/1.38 ( ! [X2 : b,X1 : b] : ((((sK1 @ sK4 @ X1 @ X2)) = ((sK1 @ sK5 @ X1 @ X2)))) )),
% 6.45/1.38 inference(argument_congruence,[],[f33])).
% 6.45/1.38 thf(f430,plain,(
% 6.45/1.38 ( ! [X2 : b,X1 : b] : (($false = ((sK1 @ sK5 @ X1 @ X2))) | ($true = ((sK1 @ sK4 @ X1 @ X2)))) )),
% 6.45/1.38 inference(iff_proxy_clausification,[],[f429])).
% 6.45/1.38 thf(f434,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($false = ((sK0 @ sK4 @ X0)))) ) | ~spl6_7),
% 6.45/1.38 inference(backward_subsumption_resolution,[],[f143,f401])).
% 6.45/1.38 thf(f448,plain,(
% 6.45/1.38 spl6_5 | ~spl6_7),
% 6.45/1.38 inference(avatar_split_clause,[],[f434,f400,f348])).
% 6.45/1.38 thf(f1044,definition,(
% 6.45/1.38 spl6_13 <=> ! [X0 : a] : ($false = ((sK0 @ X0 @ sK4)))),
% 6.45/1.38 introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition])).
% 6.45/1.38 thf(f1045,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($false = ((sK0 @ X0 @ sK4)))) ) | ~spl6_13),
% 6.45/1.38 inference(avatar_component_clause,[],[f1044])).
% 6.45/1.38 thf(f1295,definition,(
% 6.45/1.38 spl6_18 <=> ! [X0 : a] : ($false = ((sK0 @ sK5 @ X0)))),
% 6.45/1.38 introduced(definition,[new_symbols(definition,[spl6_18])],[avatar_definition])).
% 6.45/1.38 thf(f1296,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($false = ((sK0 @ sK5 @ X0)))) ) | ~spl6_18),
% 6.45/1.38 inference(avatar_component_clause,[],[f1295])).
% 6.45/1.38 thf(f1326,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = $false) | ($false = ((sK0 @ X0 @ sK4)))) ) | ~spl6_5),
% 6.45/1.38 inference(constrained_superposition,[],[f51,f349])).
% 6.45/1.38 thf(f1341,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($false = ((sK0 @ X0 @ sK4)))) ) | ~spl6_5),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f1326])).
% 6.45/1.38 thf(f1356,plain,(
% 6.45/1.38 spl6_13 | ~spl6_5),
% 6.45/1.38 inference(avatar_split_clause,[],[f1341,f348,f1044])).
% 6.45/1.38 thf(f1457,definition,(
% 6.45/1.38 spl6_21 <=> ! [X0 : a] : ($false = ((sK0 @ X0 @ sK5)))),
% 6.45/1.38 introduced(definition,[new_symbols(definition,[spl6_21])],[avatar_definition])).
% 6.45/1.38 thf(f1458,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($false = ((sK0 @ X0 @ sK5)))) ) | ~spl6_21),
% 6.45/1.38 inference(avatar_component_clause,[],[f1457])).
% 6.45/1.38 thf(f1487,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = $false) | ($false = ((sK0 @ sK5 @ X0)))) ) | ~spl6_21),
% 6.45/1.38 inference(constrained_superposition,[],[f51,f1458])).
% 6.45/1.38 thf(f1508,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($false = ((sK0 @ sK5 @ X0)))) ) | ~spl6_21),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f1487])).
% 6.45/1.38 thf(f1525,plain,(
% 6.45/1.38 spl6_18 | ~spl6_21),
% 6.45/1.38 inference(avatar_split_clause,[],[f1508,f1457,f1295])).
% 6.45/1.38 thf(f1536,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = $false) | ($true = ((sK1 @ sK5 @ (sK2 @ sK4) @ (sK2 @ sK5)))) | ($false = ((sK0 @ X0 @ sK5)))) )),
% 6.45/1.38 inference(constrained_superposition,[],[f217,f36])).
