%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PHI002^2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:20:19 AM UTC 2026
% Result : Theorem 6.49s 1.14s
% Output : Refutation 6.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI002^2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n018.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:19:12 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 4.12/0.95 % (49916)Will run a generic schedule for satisfiability detection.
% 4.12/0.95 % (49921)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3060110805_2999 on theBenchmark for (2999ds/0Mi)
% 4.12/0.95 % (49924)dis+10_1_sil=32000:sp=arity:random_seed=1010285296:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.12/0.95 % (49923)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2005173902:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.12/0.95 % (49925)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2799887190:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.12/0.95 % (49926)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=109348127:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.12/0.95 % (49927)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2572345902:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.12/0.95 % (49925)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.12/0.95 % Exception at run slice level
% 4.12/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.12/0.95 % (49922)% WARNING: option uhcvi not known.
% 4.12/0.95 % (49922)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1754256229:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.12/0.95 % (49922)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.12/0.95 % (49922)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.12/0.95 % (49934)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3270717356:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.12/0.95 % Exception at run slice level
% 4.12/0.95 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.12/0.95 % (49937)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1070240256:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.12/0.95 % (49924)Instruction limit reached!
% 4.12/0.95 % (49924)------------------------------
% 4.12/0.95 % (49924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.95 % (49924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.95 % (49924)CaDiCaL version: 2.1.3
% 4.12/0.95 % (49924)Termination reason: Instruction limit
% 4.12/0.95 % (49924)Termination phase: Saturation
% 4.12/0.95 % (49924)Time elapsed: 0.051 s
% 4.12/0.95 % (49924)Peak memory usage: 12 MB
% 4.12/0.95 % (49924)Instructions burned: 103 (million)
% 4.12/0.95 % (49925)Instruction limit reached!
% 4.12/0.95 % (49925)------------------------------
% 4.12/0.95 % (49925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.95 % (49925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.95 % (49925)CaDiCaL version: 2.1.3
% 4.12/0.95 % (49925)Termination reason: Instruction limit
% 4.12/0.95 % (49925)Termination phase: Saturation
% 4.12/0.95 % (49925)Time elapsed: 0.060 s
% 4.12/0.95 % (49925)Peak memory usage: 13 MB
% 4.12/0.95 % (49925)Instructions burned: 117 (million)
% 4.12/0.95 % (49926)Instruction limit reached!
% 4.12/0.95 % (49926)------------------------------
% 4.12/0.95 % (49926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.95 % (49926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/0.95 % (49926)CaDiCaL version: 2.1.3
% 4.12/0.95 % (49926)Termination reason: Instruction limit
% 4.12/0.95 % (49926)Termination phase: Saturation
% 4.12/0.95 % (49926)Time elapsed: 0.064 s
% 4.12/0.95 % (49926)Peak memory usage: 13 MB
% 4.12/0.95 % (49926)Instructions burned: 131 (million)
% 4.12/0.95 % (49939)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=547260751:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.12/0.95 % (49939)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.12/0.95 % (49939)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.12/0.95 % (49927)Instruction limit reached!
% 4.12/0.95 % (49927)------------------------------
% 4.12/0.95 % (49927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.12/0.95 % (49927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.14 % (49927)CaDiCaL version: 2.1.3
% 6.49/1.14 % (49927)Termination reason: Instruction limit
% 6.49/1.14 % (49927)Termination phase: Saturation
% 6.49/1.14 % (49927)Time elapsed: 0.078 s
% 6.49/1.14 % (49927)Peak memory usage: 13 MB
% 6.49/1.14 % (49927)Instructions burned: 159 (million)
% 6.49/1.14 % (49940)ott-21_1_sil=16000:fs=off:random_seed=3084772181:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 6.49/1.14 % (49941)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1954704660:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 6.49/1.14 % (49944)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2962211906:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.49/1.14 % Exception at run slice level
% 6.49/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.49/1.14 % (49937)Instruction limit reached!
% 6.49/1.14 % (49937)------------------------------
% 6.49/1.14 % (49937)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.14 % (49937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.14 % (49937)CaDiCaL version: 2.1.3
% 6.49/1.14 % (49937)Termination reason: Instruction limit
% 6.49/1.14 % (49937)Termination phase: Saturation
% 6.49/1.14 % (49937)Time elapsed: 0.066 s
% 6.49/1.14 % (49937)Peak memory usage: 13 MB
% 6.49/1.14 % (49937)Instructions burned: 132 (million)
% 6.49/1.14 % (49947)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1468955089:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.49/1.14 % (49948)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3656718333:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.49/1.14 % Exception at run slice level
% 6.49/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.49/1.14 % (49951)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=47285105: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)
% 6.49/1.14 % (49951)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.49/1.14 % (49940)Instruction limit reached!
% 6.49/1.14 % (49940)------------------------------
% 6.49/1.14 % (49940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.14 % (49940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.14 % (49940)CaDiCaL version: 2.1.3
% 6.49/1.14 % (49940)Termination reason: Instruction limit
% 6.49/1.14 % (49940)Termination phase: Saturation
% 6.49/1.14 % (49940)Time elapsed: 0.085 s
% 6.49/1.14 % (49940)Peak memory usage: 12 MB
% 6.49/1.14 % (49940)Instructions burned: 181 (million)
% 6.49/1.14 % (49953)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1663740398:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 6.49/1.14 % (49953)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.49/1.14 % (49941)Instruction limit reached!
% 6.49/1.14 % (49941)------------------------------
% 6.49/1.14 % (49941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.14 % (49941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.14 % (49941)CaDiCaL version: 2.1.3
% 6.49/1.14 % (49941)Termination reason: Instruction limit
% 6.49/1.14 % (49941)Termination phase: Saturation
% 6.49/1.14 % (49941)Time elapsed: 0.228 s
% 6.49/1.14 % (49941)Peak memory usage: 14 MB
% 6.49/1.14 % (49941)Instructions burned: 477 (million)
% 6.49/1.14 % (49955)fmb+10_1_sil=64000:random_seed=1630530901:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 6.49/1.14 % (49955)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.49/1.14 % Exception at run slice level
% 6.49/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.49/1.14 % (49957)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1202167186:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 6.49/1.14 % Exception at run slice level
% 6.49/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.49/1.14 % (49959)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=229493767:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 6.49/1.14 % Exception at run slice level
% 6.49/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.49/1.14 % (49939)Instruction limit reached!
