%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRA028^1 : TPTP v9.3.1. Released v3.6.0.
% 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 08:03:29 AM UTC 2026
% Result : Theorem 6.06s 1.17s
% Output : Refutation 6.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA028^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.24 % Computer : n007.cluster.edu
% 0.12/0.24 % Model : x86_64 x86_64
% 0.12/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.24 % Memory : 8046.5625MB
% 0.12/0.24 % OS : Linux 6.8.0-71-generic
% 0.12/0.24 % CPULimit : 300
% 0.12/0.24 % WCLimit : 300
% 0.12/0.24 % DateTime : Tue Sep 29 18:36:41 UTC 2026
% 0.12/0.24 % CPUTime :
% 0.12/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.25/0.29 Running first-order model finding
% 0.25/0.29 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
% 6.06/1.17 % (3764292)Will run a generic schedule for satisfiability detection.
% 6.06/1.17 % (3764298)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3534998266_3000 on theBenchmark for (3000ds/0Mi)
% 6.06/1.17 % Exception at run slice level
% 6.06/1.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.06/1.17 % (3764303)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2322896976:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 6.06/1.17 % (3764299)% WARNING: option uhcvi not known.
% 6.06/1.17 % (3764303)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.06/1.17 % (3764309)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1745526985:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.06/1.17 % Exception at run slice level
% 6.06/1.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.06/1.17 % (3764299)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1169163047:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 6.06/1.17 % (3764300)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=948536602:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 6.06/1.17 % (3764301)dis+10_1_sil=32000:sp=arity:random_seed=3095488414:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 6.06/1.17 % (3764304)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3508013088:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 6.06/1.17 % (3764305)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1895875360:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 6.06/1.17 % (3764299)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.06/1.17 % (3764299)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.06/1.17 % (3764314)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4046094034:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.06/1.17 % (3764303)Instruction limit reached!
% 6.06/1.17 % (3764303)------------------------------
% 6.06/1.17 % (3764303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.06/1.17 % (3764303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.17 % (3764303)CaDiCaL version: 2.1.3
% 6.06/1.17 % (3764303)Termination reason: Instruction limit
% 6.06/1.17 % (3764303)Termination phase: Saturation
% 6.06/1.17 % (3764303)Time elapsed: 0.063 s
% 6.06/1.17 % (3764303)Peak memory usage: 12 MB
% 6.06/1.17 % (3764303)Instructions burned: 117 (million)
% 6.06/1.17 % (3764314)Instruction limit reached!
% 6.06/1.17 % (3764314)------------------------------
% 6.06/1.17 % (3764314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.06/1.17 % (3764314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.17 % (3764314)CaDiCaL version: 2.1.3
% 6.06/1.17 % (3764314)Termination reason: Instruction limit
% 6.06/1.17 % (3764314)Termination phase: Saturation
% 6.06/1.17 % (3764314)Time elapsed: 0.062 s
% 6.06/1.17 % (3764314)Peak memory usage: 12 MB
% 6.06/1.17 % (3764314)Instructions burned: 132 (million)
% 6.06/1.17 % (3764325)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=3626693261:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 6.06/1.17 % (3764325)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.06/1.17 % (3764325)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.06/1.17 % (3764301)Instruction limit reached!
% 6.06/1.17 % (3764301)------------------------------
% 6.06/1.17 % (3764301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.06/1.17 % (3764301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.17 % (3764301)CaDiCaL version: 2.1.3
% 6.06/1.17 % (3764301)Termination reason: Instruction limit
% 6.06/1.17 % (3764301)Termination phase: Saturation
% 6.06/1.17 % (3764301)Time elapsed: 0.087 s
% 6.06/1.17 % (3764301)Peak memory usage: 12 MB
% 6.06/1.17 % (3764301)Instructions burned: 103 (million)
% 6.06/1.17 % (3764328)ott-21_1_sil=16000:fs=off:random_seed=547048977:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.06/1.17 % (3764304)Instruction limit reached!
% 6.06/1.17 % (3764304)------------------------------
% 6.06/1.17 % (3764304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.06/1.17 % (3764304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.17 % (3764304)CaDiCaL version: 2.1.3
% 6.06/1.17 % (3764304)Termination reason: Instruction limit
% 6.06/1.17 % (3764304)Termination phase: Saturation
% 6.06/1.17 % (3764304)Time elapsed: 0.105 s
% 6.06/1.17 % (3764304)Peak memory usage: 12 MB
% 6.06/1.17 % (3764304)Instructions burned: 131 (million)
% 6.06/1.17 % (3764330)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1220316739:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.06/1.17 % (3764333)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2124622682:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.06/1.17 % Exception at run slice level
% 6.06/1.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.06/1.17 % (3764305)Instruction limit reached!
% 6.06/1.17 % (3764305)------------------------------
% 6.06/1.17 % (3764305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.06/1.17 % (3764305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.17 % (3764305)CaDiCaL version: 2.1.3
% 6.06/1.17 % (3764305)Termination reason: Instruction limit
% 6.06/1.17 % (3764305)Termination phase: Saturation
% 6.06/1.17 % (3764305)Time elapsed: 0.134 s
% 6.06/1.17 % (3764305)Peak memory usage: 12 MB
% 6.06/1.17 % (3764305)Instructions burned: 159 (million)
% 6.06/1.17 % (3764337)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1196592820:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.06/1.17 % (3764339)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3563559243:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.06/1.17 % Exception at run slice level
% 6.06/1.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.06/1.17 % (3764343)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=3550431249: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)
% 6.06/1.17 % (3764343)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.06/1.17 % (3764328)Instruction limit reached!
% 6.06/1.17 % (3764328)------------------------------
% 6.06/1.17 % (3764328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.06/1.17 % (3764328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.17 % (3764328)CaDiCaL version: 2.1.3
% 6.06/1.17 % (3764328)Termination reason: Instruction limit
% 6.06/1.17 % (3764328)Termination phase: Saturation
% 6.06/1.17 % (3764328)Time elapsed: 0.145 s
% 6.06/1.17 % (3764328)Peak memory usage: 12 MB
% 6.06/1.17 % (3764328)Instructions burned: 181 (million)
% 6.06/1.17 % (3764352)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3798805104:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 6.06/1.17 % (3764352)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.06/1.17 % (3764330)Instruction limit reached!
% 6.06/1.17 % (3764330)------------------------------
% 6.06/1.17 % (3764330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.06/1.17 % (3764330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.17 % (3764330)CaDiCaL version: 2.1.3
% 6.06/1.17 % (3764330)Termination reason: Instruction limit
% 6.06/1.17 % (3764330)Termination phase: Saturation
% 6.06/1.17 % (3764330)Time elapsed: 0.395 s
% 6.06/1.17 % (3764330)Peak memory usage: 13 MB
% 6.06/1.17 % (3764330)Instructions burned: 478 (million)
% 6.06/1.17 % (3764368)fmb+10_1_sil=64000:random_seed=3753310512:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 6.06/1.17 % (3764368)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.06/1.17 % Exception at run slice level
% 6.06/1.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.06/1.17 % (3764371)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1144201634:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 6.06/1.17 % Exception at run slice level
% 6.06/1.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.06/1.17 % (3764376)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2234378260:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 6.06/1.17 % Exception at run slice level
% 6.06/1.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.06/1.17 % (3764325)Instruction limit reached!