% 6.45/1.38 thf(f1609,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = ((sK1 @ sK5 @ (sK2 @ sK4) @ (sK2 @ sK5)))) | ($false = ((sK0 @ X0 @ sK5)))) )),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f1536])).
% 6.45/1.38 thf(f1627,plain,(
% 6.45/1.38 spl6_21 | spl6_8),
% 6.45/1.38 inference(avatar_split_clause,[],[f1609,f403,f1457])).
% 6.45/1.38 thf(f2093,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true != $true) | ($true = ((sK1 @ sK5 @ (sK2 @ sK4) @ (sK3 @ sK5)))) | ($true != ((sK0 @ sK5 @ X0))) | ($false = ((sK0 @ sK5 @ sK5)))) ) | ~spl6_8),
% 6.45/1.38 inference(constrained_superposition,[],[f155,f405])).
% 6.45/1.38 thf(f2094,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = ((sK1 @ sK5 @ (sK2 @ sK4) @ (sK3 @ sK5)))) | ($true != ((sK0 @ sK5 @ X0))) | ($false = ((sK0 @ sK5 @ sK5)))) ) | ~spl6_8),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f2093])).
% 6.45/1.38 thf(f2099,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = $false) | ($true = ((sK1 @ sK5 @ (sK2 @ sK4) @ (sK3 @ sK5)))) | ($true != ((sK0 @ sK5 @ X0)))) ) | ~spl6_8),
% 6.45/1.38 inference(forward_demodulation,[],[f2094,f64])).
% 6.45/1.38 thf(f2100,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = ((sK1 @ sK5 @ (sK2 @ sK4) @ (sK3 @ sK5)))) | ($true != ((sK0 @ sK5 @ X0)))) ) | ~spl6_8),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f2099])).
% 6.45/1.38 thf(f2114,definition,(
% 6.45/1.38 spl6_38 <=> ($true = ((sK1 @ sK5 @ (sK2 @ sK4) @ (sK3 @ sK5))))),
% 6.45/1.38 introduced(definition,[new_symbols(definition,[spl6_38])],[avatar_definition])).
% 6.45/1.38 thf(f2116,plain,(
% 6.45/1.38 ($true = ((sK1 @ sK5 @ (sK2 @ sK4) @ (sK3 @ sK5)))) | ~spl6_38),
% 6.45/1.38 inference(avatar_component_clause,[],[f2114])).
% 6.45/1.38 thf(f2117,plain,(
% 6.45/1.38 spl6_7 | spl6_38 | ~spl6_8),
% 6.45/1.38 inference(avatar_split_clause,[],[f2100,f403,f2114,f400])).
% 6.45/1.38 thf(f2847,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($true = $false) | ($false = ((sK0 @ X0 @ sK4)))) ) | ~spl6_18),
% 6.45/1.38 inference(constrained_superposition,[],[f189,f1296])).
% 6.45/1.38 thf(f2854,plain,(
% 6.45/1.38 ( ! [X0 : a] : (($false = ((sK0 @ X0 @ sK4)))) ) | ~spl6_18),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f2847])).
% 6.45/1.38 thf(f2881,plain,(
% 6.45/1.38 spl6_13 | ~spl6_18),
% 6.45/1.38 inference(avatar_split_clause,[],[f2854,f1295,f1044])).
% 6.45/1.38 thf(f7953,plain,(
% 6.45/1.38 ($true = $false) | ~spl6_13),
% 6.45/1.38 inference(constrained_superposition,[],[f1045,f165])).
% 6.45/1.38 thf(f8059,plain,(
% 6.45/1.38 $false | ~spl6_13),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f7953])).
% 6.45/1.38 thf(f8060,plain,(
% 6.45/1.38 ~spl6_13),
% 6.45/1.38 inference(avatar_contradiction_clause,[],[f8059])).