% 6.49/1.14 % (49939)------------------------------
% 6.49/1.14 % (49939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.14 % (49939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.14 % (49939)CaDiCaL version: 2.1.3
% 6.49/1.14 % (49939)Termination reason: Instruction limit
% 6.49/1.14 % (49939)Termination phase: Saturation
% 6.49/1.14 % (49939)Time elapsed: 0.308 s
% 6.49/1.14 % (49939)Peak memory usage: 15 MB
% 6.49/1.14 % (49939)Instructions burned: 686 (million)
% 6.49/1.14 % (49961)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4031889306:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 6.49/1.14 % (49961)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.49/1.14 % (49962)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3446087796:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 6.49/1.14 % (49962)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.49/1.14 % (49962)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.49/1.14 % (49951)Instruction limit reached!
% 6.49/1.14 % (49951)------------------------------
% 6.49/1.14 % (49951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.14 % (49951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.14 % (49951)CaDiCaL version: 2.1.3
% 6.49/1.14 % (49951)Termination reason: Instruction limit
% 6.49/1.14 % (49951)Termination phase: Saturation
% 6.49/1.14 % (49951)Time elapsed: 0.322 s
% 6.49/1.14 % (49951)Peak memory usage: 19 MB
% 6.49/1.14 % (49951)Instructions burned: 694 (million)
% 6.49/1.14 % (49965)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3825082446:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 6.49/1.14 % Exception at run slice level
% 6.49/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.49/1.14 % (49967)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1386396066:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 6.49/1.14 % Exception at run slice level
% 6.49/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.49/1.14 % (49969)ott-2_1_sil=16000:newcnf=on:random_seed=3638314538:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 6.49/1.14 % (49969)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.49/1.14 % (49953)Instruction limit reached!
% 6.49/1.14 % (49953)------------------------------
% 6.49/1.14 % (49953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.14 % (49953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.14 % (49953)CaDiCaL version: 2.1.3
% 6.49/1.14 % (49953)Termination reason: Instruction limit
% 6.49/1.14 % (49953)Termination phase: Saturation
% 6.49/1.14 % (49953)Time elapsed: 0.409 s
% 6.49/1.14 % (49953)Peak memory usage: 15 MB
% 6.49/1.14 % (49953)Instructions burned: 880 (million)
% 6.49/1.14 % (49971)ott+10_1_sil=32000:tgt=ground:random_seed=1520521887:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 6.49/1.14 % (49947)Instruction limit reached!
% 6.49/1.14 % (49947)------------------------------
% 6.49/1.14 % (49947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.14 % (49947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.14 % (49947)CaDiCaL version: 2.1.3
% 6.49/1.14 % (49947)Termination reason: Instruction limit
% 6.49/1.14 % (49947)Termination phase: Saturation
% 6.49/1.14 % (49947)Time elapsed: 0.533 s
% 6.49/1.14 % (49947)Peak memory usage: 17 MB
% 6.49/1.14 % (49947)Instructions burned: 1180 (million)
% 6.49/1.14 % (49973)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1244901865:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 6.49/1.14 % Exception at run slice level
% 6.49/1.14 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.49/1.14 % (49975)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1711883125:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 6.49/1.14 % (49975)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.49/1.14 % (49961) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-49916-49961"...
% 6.49/1.14 % (49961)...printing done.
% 6.49/1.14 % (49961)Refutation found. Thanks to Tanya!
% 6.49/1.14 % SZS status Theorem for theBenchmark
% 6.49/1.14 % SZS output start Proof for theBenchmark
% 6.49/1.14 thf(type_def_5, type, mu: $tType).
% 6.49/1.14 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 6.49/1.14 thf(func_def_0, type, meq_ind: (mu > mu > $i > $o)).
% 6.49/1.14 thf(func_def_1, type, mtrue: ($i > $o)).
% 6.49/1.14 thf(func_def_2, type, mfalse: ($i > $o)).
% 6.49/1.14 thf(func_def_3, type, mnot: (($i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_5, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_6, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_7, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_8, type, mimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_9, type, mequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_10, type, mxor: (($i > $o) > ($i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_11, type, mforall_ind: ((mu > $i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_12, type, mforall_indset: (((mu > $i > $o) > $i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_13, type, mforall_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_14, type, mexists_ind: ((mu > $i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_15, type, mexists_indset: (((mu > $i > $o) > $i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_16, type, mexists_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_17, type, mbox_generic: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_18, type, mdia_generic: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_19, type, rel: ($i > $i > $o)).
% 6.49/1.14 thf(func_def_20, type, mbox: (($i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_21, type, mdia: (($i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_22, type, mvalid: (($i > $o) > $o)).
% 6.49/1.14 thf(func_def_23, type, minvalid: (($i > $o) > $o)).
% 6.49/1.14 thf(func_def_24, type, positive: ((mu > $i > $o) > $i > $o)).
% 6.49/1.14 thf(func_def_25, type, db2: !>[X0: $tType]:(X0)).
% 6.49/1.14 thf(func_def_26, type, db1: !>[X0: $tType]:(X0)).
% 6.49/1.14 thf(func_def_27, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.49/1.14 thf(func_def_28, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.49/1.14 thf(func_def_31, type, vNOT: ($o > $o)).
% 6.49/1.14 thf(func_def_32, type, db0: !>[X0: $tType]:(X0)).
% 6.49/1.14 thf(func_def_33, type, vOR: ($o > $o > $o)).
% 6.49/1.14 thf(func_def_34, type, vAND: ($o > $o > $o)).
% 6.49/1.14 thf(func_def_35, type, vIMP: ($o > $o > $o)).
% 6.49/1.14 thf(func_def_36, type, vIFF: ($o > $o > $o)).
% 6.49/1.14 thf(func_def_37, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.49/1.14 thf(func_def_38, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.49/1.14 thf(func_def_39, type, db3: !>[X0: $tType]:(X0)).
% 6.49/1.14 thf(func_def_40, type, db4: !>[X0: $tType]:(X0)).
% 6.49/1.14 thf(func_def_42, type, sK1: (mu > $i > $o)).
% 6.49/1.14 thf(func_def_43, type, db5: !>[X0: $tType]:(X0)).
% 6.49/1.14 thf(func_def_44, type, sK2: ((mu > $i > $o) > $i > (mu > $i > $o) > $i)).
% 6.49/1.14 thf(func_def_45, type, sK3: ((mu > $i > $o) > $i > (mu > $i > $o) > mu)).
% 6.49/1.14 thf(func_def_46, type, sK4: ((mu > $i > $o) > mu)).
% 6.49/1.14 thf(func_def_47, type, sK5: ((mu > $i > $o) > $i)).