% 6.06/1.17 % (3764325)------------------------------
% 6.06/1.17 % (3764325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.06/1.17 % (3764325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.17 % (3764325)CaDiCaL version: 2.1.3
% 6.06/1.17 % (3764325)Termination reason: Instruction limit
% 6.06/1.17 % (3764325)Termination phase: Saturation
% 6.06/1.17 % (3764325)Time elapsed: 0.527 s
% 6.06/1.17 % (3764325)Peak memory usage: 14 MB
% 6.06/1.17 % (3764325)Instructions burned: 684 (million)
% 6.06/1.17 % (3764386)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2456104782:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 6.06/1.17 % (3764386)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.06/1.17 % (3764388)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=908612313:i=1472:ins=7:fdi=8:gsp=on_2993 on theBenchmark for (2993ds/1472Mi)
% 6.06/1.17 % (3764388)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.06/1.17 % (3764388)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.06/1.17 % (3764343)Instruction limit reached!
% 6.06/1.17 % (3764343)------------------------------
% 6.06/1.17 % (3764343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.06/1.17 % (3764343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.17 % (3764343)CaDiCaL version: 2.1.3
% 6.06/1.17 % (3764343)Termination reason: Instruction limit
% 6.06/1.17 % (3764343)Termination phase: Saturation
% 6.06/1.17 % (3764343)Time elapsed: 0.533 s
% 6.06/1.17 % (3764343)Peak memory usage: 15 MB
% 6.06/1.17 % (3764343)Instructions burned: 692 (million)
% 6.06/1.17 % (3764395)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=895194110:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 6.06/1.17 % Exception at run slice level
% 6.06/1.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.06/1.17 % (3764401)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3932143203:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 6.06/1.17 % Exception at run slice level
% 6.06/1.17 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.06/1.17 % (3764404)ott-2_1_sil=16000:newcnf=on:random_seed=702467814:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2991 on theBenchmark for (2991ds/869Mi)
% 6.06/1.17 % (3764404)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.06/1.17 % (3764300) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3764292-3764300"...
% 6.06/1.17 % (3764300)...printing done.
% 6.06/1.17 % (3764300)Refutation found. Thanks to Tanya!
% 6.06/1.17 % SZS status Theorem for theBenchmark
% 6.06/1.17 % SZS output start Proof for theBenchmark
% 6.06/1.17 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 6.06/1.17 thf(func_def_3, type, sK0: (($o > $o) > ($o > $o) > $o)).
% 6.06/1.17 thf(func_def_4, type, vNOT: ($o > $o)).
% 6.06/1.17 thf(func_def_6, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.06/1.17 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 6.06/1.17 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.06/1.17 thf(func_def_9, type, sK2: (($o > $o) > $o)).
% 6.06/1.17 thf(func_def_10, type, sK3: (($o > $o) > $o)).
% 6.06/1.17 thf(func_def_11, type, sK4: (($o > $o) > $o)).
% 6.06/1.17 thf(func_def_12, type, sK5: $o).
% 6.06/1.17 thf(func_def_13, type, sK6: (($o > $o) > $o)).
% 6.06/1.17 thf(f1,conjecture,(
% 6.06/1.17 ! [X0 : (($o > $o) > ($o > $o) > $o)] : (! [X1 : ($o > $o),X2 : ($o > $o)] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)) => (? [X3 : ($o > $o),X4 : ($o > $o),X6 : ($o > $o),X7 : ($o > $o),X5 : (($o > $o) > $o),X8 : (($o > $o) > $o),X9 : (($o > $o) > $o)] : (~(X0 @ X7 @ X6) & ~(X0 @ X7 @ X4) & ~(X0 @ X7 @ X3) & ~(X0 @ X6 @ X4) & ~(X0 @ X6 @ X3) & ~(X0 @ X4 @ X3) & ~(X9 @ X7) & (X9 @ X6) & ~(X9 @ X4) & ~(X9 @ X3) & ~(X8 @ X7) & ~(X8 @ X6) & (X8 @ X4) & ~(X8 @ X3) & ~(X5 @ X7) & ~(X5 @ X6) & ~(X5 @ X4) & (X5 @ X3)) | ? [X3 : ($o > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : ((X0 @ X4 @ X3) & ~(X5 @ X4) & (X5 @ X3))))),
% 6.06/1.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ramsey_u_2_4_4)).
% 6.06/1.17 thf(f2,negated_conjecture,(
% 6.06/1.17 ~ ! [X0 : (($o > $o) > ($o > $o) > $o)] : (! [X1 : ($o > $o),X2 : ($o > $o)] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)) => (? [X3 : ($o > $o),X4 : ($o > $o),X6 : ($o > $o),X7 : ($o > $o),X5 : (($o > $o) > $o),X8 : (($o > $o) > $o),X9 : (($o > $o) > $o)] : (~(X0 @ X7 @ X6) & ~(X0 @ X7 @ X4) & ~(X0 @ X7 @ X3) & ~(X0 @ X6 @ X4) & ~(X0 @ X6 @ X3) & ~(X0 @ X4 @ X3) & ~(X9 @ X7) & (X9 @ X6) & ~(X9 @ X4) & ~(X9 @ X3) & ~(X8 @ X7) & ~(X8 @ X6) & (X8 @ X4) & ~(X8 @ X3) & ~(X5 @ X7) & ~(X5 @ X6) & ~(X5 @ X4) & (X5 @ X3)) | ? [X3 : ($o > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : ((X0 @ X4 @ X3) & ~(X5 @ X4) & (X5 @ X3))))),
% 6.06/1.17 inference(negated_conjecture,[status(cth)],[f1])).
% 6.06/1.17 thf(f3,plain,(
% 6.06/1.17 ~ ! [X0 : (($o > $o) > ($o > $o) > $o)] : (! [X1 : ($o > $o),X2 : ($o > $o)] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)) => (? [X3 : ($o > $o),X4 : ($o > $o),X5 : ($o > $o),X6 : ($o > $o),X7 : (($o > $o) > $o),X8 : (($o > $o) > $o),X9 : (($o > $o) > $o)] : (~(X0 @ X6 @ X5) & ~(X0 @ X6 @ X4) & ~(X0 @ X6 @ X3) & ~(X0 @ X5 @ X4) & ~(X0 @ X5 @ X3) & ~(X0 @ X4 @ X3) & ~(X9 @ X6) & (X9 @ X5) & ~(X9 @ X4) & ~(X9 @ X3) & ~(X8 @ X6) & ~(X8 @ X5) & (X8 @ X4) & ~(X8 @ X3) & ~(X7 @ X6) & ~(X7 @ X5) & ~(X7 @ X4) & (X7 @ X3)) | ? [X10 : ($o > $o),X11 : ($o > $o),X12 : (($o > $o) > $o)] : ((X0 @ X11 @ X10) & ~(X12 @ X11) & (X12 @ X10))))),
% 6.06/1.17 inference(rectify,[],[f2])).