% 6.45/1.38 thf(f29505,plain,(
% 6.45/1.38 ($true = $false) | ($true = ((sK1 @ sK4 @ (sK2 @ sK4) @ (sK3 @ sK5)))) | ~spl6_38),
% 6.45/1.38 inference(constrained_superposition,[],[f430,f2116])).
% 6.45/1.38 thf(f29601,plain,(
% 6.45/1.38 ($true = ((sK1 @ sK4 @ (sK2 @ sK4) @ (sK3 @ sK5)))) | ~spl6_38),
% 6.45/1.38 inference(trivial_inequality_removal,[],[f29505])).
% 6.45/1.38 thf(f29673,plain,(
% 6.45/1.38 $false | ~spl6_38),
% 6.45/1.38 inference(forward_subsumption_resolution,[],[f29601,f18])).
% 6.45/1.38 thf(f29674,plain,(
% 6.45/1.38 ~spl6_38),
% 6.45/1.38 inference(avatar_contradiction_clause,[],[f29673])).
% 6.45/1.38 cnf(s14, plain, spl6_5 | ~spl6_7, inference(sat_conversion,[],[f448])).
% 6.45/1.38 cnf(s39, plain, ~spl6_5 | spl6_13, inference(sat_conversion,[],[f1356])).
% 6.45/1.38 cnf(s49, plain, spl6_18 | ~spl6_21, inference(sat_conversion,[],[f1525])).
% 6.45/1.38 cnf(s60, plain, spl6_8 | spl6_21, inference(sat_conversion,[],[f1627])).
% 6.45/1.38 cnf(s81, plain, spl6_7 | ~spl6_8 | spl6_38, inference(sat_conversion,[],[f2117])).
% 6.45/1.38 cnf(s106, plain, spl6_13 | ~spl6_18, inference(sat_conversion,[],[f2881])).
% 6.45/1.38 cnf(s244, plain, ~spl6_13, inference(sat_conversion,[],[f8060])).
% 6.45/1.38 cnf(s1426, plain, ~spl6_38, inference(sat_conversion,[],[f29674])).
% 6.45/1.38 cnf(s1491, plain, ~spl6_18, inference(rat,[],[s106,s244])).
% 6.45/1.38 cnf(s1533, plain, spl6_7 | ~spl6_8, inference(rat,[],[s81,s1426])).
% 6.45/1.38 cnf(s1538, plain, ~spl6_21, inference(rat,[],[s49,s1491])).
% 6.45/1.39 cnf(s1539, plain, spl6_8, inference(rat,[],[s60,s1538])).
% 6.45/1.39 cnf(s1542, plain, spl6_7, inference(rat,[],[s1533,s1539])).
% 6.45/1.39 cnf(s1543, plain, ~spl6_5, inference(rat,[],[s39,s244])).
% 6.45/1.39 cnf(s1562, plain, $false, inference(rat,[],[s14,s1542,s1543])).
% 6.45/1.39 thf(f29699,plain,(
% 6.45/1.39 $false),
% 6.45/1.39 inference(avatar_sat_refutation,[],[s1562])).
% 6.45/1.39 % SZS output end Proof for theBenchmark
% 6.45/1.39 % (3473910)------------------------------
% 6.45/1.39 % (3473910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.45/1.39 % (3473910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.45/1.39 % (3473910)CaDiCaL version: 2.1.3
% 6.45/1.39 % (3473910)Termination reason: Refutation
% 6.45/1.39 % (3473910)Time elapsed: 0.997 s
% 6.45/1.39 % (3473910)Peak memory usage: 17 MB
% 6.45/1.39 % (3473910)Instructions burned: 2453 (million)
% 6.45/1.39 % (3473904)Success in time 1.035 s
% 6.45/1.39 % Vampire exiting
%------------------------------------------------------------------------------