% 6.49/1.14 thf(func_def_48, type, sK6: ($i > (mu > $i > mu > $i > $o) > (mu > $i > $o) > mu)).
% 6.49/1.14 thf(func_def_50, type, sK8: ((mu > $i > $o) > (mu > $i > $o) > mu)).
% 6.49/1.14 thf(func_def_51, type, sK9: ((mu > $i > $o) > (mu > $i > $o) > mu)).
% 6.49/1.14 thf(func_def_52, type, sK10: ((mu > $i > $o) > mu)).
% 6.49/1.14 thf(func_def_53, type, sK11: ((mu > $i > $o) > mu)).
% 6.49/1.14 thf(func_def_54, type, sK12: ((mu > $i > $o) > mu)).
% 6.49/1.14 thf(func_def_55, type, sK13: ((mu > $i > $i) > (mu > $i > $o) > mu)).
% 6.49/1.14 thf(func_def_56, type, sK14: ((mu > $i > $o) > $i)).
% 6.49/1.14 thf(func_def_57, type, sK15: ((mu > $i > $o) > $i)).
% 6.49/1.14 thf(func_def_58, type, db6: !>[X0: $tType]:(X0)).
% 6.49/1.14 thf(func_def_59, type, sK16: ((mu > $i > $o) > $i)).
% 6.49/1.14 thf(func_def_60, type, sK17: ((mu > $i > $o) > (mu > $i > mu > $i > $o) > $i > mu)).
% 6.49/1.14 thf(func_def_61, type, sK18: ($i > (mu > $i > mu > $i > $o) > (mu > $i > $o) > $i)).
% 6.49/1.14 thf(func_def_62, type, sK19: ($i > (mu > $i > $o) > (mu > $i > mu > $i > mu) > mu)).
% 6.49/1.14 thf(f4,axiom,(
% 6.49/1.14 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mnot)).
% 6.49/1.14 thf(f6,axiom,(
% 6.49/1.14 (mand = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) & (X0 @ X2))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mand)).
% 6.49/1.14 thf(f7,axiom,(
% 6.49/1.14 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) => (X1 @ X2))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mimplies)).
% 6.49/1.14 thf(f9,axiom,(
% 6.49/1.14 (mequiv = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) <=> (X1 @ X2))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mequiv)).
% 6.49/1.14 thf(f11,axiom,(
% 6.49/1.14 (mforall_ind = (^[X0 : (mu > $i > $o), X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mforall_ind)).
% 6.49/1.14 thf(f12,axiom,(
% 6.49/1.14 (mforall_indset = (^[X0 : ((mu > $i > $o) > $i > $o), X1 : $i] : (! [X2 : (mu > $i > $o)] : (X0 @ X2 @ X1))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mforall_indset)).
% 6.49/1.14 thf(f14,axiom,(
% 6.49/1.14 (mexists_ind = (^[X0 : (mu > $i > $o), X1 : $i] : (? [X2 : mu] : (X0 @ X2 @ X1))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mexists_ind)).
% 6.49/1.14 thf(f17,axiom,(
% 6.49/1.14 (mbox_generic = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mbox_generic)).
% 6.49/1.14 thf(f18,axiom,(
% 6.49/1.14 (mdia_generic = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (? [X3 : $i] : ((X1 @ X3) & (X0 @ X2 @ X3)))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mdia_generic)).
% 6.49/1.14 thf(f19,axiom,(
% 6.49/1.14 (mbox = ((mbox_generic @ rel)))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mbox)).
% 6.49/1.14 thf(f20,axiom,(
% 6.49/1.14 (mdia = ((mdia_generic @ rel)))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mdia)).
% 6.49/1.14 thf(f21,axiom,(
% 6.49/1.14 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/Axioms/LCL016^0.ax',mvalid)).
% 6.49/1.14 thf(f23,axiom,(
% 6.49/1.14 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mequiv @ (positive @ (^[X1 : mu] : ((mnot @ (X0 @ X1))))) @ (mnot @ (positive @ X0)))))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA1)).
% 6.49/1.14 thf(f24,axiom,(
% 6.49/1.14 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mforall_indset @ (^[X1 : (mu > $i > $o)] : ((mimplies @ (mand @ (positive @ X0) @ (mbox @ (mforall_ind @ (^[X2 : mu] : ((mimplies @ (X0 @ X2) @ (X1 @ X2))))))) @ (positive @ X1)))))))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA2)).
% 6.49/1.14 thf(f25,conjecture,(
% 6.49/1.14 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mimplies @ (positive @ X0) @ (mdia @ (mexists_ind @ (^[X1 : mu] : ((X0 @ X1))))))))))),
% 6.49/1.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thmT1)).
% 6.49/1.14 thf(f26,negated_conjecture,(
% 6.49/1.14 ~(mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mimplies @ (positive @ X0) @ (mdia @ (mexists_ind @ (^[X1 : mu] : ((X0 @ X1))))))))))),
% 6.49/1.14 inference(negated_conjecture,[status(cth)],[f25])).
% 6.49/1.14 thf(f30,plain,(
% 6.49/1.14 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 6.49/1.14 inference(rectify,[],[f4])).
% 6.49/1.14 thf(f31,plain,(
% 6.49/1.14 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 6.49/1.14 inference(fool_elimination,[],[f30])).
% 6.49/1.14 thf(f34,plain,(
% 6.49/1.14 (mand = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) & (X0 @ X2))))),
% 6.49/1.14 inference(rectify,[],[f6])).
% 6.49/1.14 thf(f35,plain,(
% 6.49/1.14 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 6.49/1.14 inference(fool_elimination,[],[f34])).
% 6.49/1.14 thf(f36,plain,(
% 6.49/1.14 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) => (X1 @ X2))))),
% 6.49/1.14 inference(rectify,[],[f7])).
% 6.49/1.14 thf(f37,plain,(
% 6.49/1.14 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 6.49/1.14 inference(fool_elimination,[],[f36])).
% 6.49/1.14 thf(f40,plain,(
% 6.49/1.14 (mequiv = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) <=> (X1 @ X2))))),
% 6.49/1.14 inference(rectify,[],[f9])).
% 6.49/1.14 thf(f41,plain,(
% 6.49/1.14 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 6.49/1.14 inference(fool_elimination,[],[f40])).
% 6.49/1.14 thf(f44,plain,(
% 6.49/1.14 (mforall_ind = (^[X0 : (mu > $i > $o), X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))))),
% 6.49/1.14 inference(rectify,[],[f11])).
% 6.49/1.14 thf(f45,plain,(
% 6.49/1.14 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 6.49/1.14 inference(fool_elimination,[],[f44])).