% 6.06/1.17 thf(f4,plain,(
% 6.06/1.17 ~ ! [X0 : (($o > $o) > ($o > $o) > $o)] : (! [X1 : ($o > $o),X2 : ($o > $o)] : ((((X0 @ X1 @ X2)) = $true) => (((X0 @ X2 @ X1)) = $true)) => (? [X3 : ($o > $o),X4 : ($o > $o),X5 : ($o > $o),X6 : ($o > $o),X7 : (($o > $o) > $o),X8 : (($o > $o) > $o),X9 : (($o > $o) > $o)] : (~ (((X0 @ X6 @ X5)) = $true) & ~ (((X0 @ X6 @ X4)) = $true) & ~ (((X0 @ X6 @ X3)) = $true) & ~ (((X0 @ X5 @ X4)) = $true) & ~ (((X0 @ X5 @ X3)) = $true) & ~ (((X0 @ X4 @ X3)) = $true) & ~ (((X9 @ X6)) = $true) & (((X9 @ X5)) = $true) & ~ (((X9 @ X4)) = $true) & ~ (((X9 @ X3)) = $true) & ~ (((X8 @ X6)) = $true) & ~ (((X8 @ X5)) = $true) & (((X8 @ X4)) = $true) & ~ (((X8 @ X3)) = $true) & ~ (((X7 @ X6)) = $true) & ~ (((X7 @ X5)) = $true) & ~ (((X7 @ X4)) = $true) & (((X7 @ X3)) = $true)) | ? [X10 : ($o > $o),X11 : ($o > $o),X12 : (($o > $o) > $o)] : ((((X0 @ X11 @ X10)) = $true) & ~ (((X12 @ X11)) = $true) & (((X12 @ X10)) = $true))))),
% 6.06/1.17 inference(fool_elimination,[],[f3])).
% 6.06/1.17 thf(f5,plain,(
% 6.06/1.17 ~ ! [X0 : (($o > $o) > ($o > $o) > $o)] : (! [X1 : ($o > $o),X2 : ($o > $o)] : ((((X0 @ X1 @ X2)) = $true) => (((X0 @ X2 @ X1)) = $true)) => (? [X3 : ($o > $o),X4 : ($o > $o),X5 : ($o > $o),X6 : ($o > $o),X7 : (($o > $o) > $o),X8 : (($o > $o) > $o),X9 : (($o > $o) > $o)] : ((((X0 @ X6 @ X5)) != $true) & (((X0 @ X6 @ X4)) != $true) & (((X0 @ X6 @ X3)) != $true) & (((X0 @ X5 @ X4)) != $true) & (((X0 @ X5 @ X3)) != $true) & (((X0 @ X4 @ X3)) != $true) & (((X9 @ X6)) != $true) & (((X9 @ X5)) = $true) & (((X9 @ X4)) != $true) & (((X9 @ X3)) != $true) & (((X8 @ X6)) != $true) & (((X8 @ X5)) != $true) & (((X8 @ X4)) = $true) & (((X8 @ X3)) != $true) & (((X7 @ X6)) != $true) & (((X7 @ X5)) != $true) & (((X7 @ X4)) != $true) & (((X7 @ X3)) = $true)) | ? [X10 : ($o > $o),X11 : ($o > $o),X12 : (($o > $o) > $o)] : ((((X0 @ X11 @ X10)) = $true) & (((X12 @ X11)) != $true) & (((X12 @ X10)) = $true))))),
% 6.06/1.17 inference(flattening,[],[f4])).
% 6.06/1.17 thf(f6,plain,(
% 6.06/1.17 ? [X0 : (($o > $o) > ($o > $o) > $o)] : ((! [X3 : ($o > $o),X4 : ($o > $o),X5 : ($o > $o),X6 : ($o > $o),X7 : (($o > $o) > $o),X8 : (($o > $o) > $o),X9 : (($o > $o) > $o)] : ((((X0 @ X6 @ X5)) = $true) | (((X0 @ X6 @ X4)) = $true) | (((X0 @ X6 @ X3)) = $true) | (((X0 @ X5 @ X4)) = $true) | (((X0 @ X5 @ X3)) = $true) | (((X0 @ X4 @ X3)) = $true) | (((X9 @ X6)) = $true) | (((X9 @ X5)) != $true) | (((X9 @ X4)) = $true) | (((X9 @ X3)) = $true) | (((X8 @ X6)) = $true) | (((X8 @ X5)) = $true) | (((X8 @ X4)) != $true) | (((X8 @ X3)) = $true) | (((X7 @ X6)) = $true) | (((X7 @ X5)) = $true) | (((X7 @ X4)) = $true) | (((X7 @ X3)) != $true)) & ! [X10 : ($o > $o),X11 : ($o > $o),X12 : (($o > $o) > $o)] : ((((X0 @ X11 @ X10)) != $true) | (((X12 @ X11)) = $true) | (((X12 @ X10)) != $true))) & ! [X1 : ($o > $o),X2 : ($o > $o)] : ((((X0 @ X2 @ X1)) = $true) | (((X0 @ X1 @ X2)) != $true)))),
% 6.06/1.17 inference(ennf_transformation,[],[f5])).
% 6.06/1.17 thf(f7,plain,(
% 6.06/1.17 ? [X0 : (($o > $o) > ($o > $o) > $o)] : (! [X3 : ($o > $o),X4 : ($o > $o),X5 : ($o > $o),X6 : ($o > $o),X7 : (($o > $o) > $o),X8 : (($o > $o) > $o),X9 : (($o > $o) > $o)] : ((((X0 @ X6 @ X5)) = $true) | (((X0 @ X6 @ X4)) = $true) | (((X0 @ X6 @ X3)) = $true) | (((X0 @ X5 @ X4)) = $true) | (((X0 @ X5 @ X3)) = $true) | (((X0 @ X4 @ X3)) = $true) | (((X9 @ X6)) = $true) | (((X9 @ X5)) != $true) | (((X9 @ X4)) = $true) | (((X9 @ X3)) = $true) | (((X8 @ X6)) = $true) | (((X8 @ X5)) = $true) | (((X8 @ X4)) != $true) | (((X8 @ X3)) = $true) | (((X7 @ X6)) = $true) | (((X7 @ X5)) = $true) | (((X7 @ X4)) = $true) | (((X7 @ X3)) != $true)) & ! [X10 : ($o > $o),X11 : ($o > $o),X12 : (($o > $o) > $o)] : ((((X0 @ X11 @ X10)) != $true) | (((X12 @ X11)) = $true) | (((X12 @ X10)) != $true)) & ! [X1 : ($o > $o),X2 : ($o > $o)] : ((((X0 @ X2 @ X1)) = $true) | (((X0 @ X1 @ X2)) != $true)))),
% 6.06/1.17 inference(flattening,[],[f6])).
% 6.06/1.17 thf(f8,plain,(
% 6.06/1.17 ? [X0 : (($o > $o) > ($o > $o) > $o)] : (! [X1 : ($o > $o),X2 : ($o > $o),X3 : ($o > $o),X4 : ($o > $o),X5 : (($o > $o) > $o),X6 : (($o > $o) > $o),X7 : (($o > $o) > $o)] : ((((X0 @ X4 @ X3)) = $true) | ($true = ((X0 @ X4 @ X2))) | ($true = ((X0 @ X4 @ X1))) | ($true = ((X0 @ X3 @ X2))) | ($true = ((X0 @ X3 @ X1))) | (((X0 @ X2 @ X1)) = $true) | (((X7 @ X4)) = $true) | (((X7 @ X3)) != $true) | ($true = ((X7 @ X2))) | ($true = ((X7 @ X1))) | ($true = ((X6 @ X4))) | ($true = ((X6 @ X3))) | ($true != ((X6 @ X2))) | ($true = ((X6 @ X1))) | (((X5 @ X4)) = $true) | (((X5 @ X3)) = $true) | ($true = ((X5 @ X2))) | ($true != ((X5 @ X1)))) & ! [X8 : ($o > $o),X9 : ($o > $o),X10 : (($o > $o) > $o)] : (($true != ((X0 @ X9 @ X8))) | ($true = ((X10 @ X9))) | ($true != ((X10 @ X8)))) & ! [X11 : ($o > $o),X12 : ($o > $o)] : (($true = ((X0 @ X12 @ X11))) | ($true != ((X0 @ X11 @ X12)))))),
% 6.06/1.17 inference(rectify,[],[f7])).
% 6.06/1.17 thf(f9,plain,(
% 6.06/1.17 ! [X1 : ($o > $o),X2 : ($o > $o),X3 : ($o > $o),X4 : ($o > $o),X5 : (($o > $o) > $o),X6 : (($o > $o) > $o),X7 : (($o > $o) > $o)] : (($true = ((sK0 @ X4 @ X3))) | ($true = ((sK0 @ X4 @ X2))) | ($true = ((sK0 @ X4 @ X1))) | ($true = ((sK0 @ X3 @ X2))) | ($true = ((sK0 @ X3 @ X1))) | ($true = ((sK0 @ X2 @ X1))) | (((X7 @ X4)) = $true) | (((X7 @ X3)) != $true) | ($true = ((X7 @ X2))) | ($true = ((X7 @ X1))) | ($true = ((X6 @ X4))) | ($true = ((X6 @ X3))) | ($true != ((X6 @ X2))) | ($true = ((X6 @ X1))) | (((X5 @ X4)) = $true) | (((X5 @ X3)) = $true) | ($true = ((X5 @ X2))) | ($true != ((X5 @ X1)))) & ! [X8 : ($o > $o),X9 : ($o > $o),X10 : (($o > $o) > $o)] : (($true != ((sK0 @ X9 @ X8))) | ($true = ((X10 @ X9))) | ($true != ((X10 @ X8)))) & ! [X11 : ($o > $o),X12 : ($o > $o)] : (($true = ((sK0 @ X12 @ X11))) | ($true != ((sK0 @ X11 @ X12))))),
% 6.06/1.17 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8])).
% 6.06/1.17 thf(f11,plain,(
% 6.06/1.17 ( ! [X10 : (($o > $o) > $o),X8 : ($o > $o),X9 : ($o > $o)] : (($true != ((sK0 @ X9 @ X8))) | ($true = ((X10 @ X9))) | ($true != ((X10 @ X8)))) )),
% 6.06/1.17 inference(cnf_transformation,[],[f9])).
% 6.06/1.17 thf(f12,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X6 : (($o > $o) > $o),X7 : (($o > $o) > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : (($true = ((sK0 @ X4 @ X3))) | ($true = ((sK0 @ X4 @ X2))) | ($true = ((sK0 @ X4 @ X1))) | ($true = ((sK0 @ X3 @ X2))) | ($true = ((sK0 @ X3 @ X1))) | ($true = ((sK0 @ X2 @ X1))) | (((X7 @ X4)) = $true) | (((X7 @ X3)) != $true) | ($true = ((X7 @ X2))) | ($true = ((X7 @ X1))) | ($true = ((X6 @ X4))) | ($true = ((X6 @ X3))) | ($true != ((X6 @ X2))) | ($true = ((X6 @ X1))) | (((X5 @ X4)) = $true) | (((X5 @ X3)) = $true) | ($true = ((X5 @ X2))) | ($true != ((X5 @ X1)))) )),
% 6.06/1.17 inference(cnf_transformation,[],[f9])).
% 6.06/1.17 thf(f13,definition,(
% 6.06/1.17 ($true != $false)),
% 6.06/1.17 introduced(theory,[fool_distinctness_axiom])).
% 6.06/1.17 thf(f78,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X6 : (($o > $o) > $o),X7 : (($o > $o) > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : (($true = ((sK0 @ X4 @ X2))) | ($true = ((sK0 @ X4 @ X1))) | ($true = ((sK0 @ X3 @ X2))) | ($true = ((sK0 @ X3 @ X1))) | ($true = ((sK0 @ X2 @ X1))) | (((X7 @ X4)) = $true) | (((X7 @ X3)) != $true) | ($true = ((X7 @ X2))) | ($true = ((X7 @ X1))) | ($true = ((X6 @ X4))) | ($true = ((X6 @ X3))) | ($true != ((X6 @ X2))) | ($true = ((X6 @ X1))) | (((X5 @ X4)) = $true) | (((X5 @ X3)) = $true) | ($true = ((X5 @ X2))) | ($true != ((X5 @ X1)))) )),
% 6.06/1.17 inference(forward_subsumption_resolution,[],[f12,f11])).
% 6.06/1.17 thf(f79,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X6 : (($o > $o) > $o),X7 : (($o > $o) > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : (($true = ((sK0 @ X4 @ X1))) | ($true = ((sK0 @ X3 @ X2))) | ($true = ((sK0 @ X3 @ X1))) | ($true = ((sK0 @ X2 @ X1))) | (((X7 @ X4)) = $true) | (((X7 @ X3)) != $true) | ($true = ((X7 @ X2))) | ($true = ((X7 @ X1))) | ($true = ((X6 @ X4))) | ($true = ((X6 @ X3))) | ($true != ((X6 @ X2))) | ($true = ((X6 @ X1))) | (((X5 @ X4)) = $true) | (((X5 @ X3)) = $true) | ($true = ((X5 @ X2))) | ($true != ((X5 @ X1)))) )),
% 6.06/1.17 inference(forward_subsumption_resolution,[],[f78,f11])).
% 6.06/1.17 thf(f80,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X6 : (($o > $o) > $o),X7 : (($o > $o) > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : (($true = ((sK0 @ X3 @ X2))) | ($true = ((sK0 @ X3 @ X1))) | ($true = ((sK0 @ X2 @ X1))) | (((X7 @ X4)) = $true) | (((X7 @ X3)) != $true) | ($true = ((X7 @ X2))) | ($true = ((X7 @ X1))) | ($true = ((X6 @ X4))) | ($true = ((X6 @ X3))) | ($true != ((X6 @ X2))) | ($true = ((X6 @ X1))) | (((X5 @ X4)) = $true) | (((X5 @ X3)) = $true) | ($true = ((X5 @ X2))) | ($true != ((X5 @ X1)))) )),
% 6.06/1.17 inference(forward_subsumption_resolution,[],[f79,f11])).