% 6.49/1.14 thf(f46,plain,(
% 6.49/1.14 (mforall_indset = (^[X0 : ((mu > $i > $o) > $i > $o), X1 : $i] : (! [X2 : (mu > $i > $o)] : (X0 @ X2 @ X1))))),
% 6.49/1.14 inference(rectify,[],[f12])).
% 6.49/1.14 thf(f47,plain,(
% 6.49/1.14 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 6.49/1.14 inference(fool_elimination,[],[f46])).
% 6.49/1.14 thf(f50,plain,(
% 6.49/1.14 (mexists_ind = (^[X0 : (mu > $i > $o), X1 : $i] : (? [X2 : mu] : (X0 @ X2 @ X1))))),
% 6.49/1.14 inference(rectify,[],[f14])).
% 6.49/1.14 thf(f51,plain,(
% 6.49/1.14 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 6.49/1.14 inference(fool_elimination,[],[f50])).
% 6.49/1.14 thf(f56,plain,(
% 6.49/1.14 (mbox_generic = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 6.49/1.14 inference(rectify,[],[f17])).
% 6.49/1.14 thf(f57,plain,(
% 6.49/1.14 (mbox_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 6.49/1.14 inference(fool_elimination,[],[f56])).
% 6.49/1.14 thf(f58,plain,(
% 6.49/1.14 (mdia_generic = (^[X0 : ($i > $i > $o), X1 : ($i > $o), X2 : $i] : (? [X3 : $i] : ((X1 @ X3) & (X0 @ X2 @ X3)))))),
% 6.49/1.14 inference(rectify,[],[f18])).
% 6.49/1.14 thf(f59,plain,(
% 6.49/1.14 (mdia_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 6.49/1.14 inference(fool_elimination,[],[f58])).
% 6.49/1.14 thf(f60,plain,(
% 6.49/1.14 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 6.49/1.14 inference(rectify,[],[f21])).
% 6.49/1.14 thf(f61,plain,(
% 6.49/1.14 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 6.49/1.14 inference(fool_elimination,[],[f60])).
% 6.49/1.14 thf(f64,plain,(
% 6.49/1.14 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mequiv @ (positive @ (^[X1 : mu] : ((mnot @ (X0 @ X1))))) @ (mnot @ (positive @ X0)))))))),
% 6.49/1.14 inference(rectify,[],[f23])).
% 6.49/1.14 thf(f65,plain,(
% 6.49/1.14 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mequiv @ (positive @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))) @ (mnot @ (positive @ Y0))))))))),
% 6.49/1.14 inference(fool_elimination,[],[f64])).
% 6.49/1.14 thf(f66,plain,(
% 6.49/1.14 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mforall_indset @ (^[X1 : (mu > $i > $o)] : ((mimplies @ (mand @ (positive @ X0) @ (mbox @ (mforall_ind @ (^[X2 : mu] : ((mimplies @ (X0 @ X2) @ (X1 @ X2))))))) @ (positive @ X1)))))))))),
% 6.49/1.14 inference(rectify,[],[f24])).
% 6.49/1.14 thf(f67,plain,(
% 6.49/1.14 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (mand @ (positive @ Y0) @ (mbox @ (mforall_ind @ (^[Y2 : mu]: (mimplies @ (Y0 @ Y2) @ (Y1 @ Y2)))))) @ (positive @ Y1)))))))))),
% 6.49/1.14 inference(fool_elimination,[],[f66])).
% 6.49/1.14 thf(f68,plain,(
% 6.49/1.14 ~(mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mimplies @ (positive @ X0) @ (mdia @ (mexists_ind @ (^[X1 : mu] : ((X0 @ X1))))))))))),
% 6.49/1.14 inference(rectify,[],[f26])).
% 6.49/1.14 thf(f69,plain,(
% 6.49/1.14 ~ ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ Y0) @ (mdia @ (mexists_ind @ (^[Y1 : mu]: (Y0 @ Y1))))))))))),
% 6.49/1.14 inference(fool_elimination,[],[f68])).
% 6.49/1.14 thf(f70,plain,(
% 6.49/1.14 ($true != ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ Y0) @ (mdia @ (mexists_ind @ (^[Y1 : mu]: (Y0 @ Y1))))))))))),
% 6.49/1.14 inference(flattening,[],[f69])).
% 6.49/1.14 thf(f74,plain,(
% 6.49/1.14 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f31])).
% 6.49/1.14 thf(f76,plain,(
% 6.49/1.14 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f35])).
% 6.49/1.14 thf(f77,plain,(
% 6.49/1.14 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f37])).
% 6.49/1.14 thf(f79,plain,(
% 6.49/1.14 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f41])).
% 6.49/1.14 thf(f81,plain,(
% 6.49/1.14 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f45])).
% 6.49/1.14 thf(f82,plain,(
% 6.49/1.14 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f47])).
% 6.49/1.14 thf(f84,plain,(
% 6.49/1.14 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f51])).
% 6.49/1.14 thf(f87,plain,(
% 6.49/1.14 (mbox_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f57])).
% 6.49/1.14 thf(f88,plain,(
% 6.49/1.14 (mdia_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f59])).
% 6.49/1.14 thf(f89,plain,(
% 6.49/1.14 (mbox = ((mbox_generic @ rel)))),
% 6.49/1.14 inference(cnf_transformation,[],[f19])).
% 6.49/1.14 thf(f90,plain,(
% 6.49/1.14 (mdia = ((mdia_generic @ rel)))),
% 6.49/1.14 inference(cnf_transformation,[],[f20])).
% 6.49/1.14 thf(f91,plain,(
% 6.49/1.14 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 6.49/1.14 inference(cnf_transformation,[],[f61])).
% 6.49/1.14 thf(f93,plain,(
% 6.49/1.14 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mequiv @ (positive @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))) @ (mnot @ (positive @ Y0))))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f65])).
% 6.49/1.14 thf(f94,plain,(
% 6.49/1.14 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (mand @ (positive @ Y0) @ (mbox @ (mforall_ind @ (^[Y2 : mu]: (mimplies @ (Y0 @ Y2) @ (Y1 @ Y2)))))) @ (positive @ Y1)))))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f67])).
% 6.49/1.14 thf(f95,plain,(
% 6.49/1.14 ($true != ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ Y0) @ (mdia @ (mexists_ind @ (^[Y1 : mu]: (Y0 @ Y1))))))))))),
% 6.49/1.14 inference(cnf_transformation,[],[f70])).
% 6.49/1.14 thf(f97,definition,(
% 6.49/1.14 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 6.49/1.14 introduced(theory,[fool_exhaustiveness_axiom])).