% 6.06/1.17 thf(f81,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X6 : (($o > $o) > $o),X7 : (($o > $o) > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : (($true = ((sK0 @ X3 @ X1))) | ($true = ((sK0 @ X2 @ X1))) | (((X7 @ X4)) = $true) | (((X7 @ X3)) != $true) | ($true = ((X7 @ X2))) | ($true = ((X7 @ X1))) | ($true = ((X6 @ X4))) | ($true = ((X6 @ X3))) | ($true != ((X6 @ X2))) | ($true = ((X6 @ X1))) | (((X5 @ X4)) = $true) | (((X5 @ X3)) = $true) | ($true = ((X5 @ X2))) | ($true != ((X5 @ X1)))) )),
% 6.06/1.17 inference(forward_subsumption_resolution,[],[f80,f11])).
% 6.06/1.17 thf(f82,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X6 : (($o > $o) > $o),X7 : (($o > $o) > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : (($true = ((sK0 @ X2 @ X1))) | (((X7 @ X4)) = $true) | (((X7 @ X3)) != $true) | ($true = ((X7 @ X2))) | ($true = ((X7 @ X1))) | ($true = ((X6 @ X4))) | ($true = ((X6 @ X3))) | ($true != ((X6 @ X2))) | ($true = ((X6 @ X1))) | (((X5 @ X4)) = $true) | (((X5 @ X3)) = $true) | ($true = ((X5 @ X2))) | ($true != ((X5 @ X1)))) )),
% 6.06/1.17 inference(forward_subsumption_resolution,[],[f81,f11])).
% 6.06/1.17 thf(f83,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X6 : (($o > $o) > $o),X7 : (($o > $o) > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : (($true != ((X6 @ X2))) | (((X7 @ X3)) != $true) | ($true = ((X7 @ X2))) | ($true = ((X7 @ X1))) | ($true = ((X6 @ X4))) | ($true = ((X6 @ X3))) | (((X7 @ X4)) = $true) | ($true = ((X6 @ X1))) | (((X5 @ X4)) = $true) | (((X5 @ X3)) = $true) | ($true = ((X5 @ X2))) | ($true != ((X5 @ X1)))) )),
% 6.06/1.17 inference(forward_subsumption_resolution,[],[f82,f11])).
% 6.06/1.17 thf(f85,definition,(
% 6.06/1.17 spl1_4 <=> ! [X0 : $o] : ($true = X0)),
% 6.06/1.17 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 6.06/1.17 thf(f86,plain,(
% 6.06/1.17 ( ! [X0 : $o] : (($true = X0)) ) | ~spl1_4),
% 6.06/1.17 inference(avatar_component_clause,[],[f85])).
% 6.06/1.17 thf(f88,definition,(
% 6.06/1.17 spl1_5 <=> ! [X0 : $o] : ($false = X0)),
% 6.06/1.17 introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition])).
% 6.06/1.17 thf(f89,plain,(
% 6.06/1.17 ( ! [X0 : $o] : (($false = X0)) ) | ~spl1_5),
% 6.06/1.17 inference(avatar_component_clause,[],[f88])).
% 6.06/1.17 thf(f105,plain,(
% 6.06/1.17 ( ! [X2 : (($o > $o) > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : ((X0 = X1) | ($true != ((X2 @ X0))) | ($true = ((X1 = X3))) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X1))) | ($true = ((X1 = X4))) | ($true = ((X2 @ X3))) | (((X5 @ X4)) = $true) | ($true = ((X5 @ X1))) | ($true = ((X5 @ X0))) | (((X5 @ X3)) != $true)) )),
% 6.06/1.17 inference(leibniz_equality_elimination,[],[f83])).
% 6.06/1.17 thf(f149,plain,(
% 6.06/1.17 ( ! [X2 : (($o > $o) > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : ((X0 = X1) | ($true != ((X2 @ X0))) | (X1 = X3) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X1))) | ($true = ((X1 = X4))) | ($true = ((X2 @ X3))) | (((X5 @ X4)) = $true) | ($true = ((X5 @ X1))) | ($true = ((X5 @ X0))) | (((X5 @ X3)) != $true)) )),
% 6.06/1.17 inference(equality_proxy_clausification,[],[f105])).
% 6.06/1.17 thf(f150,plain,(
% 6.06/1.17 ( ! [X2 : (($o > $o) > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o),X4 : ($o > $o),X5 : (($o > $o) > $o)] : (($true != ((X2 @ X0))) | (X0 = X1) | (X1 = X3) | ($true = ((X2 @ X4))) | ($true = ((X2 @ X1))) | (X1 = X4) | ($true = ((X2 @ X3))) | (((X5 @ X4)) = $true) | ($true = ((X5 @ X1))) | ($true = ((X5 @ X0))) | (((X5 @ X3)) != $true)) )),
% 6.06/1.17 inference(equality_proxy_clausification,[],[f149])).
% 6.06/1.17 thf(f156,plain,(
% 6.06/1.17 ( ! [X0 : $o] : (($false != X0)) ) | ~spl1_4),
% 6.06/1.17 inference(constrained_superposition,[],[f13,f86])).
% 6.06/1.17 thf(f184,plain,(
% 6.06/1.17 $false | ~spl1_4),
% 6.06/1.17 inference(equality_resolution,[],[f156])).
% 6.06/1.17 thf(f185,plain,(
% 6.06/1.17 ~spl1_4),
% 6.06/1.17 inference(avatar_contradiction_clause,[],[f184])).
% 6.06/1.17 thf(f419,plain,(
% 6.06/1.17 ($false != $false) | ~spl1_5),
% 6.06/1.17 inference(constrained_superposition,[],[f13,f89])).
% 6.06/1.17 thf(f424,plain,(
% 6.06/1.17 $false | ~spl1_5),
% 6.06/1.17 inference(trivial_inequality_removal,[],[f419])).
% 6.06/1.17 thf(f425,plain,(
% 6.06/1.17 ~spl1_5),
% 6.06/1.17 inference(avatar_contradiction_clause,[],[f424])).
% 6.06/1.17 thf(f493,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o),X4 : (($o > $o) > $o)] : ((X0 = X1) | (X0 = X2) | (X2 = X3) | ($true = ((X0 = X2))) | (X1 = X2) | ($true = ((X0 = X3))) | ($true = ((X4 @ X1))) | ($true = ((X4 @ X2))) | ($true = ((X4 @ X0))) | ($true != ((X4 @ X3)))) )),
% 6.06/1.17 inference(leibniz_equality_elimination,[],[f150])).
% 6.06/1.17 thf(f537,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o),X4 : (($o > $o) > $o)] : ((X0 = X1) | (X0 = X2) | (X2 = X3) | (X0 = X2) | (X1 = X2) | ($true = ((X0 = X3))) | ($true = ((X4 @ X1))) | ($true = ((X4 @ X2))) | ($true = ((X4 @ X0))) | ($true != ((X4 @ X3)))) )),
% 6.06/1.17 inference(equality_proxy_clausification,[],[f493])).
% 6.06/1.17 thf(f538,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o),X4 : (($o > $o) > $o)] : ((X0 = X1) | (X0 = X2) | (X2 = X3) | (X0 = X2) | (X1 = X2) | (X0 = X3) | ($true = ((X4 @ X1))) | ($true = ((X4 @ X2))) | ($true = ((X4 @ X0))) | ($true != ((X4 @ X3)))) )),
% 6.06/1.17 inference(equality_proxy_clausification,[],[f537])).
% 6.06/1.17 thf(f539,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o),X4 : (($o > $o) > $o)] : (($true != ((X4 @ X3))) | (X0 = X2) | (X2 = X3) | (X1 = X2) | (X0 = X3) | ($true = ((X4 @ X1))) | ($true = ((X4 @ X2))) | ($true = ((X4 @ X0))) | (X0 = X1)) )),
% 6.06/1.17 inference(duplicate_literal_removal,[],[f538])).
% 6.06/1.17 thf(f542,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o)] : ((X0 = X1) | (X2 = X3) | (X1 = X3) | (X0 = X3) | (X1 = X2) | ($true = ((X1 = X3))) | ($true = ((X1 = X2))) | (X0 = X2)) )),
% 6.06/1.17 inference(leibniz_equality_elimination,[],[f539])).
% 6.06/1.17 thf(f586,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o)] : ((X0 = X1) | (X2 = X3) | (X1 = X3) | (X0 = X3) | (X1 = X2) | (X1 = X3) | ($true = ((X1 = X2))) | (X0 = X2)) )),
% 6.06/1.17 inference(equality_proxy_clausification,[],[f542])).
% 6.06/1.17 thf(f587,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o)] : ((X0 = X1) | (X2 = X3) | (X1 = X3) | (X0 = X3) | (X1 = X2) | (X1 = X3) | (X1 = X2) | (X0 = X2)) )),
% 6.06/1.17 inference(equality_proxy_clausification,[],[f586])).
% 6.06/1.17 thf(f588,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o)] : ((X0 = X1) | (X2 = X3) | (X1 = X3) | (X0 = X3) | (X1 = X2) | (X0 = X2)) )),
% 6.06/1.17 inference(duplicate_literal_removal,[],[f587])).
% 6.06/1.17 thf(f596,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o),X4 : $o] : ((X0 = X1) | (X2 = X3) | (X1 = X3) | (X0 = X3) | (X1 = X2) | (((X0 @ X4)) = ((X2 @ X4)))) )),
% 6.06/1.17 inference(argument_congruence,[],[f588])).
% 6.06/1.17 thf(f717,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X0 : ($o > $o),X1 : ($o > $o),X4 : $o] : ((X0 = X1) | (X2 = X3) | (X1 = X3) | (X0 = X3) | (X1 = X2) | ($true = ((X0 @ X4))) | ($false = ((X2 @ X4)))) )),
% 6.06/1.17 inference(iff_proxy_clausification,[],[f596])).
% 6.06/1.17 thf(f731,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X4 : $o] : (((^[Y0 : $o]: ($false)) = X1) | (X2 = X3) | (X1 = X3) | ((^[Y0 : $o]: ($false)) = X3) | (X1 = X2) | ($true = (((^[Y0 : $o]: ($false)) @ X4))) | ($false = ((X2 @ X4)))) )),
% 6.06/1.17 inference(primitive_instantiation,[],[f717])).
% 6.06/1.17 thf(f926,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X4 : $o] : (((^[Y0 : $o]: ($false)) = X1) | (X2 = X3) | (X1 = X3) | ((^[Y0 : $o]: ($false)) = X3) | (X1 = X2) | ($true = $false) | ($false = ((X2 @ X4)))) )),
% 6.06/1.17 inference(beta-eta_normalization,[],[f731])).
% 6.06/1.17 thf(f927,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X4 : $o] : (((^[Y0 : $o]: ($false)) = X1) | (X2 = X3) | (X1 = X3) | ((^[Y0 : $o]: ($false)) = X3) | (X1 = X2) | ($false = ((X2 @ X4)))) )),
% 6.06/1.17 inference(trivial_inequality_removal,[],[f926])).
% 6.06/1.17 thf(f2116,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X4 : $o,X5 : $o] : (((^[Y0 : $o]: ($false)) = X1) | (X2 = X3) | (X1 = X3) | (((X3 @ X5)) = (((^[Y0 : $o]: ($false)) @ X5))) | (X1 = X2) | ($false = ((X2 @ X4)))) )),
% 6.06/1.17 inference(argument_congruence,[],[f927])).
% 6.06/1.17 thf(f2369,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X4 : $o,X5 : $o] : (((^[Y0 : $o]: ($false)) = X1) | (X2 = X3) | (X1 = X3) | ($false = ((X3 @ X5))) | (X1 = X2) | ($false = ((X2 @ X4))) | ($true = (((^[Y0 : $o]: ($false)) @ X5)))) )),
% 6.06/1.17 inference(iff_proxy_clausification,[],[f2116])).
% 6.06/1.17 thf(f2370,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X4 : $o,X5 : $o] : (((^[Y0 : $o]: ($false)) = X1) | (X2 = X3) | (X1 = X3) | ($false = ((X3 @ X5))) | (X1 = X2) | ($false = ((X2 @ X4))) | ($true = $false)) )),
% 6.06/1.17 inference(beta-eta_normalization,[],[f2369])).
% 6.06/1.17 thf(f2371,plain,(
% 6.06/1.17 ( ! [X2 : ($o > $o),X3 : ($o > $o),X1 : ($o > $o),X4 : $o,X5 : $o] : (((^[Y0 : $o]: ($false)) = X1) | (X2 = X3) | (X1 = X3) | ($false = ((X3 @ X5))) | (X1 = X2) | ($false = ((X2 @ X4)))) )),
% 6.06/1.17 inference(trivial_inequality_removal,[],[f2370])).
% 6.06/1.17 thf(f2473,plain,(
% 6.06/1.17 ( ! [X2 : $o,X0 : ($o > $o),X1 : ($o > $o)] : (($false != $false) | ((^[Y0 : $o]: ($false)) = X0) | ((^[Y0 : $o]: ($true)) = X1) | (X0 = X1) | ($false = ((X1 @ X2))) | ((^[Y0 : $o]: ($true)) = X0)) )),
% 6.06/1.17 inference(constrained_superposition,[],[f13,f2371])).
% 6.06/1.17 thf(f2588,plain,(
% 6.06/1.17 ( ! [X2 : $o,X0 : ($o > $o),X1 : ($o > $o)] : (((^[Y0 : $o]: ($true)) = X0) | ($false = ((X1 @ X2))) | (X0 = X1) | ((^[Y0 : $o]: ($true)) = X1) | ((^[Y0 : $o]: ($false)) = X0)) )),
% 6.06/1.17 inference(trivial_inequality_removal,[],[f2473])).