% 6.49/1.14 thf(f98,plain,(
% 6.49/1.14 (mbox = (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ rel)))),
% 6.49/1.14 inference(definition_unfolding,[],[f89,f87])).
% 6.49/1.14 thf(f99,plain,(
% 6.49/1.14 (mdia = (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ rel)))),
% 6.49/1.14 inference(definition_unfolding,[],[f90,f88])).
% 6.49/1.14 thf(f100,plain,(
% 6.49/1.14 ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y1 @ Y3) = (Y2 @ Y3))))))) @ (positive @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ (positive @ Y0))))))))),
% 6.49/1.14 inference(definition_unfolding,[],[f93,f91,f82,f79,f74,f74])).
% 6.49/1.14 thf(f101,plain,(
% 6.49/1.14 ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu > $i > $o]: ((^[Y1 : (mu > $i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (positive @ Y0) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ rel @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (Y0 @ Y2) @ (Y1 @ Y2)))))) @ (positive @ Y1)))))))))),
% 6.49/1.14 inference(definition_unfolding,[],[f94,f91,f82,f82,f77,f76,f98,f81,f77])).
% 6.49/1.14 thf(f102,plain,(
% 6.49/1.14 ($true != (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y1 @ Y3) => (Y2 @ Y3))))))) @ (positive @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((Y1 @ Y3 @ Y4) & (Y2 @ Y4))))))))) @ rel @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: (Y0 @ Y1))))))))))),
% 6.49/1.14 inference(definition_unfolding,[],[f95,f91,f82,f77,f99,f84])).
% 6.49/1.14 thf(f103,plain,(
% 6.49/1.14 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((rel @ Y0 @ Y2) & (?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))))))))))),
% 6.49/1.14 inference(beta-eta_normalization,[],[f102])).
% 6.49/1.14 thf(f104,plain,(
% 6.49/1.14 ($false = (((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((rel @ Y0 @ Y2) & (?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))))))) @ sK0)))),
% 6.49/1.14 inference(sigma_proxy_clausification,[],[f103])).
% 6.49/1.14 thf(f105,plain,(
% 6.49/1.14 ($false = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ sK0) => (?? @ $i @ (^[Y1 : $i]: ((rel @ sK0 @ Y1) & (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))))))),
% 6.49/1.14 inference(beta-eta_normalization,[],[f104])).
% 6.49/1.14 thf(f106,plain,(
% 6.49/1.14 ($false = (((^[Y0 : mu > $i > $o]: ((positive @ Y0 @ sK0) => (?? @ $i @ (^[Y1 : $i]: ((rel @ sK0 @ Y1) & (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))) @ sK1)))),
% 6.49/1.14 inference(sigma_proxy_clausification,[],[f105])).
% 6.49/1.14 thf(f107,plain,(
% 6.49/1.14 ($false = (((positive @ sK1 @ sK0) => (?? @ $i @ (^[Y0 : $i]: ((rel @ sK0 @ Y0) & (?? @ mu @ (^[Y1 : mu]: (sK1 @ Y1 @ Y0)))))))))),
% 6.49/1.14 inference(beta-eta_normalization,[],[f106])).
% 6.49/1.14 thf(f108,plain,(
% 6.49/1.14 ($false = ((?? @ $i @ (^[Y0 : $i]: ((rel @ sK0 @ Y0) & (?? @ mu @ (^[Y1 : mu]: (sK1 @ Y1 @ Y0))))))))),
% 6.49/1.14 inference(imp_proxy_clausification,[],[f107])).
% 6.49/1.14 thf(f109,plain,(
% 6.49/1.14 ($true = ((positive @ sK1 @ sK0)))),
% 6.49/1.14 inference(imp_proxy_clausification,[],[f107])).
% 6.49/1.14 thf(f110,plain,(
% 6.49/1.14 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((rel @ sK0 @ Y0) & (?? @ mu @ (^[Y1 : mu]: (sK1 @ Y1 @ Y0))))) @ X1)))) )),
% 6.49/1.14 inference(pi_proxy_clausification,[],[f108])).
% 6.49/1.14 thf(f111,plain,(
% 6.49/1.14 ( ! [X1 : $i] : (($false = (((rel @ sK0 @ X1) & (?? @ mu @ (^[Y0 : mu]: (sK1 @ Y0 @ X1))))))) )),
% 6.49/1.14 inference(beta-eta_normalization,[],[f110])).
% 6.49/1.14 thf(f112,plain,(
% 6.49/1.14 ( ! [X1 : $i] : (($false = ((?? @ mu @ (^[Y0 : mu]: (sK1 @ Y0 @ X1))))) | ($false = ((rel @ sK0 @ X1)))) )),
% 6.49/1.14 inference(and_proxy_clausification,[],[f111])).
% 6.49/1.14 thf(f113,plain,(
% 6.49/1.14 ( ! [X2 : mu,X1 : $i] : (($false = (((^[Y0 : mu]: (sK1 @ Y0 @ X1)) @ X2))) | ($false = ((rel @ sK0 @ X1)))) )),
% 6.49/1.14 inference(pi_proxy_clausification,[],[f112])).
% 6.49/1.14 thf(f114,plain,(
% 6.49/1.14 ( ! [X2 : mu,X1 : $i] : (($false = ((sK1 @ X2 @ X1))) | ($false = ((rel @ sK0 @ X1)))) )),
% 6.49/1.14 inference(beta-eta_normalization,[],[f113])).
% 6.49/1.14 thf(f115,plain,(
% 6.49/1.14 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (((positive @ Y1 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((~ (rel @ Y0 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((Y1 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))))) => (positive @ Y2 @ Y0))))))))))),
% 6.49/1.14 inference(beta-eta_normalization,[],[f101])).
% 6.49/1.14 thf(f116,plain,(
% 6.49/1.14 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (((positive @ Y1 @ Y0) & (!! @ $i @ (^[Y3 : $i]: ((~ (rel @ Y0 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((Y1 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))))) => (positive @ Y2 @ Y0))))))) @ X1)))) )),
% 6.49/1.14 inference(pi_proxy_clausification,[],[f115])).
% 6.49/1.14 thf(f117,plain,(
% 6.49/1.14 ( ! [X1 : $i] : (($true = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: (((positive @ Y0 @ X1) & (!! @ $i @ (^[Y2 : $i]: ((~ (rel @ X1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))))) => (positive @ Y1 @ X1))))))))) )),
% 6.49/1.14 inference(beta-eta_normalization,[],[f116])).