% 6.06/1.17 thf(f2759,plain,(
% 6.06/1.17 ( ! [X2 : $o,X3 : $o,X0 : ($o > $o),X1 : ($o > $o)] : (((((^[Y0 : $o]: ($true)) @ X3)) = ((X0 @ X3))) | ($false = ((X1 @ X2))) | (X0 = X1) | ((^[Y0 : $o]: ($true)) = X1) | ((^[Y0 : $o]: ($false)) = X0)) )),
% 6.06/1.17 inference(argument_congruence,[],[f2588])).
% 6.06/1.17 thf(f2931,plain,(
% 6.06/1.17 ( ! [X2 : $o,X3 : $o,X0 : ($o > $o),X1 : ($o > $o)] : (($false = (((^[Y0 : $o]: ($true)) @ X3))) | ($false = ((X1 @ X2))) | (X0 = X1) | ((^[Y0 : $o]: ($true)) = X1) | ((^[Y0 : $o]: ($false)) = X0) | ($true = ((X0 @ X3)))) )),
% 6.06/1.17 inference(iff_proxy_clausification,[],[f2759])).
% 6.06/1.17 thf(f2932,plain,(
% 6.06/1.17 ( ! [X2 : $o,X3 : $o,X0 : ($o > $o),X1 : ($o > $o)] : (($true = $false) | ($false = ((X1 @ X2))) | (X0 = X1) | ((^[Y0 : $o]: ($true)) = X1) | ((^[Y0 : $o]: ($false)) = X0) | ($true = ((X0 @ X3)))) )),
% 6.06/1.17 inference(beta-eta_normalization,[],[f2931])).
% 6.06/1.17 thf(f2933,plain,(
% 6.06/1.17 ( ! [X2 : $o,X3 : $o,X0 : ($o > $o),X1 : ($o > $o)] : (($true = ((X0 @ X3))) | ($false = ((X1 @ X2))) | (X0 = X1) | ((^[Y0 : $o]: ($false)) = X0) | ((^[Y0 : $o]: ($true)) = X1)) )),
% 6.06/1.17 inference(trivial_inequality_removal,[],[f2932])).
% 6.06/1.17 thf(f2991,plain,(
% 6.06/1.17 ( ! [X0 : ($o > $o),X1 : $o] : (($false != $false) | ($true = ((X0 @ X1))) | ((^[Y0 : $o]: (Y0)) = X0) | ((^[Y0 : $o]: ($false)) = X0) | ((^[Y0 : $o]: ($true)) = (^[Y0 : $o]: (Y0)))) )),
% 6.06/1.17 inference(constrained_superposition,[],[f13,f2933])).
% 6.06/1.17 thf(f3072,plain,(
% 6.06/1.17 ( ! [X0 : ($o > $o),X1 : $o] : (($true = ((X0 @ X1))) | ((^[Y0 : $o]: (Y0)) = X0) | ((^[Y0 : $o]: ($false)) = X0) | ((^[Y0 : $o]: ($true)) = (^[Y0 : $o]: (Y0)))) )),
% 6.06/1.17 inference(trivial_inequality_removal,[],[f2991])).
% 6.06/1.17 thf(f4462,definition,(
% 6.06/1.17 spl1_15 <=> ((^[Y0 : $o]: ($true)) = (^[Y0 : $o]: (Y0)))),
% 6.06/1.17 introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition])).
% 6.06/1.17 thf(f4464,plain,(
% 6.06/1.17 ((^[Y0 : $o]: ($true)) = (^[Y0 : $o]: (Y0))) | ~spl1_15),
% 6.06/1.17 inference(avatar_component_clause,[],[f4462])).
% 6.06/1.17 thf(f4469,definition,(
% 6.06/1.17 spl1_17 <=> ! [X0 : ($o > $o),X1 : $o] : (($true = ((X0 @ X1))) | ((^[Y0 : $o]: ($false)) = X0) | ((^[Y0 : $o]: (Y0)) = X0))),
% 6.06/1.17 introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition])).
% 6.06/1.17 thf(f4470,plain,(
% 6.06/1.17 ( ! [X0 : ($o > $o),X1 : $o] : (((^[Y0 : $o]: (Y0)) = X0) | ($true = ((X0 @ X1))) | ((^[Y0 : $o]: ($false)) = X0)) ) | ~spl1_17),
% 6.06/1.17 inference(avatar_component_clause,[],[f4469])).
% 6.06/1.17 thf(f4471,plain,(
% 6.06/1.17 spl1_15 | spl1_17),
% 6.06/1.17 inference(avatar_split_clause,[],[f3072,f4469,f4462])).
% 6.06/1.17 thf(f4523,plain,(
% 6.06/1.17 ( ! [X1 : $o] : (((((^[Y0 : $o]: (Y0)) @ X1)) = (((^[Y0 : $o]: ($true)) @ X1)))) ) | ~spl1_15),
% 6.06/1.17 inference(argument_congruence,[],[f4464])).
% 6.06/1.17 thf(f4566,plain,(
% 6.06/1.17 ( ! [X1 : $o] : (($true = (((^[Y0 : $o]: (Y0)) @ X1))) | ($false = (((^[Y0 : $o]: ($true)) @ X1)))) ) | ~spl1_15),
% 6.06/1.17 inference(iff_proxy_clausification,[],[f4523])).
% 6.06/1.17 thf(f4569,plain,(
% 6.06/1.17 ( ! [X1 : $o] : (($true = X1) | ($true = $false)) ) | ~spl1_15),
% 6.06/1.17 inference(beta-eta_normalization,[],[f4566])).
% 6.06/1.17 thf(f4570,plain,(
% 6.06/1.17 ( ! [X1 : $o] : (($true = X1)) ) | ~spl1_15),
% 6.06/1.17 inference(trivial_inequality_removal,[],[f4569])).
% 6.06/1.17 thf(f4623,plain,(
% 6.06/1.17 spl1_4 | ~spl1_15),
% 6.06/1.17 inference(avatar_split_clause,[],[f4570,f4462,f85])).
% 6.06/1.17 thf(f4839,plain,(
% 6.06/1.17 ( ! [X2 : $o,X0 : ($o > $o),X1 : $o] : ((((X0 @ X2)) = (((^[Y0 : $o]: (Y0)) @ X2))) | ($true = ((X0 @ X1))) | ((^[Y0 : $o]: ($false)) = X0)) ) | ~spl1_17),
% 6.06/1.17 inference(argument_congruence,[],[f4470])).
% 6.06/1.17 thf(f5046,plain,(
% 6.06/1.17 ( ! [X2 : $o,X0 : ($o > $o),X1 : $o] : (($false = ((X0 @ X2))) | ($true = ((X0 @ X1))) | ((^[Y0 : $o]: ($false)) = X0) | ($true = (((^[Y0 : $o]: (Y0)) @ X2)))) ) | ~spl1_17),
% 6.06/1.17 inference(iff_proxy_clausification,[],[f4839])).