% 6.49/1.14 thf(f118,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = (((^[Y0 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: (((positive @ Y0 @ X1) & (!! @ $i @ (^[Y2 : $i]: ((~ (rel @ X1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))))) => (positive @ Y1 @ X1))))) @ X2)))) )),
% 6.49/1.14 inference(pi_proxy_clausification,[],[f117])).
% 6.49/1.14 thf(f119,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: (((positive @ X2 @ X1) & (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ X1 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((X2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))))) => (positive @ Y0 @ X1))))))) )),
% 6.49/1.14 inference(beta-eta_normalization,[],[f118])).
% 6.49/1.14 thf(f120,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($true = (((^[Y0 : mu > $i > $o]: (((positive @ X2 @ X1) & (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ X1 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((X2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))))) => (positive @ Y0 @ X1))) @ X3)))) )),
% 6.49/1.14 inference(pi_proxy_clausification,[],[f119])).
% 6.49/1.14 thf(f121,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($true = ((((positive @ X2 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ X1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((X2 @ Y1 @ Y0) => (X3 @ Y1 @ Y0)))))))) => (positive @ X3 @ X1))))) )),
% 6.49/1.14 inference(beta-eta_normalization,[],[f120])).
% 6.49/1.14 thf(f122,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = (((positive @ X2 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ X1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((X2 @ Y1 @ Y0) => (X3 @ Y1 @ Y0)))))))))) | ($true = ((positive @ X3 @ X1)))) )),
% 6.49/1.14 inference(imp_proxy_clausification,[],[f121])).
% 6.49/1.14 thf(f123,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel @ X1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((X2 @ Y1 @ Y0) => (X3 @ Y1 @ Y0))))))))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 6.49/1.14 inference(and_proxy_clausification,[],[f122])).
% 6.49/1.14 thf(f124,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: ((~ (rel @ X1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((X2 @ Y1 @ Y0) => (X3 @ Y1 @ Y0)))))) @ (sK2 @ X3 @ X1 @ X2)))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 6.49/1.14 inference(sigma_proxy_clausification,[],[f123])).
% 6.49/1.14 thf(f125,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = (((~ (rel @ X1 @ (sK2 @ X3 @ X1 @ X2))) | (!! @ mu @ (^[Y0 : mu]: ((X2 @ Y0 @ (sK2 @ X3 @ X1 @ X2)) => (X3 @ Y0 @ (sK2 @ X3 @ X1 @ X2)))))))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 6.49/1.14 inference(beta-eta_normalization,[],[f124])).
% 6.49/1.14 thf(f126,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = ((!! @ mu @ (^[Y0 : mu]: ((X2 @ Y0 @ (sK2 @ X3 @ X1 @ X2)) => (X3 @ Y0 @ (sK2 @ X3 @ X1 @ X2))))))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 6.49/1.14 inference(or_proxy_clausification,[],[f125])).
% 6.49/1.14 thf(f127,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = ((~ (rel @ X1 @ (sK2 @ X3 @ X1 @ X2))))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 6.49/1.14 inference(or_proxy_clausification,[],[f125])).
% 6.49/1.14 thf(f128,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($true = ((rel @ X1 @ (sK2 @ X3 @ X1 @ X2)))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 6.49/1.14 inference(not_proxy_clausification,[],[f127])).
% 6.49/1.14 thf(f129,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = (((^[Y0 : mu]: ((X2 @ Y0 @ (sK2 @ X3 @ X1 @ X2)) => (X3 @ Y0 @ (sK2 @ X3 @ X1 @ X2)))) @ (sK3 @ X3 @ X1 @ X2)))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 6.49/1.14 inference(sigma_proxy_clausification,[],[f126])).
% 6.49/1.14 thf(f130,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = (((X2 @ (sK3 @ X3 @ X1 @ X2) @ (sK2 @ X3 @ X1 @ X2)) => (X3 @ (sK3 @ X3 @ X1 @ X2) @ (sK2 @ X3 @ X1 @ X2))))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 6.49/1.14 inference(beta-eta_normalization,[],[f129])).
% 6.49/1.14 thf(f132,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($true = ((X2 @ (sK3 @ X3 @ X1 @ X2) @ (sK2 @ X3 @ X1 @ X2)))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 6.49/1.14 inference(imp_proxy_clausification,[],[f130])).
% 6.49/1.14 thf(f133,plain,(
% 6.49/1.14 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ (^[Y2 : mu]: ((^[Y3 : $i]: (~ (Y1 @ Y2 @ Y3))))) @ Y0) = (~ (positive @ Y1 @ Y0)))))))))),
% 6.49/1.14 inference(beta-eta_normalization,[],[f100])).
% 6.49/1.14 thf(f134,plain,(
% 6.49/1.14 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ (^[Y2 : mu]: ((^[Y3 : $i]: (~ (Y1 @ Y2 @ Y3))))) @ Y0) = (~ (positive @ Y1 @ Y0)))))) @ X1)))) )),
% 6.49/1.14 inference(pi_proxy_clausification,[],[f133])).
% 6.49/1.14 thf(f135,plain,(
% 6.49/1.14 ( ! [X1 : $i] : (($true = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ (^[Y1 : mu]: ((^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))) @ X1) = (~ (positive @ Y0 @ X1)))))))) )),
% 6.49/1.14 inference(beta-eta_normalization,[],[f134])).
% 6.49/1.14 thf(f136,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = (((^[Y0 : mu > $i > $o]: ((positive @ (^[Y1 : mu]: ((^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))) @ X1) = (~ (positive @ Y0 @ X1)))) @ X2)))) )),
% 6.49/1.14 inference(pi_proxy_clausification,[],[f135])).
% 6.49/1.14 thf(f137,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = (((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1) = (~ (positive @ X2 @ X1)))))) )),
% 6.49/1.14 inference(beta-eta_normalization,[],[f136])).
% 6.49/1.14 thf(f138,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X1 : $i] : ((((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1)) = ((~ (positive @ X2 @ X1))))) )),
% 6.49/1.14 inference(iff_proxy_clausification,[],[f137])).
% 6.49/1.14 thf(f140,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1))) | ($true = ((~ (positive @ X2 @ X1))))) )),
% 6.49/1.14 inference(iff_proxy_clausification,[],[f138])).
% 6.49/1.14 thf(f141,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 6.49/1.14 inference(not_proxy_clausification,[],[f140])).
% 6.49/1.14 thf(f243,plain,(
% 6.49/1.14 ( ! [X3 : (mu > $i > $o),X1 : $i] : (($true = (((^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ (sK3 @ X3 @ X1 @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false))))) @ (sK2 @ X3 @ X1 @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))))))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ X1)))) )),
% 6.49/1.14 inference(primitive_instantiation,[],[f132])).
% 6.49/1.14 thf(f252,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > mu),X3 : (mu > $i > $i),X0 : mu,X1 : $i,X4 : (mu > $i > $o),X5 : $i] : (($true = $false) | ($false = ((rel @ sK0 @ X1))) | ($true = ((positive @ X4 @ X5))) | ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ (X2 @ Y0 @ Y1) @ (X3 @ Y0 @ Y1))))) @ X5))) | (((X2 @ (sK3 @ X4 @ X5 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ (X2 @ Y0 @ Y1) @ (X3 @ Y0 @ Y1)))))) @ (sK2 @ X4 @ X5 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ (X2 @ Y0 @ Y1) @ (X3 @ Y0 @ Y1)))))))) != X0) | (((X3 @ (sK3 @ X4 @ X5 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ (X2 @ Y0 @ Y1) @ (X3 @ Y0 @ Y1)))))) @ (sK2 @ X4 @ X5 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ (X2 @ Y0 @ Y1) @ (X3 @ Y0 @ Y1)))))))) != X1)) )),
% 6.49/1.14 inference(constrained_superposition,[],[f114,f132])).
% 6.49/1.14 thf(f270,plain,(
% 6.49/1.14 ( ! [X2 : (mu > $i > mu),X3 : (mu > $i > $i),X0 : mu,X1 : $i,X4 : (mu > $i > $o),X5 : $i] : (($false = ((rel @ sK0 @ X1))) | ($true = ((positive @ X4 @ X5))) | ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ (X2 @ Y0 @ Y1) @ (X3 @ Y0 @ Y1))))) @ X5))) | (((X2 @ (sK3 @ X4 @ X5 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ (X2 @ Y0 @ Y1) @ (X3 @ Y0 @ Y1)))))) @ (sK2 @ X4 @ X5 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ (X2 @ Y0 @ Y1) @ (X3 @ Y0 @ Y1)))))))) != X0) | (((X3 @ (sK3 @ X4 @ X5 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ (X2 @ Y0 @ Y1) @ (X3 @ Y0 @ Y1)))))) @ (sK2 @ X4 @ X5 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ (X2 @ Y0 @ Y1) @ (X3 @ Y0 @ Y1)))))))) != X1)) )),
% 6.49/1.14 inference(trivial_inequality_removal,[],[f252])).
% 6.49/1.14 thf(f284,plain,(
% 6.49/1.14 ( ! [X3 : (mu > $i > $o),X1 : $i] : (($true = $false) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ X1)))) )),
% 6.49/1.14 inference(beta-eta_normalization,[],[f243])).
% 6.49/1.14 thf(f285,plain,(
% 6.49/1.14 ( ! [X3 : (mu > $i > $o),X1 : $i] : (($true = ((positive @ X3 @ X1))) | ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ X1)))) )),
% 6.49/1.14 inference(trivial_inequality_removal,[],[f284])).
% 6.49/1.14 thf(f401,definition,(
% 6.49/1.14 spl7_1 <=> ($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ sK0)))),
% 6.49/1.14 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 6.49/1.14 thf(f402,plain,(
% 6.49/1.14 ($true != ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ sK0))) | spl7_1),
% 6.49/1.14 inference(avatar_component_clause,[],[f401])).
% 6.49/1.14 thf(f403,plain,(
% 6.49/1.14 ($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ sK0))) | ~spl7_1),
% 6.49/1.14 inference(avatar_component_clause,[],[f401])).
% 6.49/1.14 thf(f432,plain,(
% 6.49/1.14 ( ! [X2 : mu,X0 : $i,X1 : (mu > $i > $o)] : (($true = $false) | ($false = ((rel @ sK0 @ X0))) | ($true = ((positive @ X1 @ sK0))) | ((((^[Y0 : mu]: ((^[Y1 : $i]: (Y0)))) @ (sK3 @ X1 @ sK0 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1) @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))) @ (sK2 @ X1 @ sK0 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1) @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))))) != X2) | ((((^[Y0 : mu]: ((^[Y1 : $i]: (Y1)))) @ (sK3 @ X1 @ sK0 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1) @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))) @ (sK2 @ X1 @ sK0 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1) @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))))) != X0)) )),
% 6.49/1.14 inference(constrained_superposition,[],[f109,f270])).
% 6.49/1.14 thf(f445,plain,(
% 6.49/1.14 ( ! [X2 : mu,X0 : $i,X1 : (mu > $i > $o)] : (($false = ((rel @ sK0 @ X0))) | ($true = ((positive @ X1 @ sK0))) | ((((^[Y0 : mu]: ((^[Y1 : $i]: (Y0)))) @ (sK3 @ X1 @ sK0 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1) @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))) @ (sK2 @ X1 @ sK0 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1) @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))))) != X2) | ((((^[Y0 : mu]: ((^[Y1 : $i]: (Y1)))) @ (sK3 @ X1 @ sK0 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1) @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))) @ (sK2 @ X1 @ sK0 @ (^[Y0 : mu]: ((^[Y1 : $i]: (sK1 @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1) @ ((^[Y2 : mu]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1)))))))) != X0)) )),
% 6.49/1.14 inference(trivial_inequality_removal,[],[f432])).
% 6.49/1.14 thf(f446,plain,(
% 6.49/1.14 ( ! [X2 : mu,X0 : $i,X1 : (mu > $i > $o)] : ((((sK3 @ X1 @ sK0 @ sK1)) != X2) | ($true = ((positive @ X1 @ sK0))) | ($false = ((rel @ sK0 @ X0))) | (((sK2 @ X1 @ sK0 @ sK1)) != X0)) )),
% 6.49/1.14 inference(beta-eta_normalization,[],[f445])).
% 6.49/1.14 thf(f653,plain,(
% 6.49/1.14 ( ! [X0 : (mu > $i > $o)] : (($true = $false) | ($true = ((positive @ X0 @ sK0)))) ) | ~spl7_1),
% 6.49/1.14 inference(constrained_superposition,[],[f285,f403])).
% 6.49/1.14 thf(f661,plain,(
% 6.49/1.14 ( ! [X0 : (mu > $i > $o)] : (($true = ((positive @ X0 @ sK0)))) ) | ~spl7_1),
% 6.49/1.14 inference(trivial_inequality_removal,[],[f653])).
% 6.49/1.14 thf(f672,plain,(
% 6.49/1.14 ( ! [X0 : (mu > $i > $o)] : (($true = $false) | ($false = ((positive @ X0 @ sK0)))) ) | ~spl7_1),
% 6.49/1.14 inference(constrained_superposition,[],[f141,f661])).