% 6.06/1.17 thf(f5047,plain,(
% 6.06/1.17 ( ! [X2 : $o,X0 : ($o > $o),X1 : $o] : (($true = ((X0 @ X1))) | ($false = ((X0 @ X2))) | ((^[Y0 : $o]: ($false)) = X0) | ($true = X2)) ) | ~spl1_17),
% 6.06/1.17 inference(beta-eta_normalization,[],[f5046])).
% 6.06/1.17 thf(f5792,plain,(
% 6.06/1.17 ( ! [X0 : $o,X1 : $o] : ((X0 = X1) | ((^[Y0 : $o]: ($false)) = ((= @ X1))) | ($true = X1)) ) | ~spl1_17),
% 6.06/1.17 inference(leibniz_equality_elimination,[],[f5047])).
% 6.06/1.17 thf(f6214,plain,(
% 6.06/1.17 ( ! [X0 : $o,X1 : $o] : (($false = X0) | ((^[Y0 : $o]: ($false)) = ((= @ X1))) | ($true = X1) | ($true = X1)) ) | ~spl1_17),
% 6.06/1.17 inference(iff_proxy_clausification,[],[f5792])).
% 6.06/1.17 thf(f6215,plain,(
% 6.06/1.17 ( ! [X0 : $o,X1 : $o] : (($false = X0) | ((^[Y0 : $o]: ($false)) = ((= @ X1))) | ($true = X1)) ) | ~spl1_17),
% 6.06/1.17 inference(duplicate_literal_removal,[],[f6214])).
% 6.06/1.17 thf(f6234,definition,(
% 6.06/1.17 spl1_21 <=> ! [X1 : $o] : (((^[Y0 : $o]: ($false)) = ((= @ X1))) | ($true = X1))),
% 6.06/1.17 introduced(definition,[new_symbols(definition,[spl1_21])],[avatar_definition])).
% 6.06/1.17 thf(f6235,plain,(
% 6.06/1.17 ( ! [X1 : $o] : (((^[Y0 : $o]: ($false)) = ((= @ X1))) | ($true = X1)) ) | ~spl1_21),
% 6.06/1.17 inference(avatar_component_clause,[],[f6234])).
% 6.06/1.17 thf(f6236,plain,(
% 6.06/1.17 spl1_21 | spl1_5 | ~spl1_17),
% 6.06/1.17 inference(avatar_split_clause,[],[f6215,f4469,f88,f6234])).
% 6.06/1.17 thf(f6352,plain,(
% 6.06/1.17 ( ! [X2 : $o,X1 : $o] : (((((^[Y0 : $o]: ($false)) @ X2)) = ((X1 = X2))) | ($true = X1)) ) | ~spl1_21),
% 6.06/1.17 inference(argument_congruence,[],[f6235])).
% 6.06/1.17 thf(f6400,plain,(
% 6.06/1.17 ( ! [X2 : $o,X1 : $o] : (($true = (((^[Y0 : $o]: ($false)) @ X2))) | ($true = X1) | ($false = ((X1 = X2)))) ) | ~spl1_21),
% 6.06/1.17 inference(iff_proxy_clausification,[],[f6352])).
% 6.06/1.17 thf(f6408,plain,(
% 6.06/1.17 ( ! [X2 : $o,X1 : $o] : (($true = (((^[Y0 : $o]: ($false)) @ X2))) | ($true = X1) | (X1 != X2)) ) | ~spl1_21),
% 6.06/1.17 inference(equality_proxy_clausification,[],[f6400])).
% 6.06/1.17 thf(f6409,plain,(
% 6.06/1.17 ( ! [X2 : $o,X1 : $o] : (($true = (((^[Y0 : $o]: ($false)) @ X2))) | ($true = X1) | ($true = X1) | ($true = X2)) ) | ~spl1_21),
% 6.06/1.17 inference(xor_proxy_clausification,[],[f6408])).
% 6.06/1.17 thf(f6413,plain,(
% 6.06/1.17 ( ! [X2 : $o,X1 : $o] : (($true = (((^[Y0 : $o]: ($false)) @ X2))) | ($true = X1) | ($true = X2)) ) | ~spl1_21),
% 6.06/1.17 inference(duplicate_literal_removal,[],[f6409])).
% 6.06/1.17 thf(f6414,plain,(
% 6.06/1.17 ( ! [X2 : $o,X1 : $o] : (($true = $false) | ($true = X1) | ($true = X2)) ) | ~spl1_21),
% 6.06/1.17 inference(beta-eta_normalization,[],[f6413])).
% 6.06/1.17 thf(f6415,plain,(
% 6.06/1.17 ( ! [X2 : $o,X1 : $o] : (($true = X1) | ($true = X2)) ) | ~spl1_21),
% 6.06/1.17 inference(trivial_inequality_removal,[],[f6414])).
% 6.06/1.17 thf(f6416,plain,(
% 6.06/1.17 spl1_4 | spl1_4 | ~spl1_21),
% 6.06/1.17 inference(avatar_split_clause,[],[f6415,f6234,f85,f85])).
% 6.06/1.17 cnf(s48, plain, ~spl1_4, inference(sat_conversion,[],[f185])).
% 6.06/1.17 cnf(s111, plain, ~spl1_5, inference(sat_conversion,[],[f425])).
% 6.06/1.17 cnf(s854, plain, spl1_15 | spl1_17, inference(sat_conversion,[],[f4471])).
% 6.06/1.17 cnf(s866, plain, spl1_4 | ~spl1_15, inference(sat_conversion,[],[f4623])).
% 6.06/1.17 cnf(s1171, plain, spl1_5 | ~spl1_17 | spl1_21, inference(sat_conversion,[],[f6236])).
% 6.06/1.17 cnf(s1210, plain, spl1_4 | spl1_4 | ~spl1_21, inference(sat_conversion,[],[f6416])).
% 6.06/1.17 cnf(s1211, plain, spl1_4 | ~spl1_21, inference(rat,[],[s1210])).
% 6.06/1.17 cnf(s1217, plain, ~spl1_21, inference(rat,[],[s1211,s48])).
% 6.06/1.17 cnf(s1218, plain, ~spl1_15, inference(rat,[],[s866,s48])).
% 6.06/1.17 cnf(s1219, plain, ~spl1_17, inference(rat,[],[s1171,s111,s1217])).
% 6.06/1.17 cnf(s1220, plain, $false, inference(rat,[],[s854,s1219,s1218])).
% 6.06/1.17 thf(f6417,plain,(
% 6.06/1.17 $false),
% 6.06/1.17 inference(avatar_sat_refutation,[],[s1220])).
% 6.06/1.17 % SZS output end Proof for theBenchmark
% 6.06/1.17 % (3764300)------------------------------
% 6.06/1.17 % (3764300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.06/1.17 % (3764300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.06/1.17 % (3764300)CaDiCaL version: 2.1.3
% 6.06/1.17 % (3764300)Termination reason: Refutation
% 6.06/1.17 % (3764300)Time elapsed: 0.830 s
% 6.06/1.17 % (3764300)Peak memory usage: 14 MB
% 6.06/1.17 % (3764300)Instructions burned: 1188 (million)
% 6.06/1.17 % (3764292)Success in time 0.869 s
% 6.06/1.17 % Vampire exiting
%------------------------------------------------------------------------------