% 6.49/1.14 thf(f686,plain,(
% 6.49/1.14 ( ! [X0 : (mu > $i > $o)] : (($false = ((positive @ X0 @ sK0)))) ) | ~spl7_1),
% 6.49/1.14 inference(trivial_inequality_removal,[],[f672])).
% 6.49/1.14 thf(f773,plain,(
% 6.49/1.14 ($true = $false) | ~spl7_1),
% 6.49/1.14 inference(constrained_superposition,[],[f686,f109])).
% 6.49/1.14 thf(f836,plain,(
% 6.49/1.14 $false | ~spl7_1),
% 6.49/1.14 inference(trivial_inequality_removal,[],[f773])).
% 6.49/1.14 thf(f837,plain,(
% 6.49/1.14 ~spl7_1),
% 6.49/1.14 inference(avatar_contradiction_clause,[],[f836])).
% 6.49/1.14 thf(f848,plain,(
% 6.49/1.14 ($true != $true) | ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ sK0))) | spl7_1),
% 6.49/1.14 inference(constrained_superposition,[],[f402,f97])).
% 6.49/1.14 thf(f849,plain,(
% 6.49/1.14 ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ sK0))) | spl7_1),
% 6.49/1.14 inference(trivial_inequality_removal,[],[f848])).
% 6.49/1.14 thf(f3196,plain,(
% 6.49/1.14 ( ! [X0 : (mu > $i > $o),X1 : $i] : ((((sK2 @ X0 @ sK0 @ sK1)) != X1) | ($false = ((rel @ sK0 @ X1))) | ($true = ((positive @ X0 @ sK0)))) )),
% 6.49/1.14 inference(equality_resolution,[],[f446])).
% 6.49/1.14 thf(f3319,plain,(
% 6.49/1.14 ( ! [X0 : (mu > $i > $o)] : (($false = ((rel @ sK0 @ (sK2 @ X0 @ sK0 @ sK1)))) | ($true = ((positive @ X0 @ sK0)))) )),
% 6.49/1.14 inference(equality_resolution,[],[f3196])).
% 6.49/1.14 thf(f3348,plain,(
% 6.49/1.14 ( ! [X0 : (mu > $i > $o)] : (($true = $false) | ($true = ((positive @ X0 @ sK0))) | ($false = ((positive @ sK1 @ sK0))) | ($true = ((positive @ X0 @ sK0)))) )),
% 6.49/1.14 inference(constrained_superposition,[],[f128,f3319])).
% 6.49/1.14 thf(f3349,plain,(
% 6.49/1.14 ( ! [X0 : (mu > $i > $o)] : (($true = $false) | ($true = ((positive @ X0 @ sK0))) | ($false = ((positive @ sK1 @ sK0)))) )),
% 6.49/1.14 inference(duplicate_literal_removal,[],[f3348])).
% 6.49/1.14 thf(f3350,plain,(
% 6.49/1.14 ( ! [X0 : (mu > $i > $o)] : (($true = ((positive @ X0 @ sK0))) | ($false = ((positive @ sK1 @ sK0)))) )),
% 6.49/1.14 inference(trivial_inequality_removal,[],[f3349])).
% 6.49/1.14 thf(f3399,definition,(
% 6.49/1.14 spl7_4 <=> ($false = ((positive @ sK1 @ sK0)))),
% 6.49/1.14 introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition])).
% 6.49/1.14 thf(f3401,plain,(
% 6.49/1.14 ($false = ((positive @ sK1 @ sK0))) | ~spl7_4),
% 6.49/1.14 inference(avatar_component_clause,[],[f3399])).
% 6.49/1.14 thf(f3403,definition,(
% 6.49/1.14 spl7_5 <=> ! [X0 : (mu > $i > $o)] : ($true = ((positive @ X0 @ sK0)))),
% 6.49/1.14 introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition])).
% 6.49/1.14 thf(f3404,plain,(
% 6.49/1.14 ( ! [X0 : (mu > $i > $o)] : (($true = ((positive @ X0 @ sK0)))) ) | ~spl7_5),
% 6.49/1.14 inference(avatar_component_clause,[],[f3403])).
% 6.49/1.14 thf(f3405,plain,(
% 6.49/1.14 spl7_4 | spl7_5),
% 6.49/1.14 inference(avatar_split_clause,[],[f3350,f3403,f3399])).
% 6.49/1.14 thf(f3416,plain,(
% 6.49/1.14 ($true = $false) | (spl7_1 | ~spl7_5)),
% 6.49/1.14 inference(constrained_superposition,[],[f3404,f849])).
% 6.49/1.14 thf(f3502,plain,(
% 6.49/1.14 $false | (spl7_1 | ~spl7_5)),
% 6.49/1.14 inference(trivial_inequality_removal,[],[f3416])).
% 6.49/1.14 thf(f3503,plain,(
% 6.49/1.14 spl7_1 | ~spl7_5),
% 6.49/1.14 inference(avatar_contradiction_clause,[],[f3502])).
% 6.49/1.14 thf(f3513,plain,(
% 6.49/1.14 ($true = $false) | ~spl7_4),
% 6.49/1.14 inference(constrained_superposition,[],[f3401,f109])).
% 6.49/1.14 thf(f3586,plain,(
% 6.49/1.14 $false | ~spl7_4),
% 6.49/1.14 inference(trivial_inequality_removal,[],[f3513])).
% 6.49/1.14 thf(f3587,plain,(
% 6.49/1.14 ~spl7_4),
% 6.49/1.14 inference(avatar_contradiction_clause,[],[f3586])).
% 6.49/1.14 cnf(s8, plain, ~spl7_1, inference(sat_conversion,[],[f837])).
% 6.49/1.14 cnf(s9, plain, spl7_4 | spl7_5, inference(sat_conversion,[],[f3405])).
% 6.49/1.14 cnf(s12, plain, spl7_1 | ~spl7_5, inference(sat_conversion,[],[f3503])).
% 6.49/1.14 cnf(s14, plain, ~spl7_4, inference(sat_conversion,[],[f3587])).
% 6.49/1.14 cnf(s15, plain, spl7_5, inference(rat,[],[s9,s14])).
% 6.49/1.14 cnf(s16, plain, spl7_1, inference(rat,[],[s12,s15])).
% 6.49/1.14 cnf(s17, plain, $false, inference(rat,[],[s8,s16])).
% 6.49/1.14 thf(f3588,plain,(
% 6.49/1.14 $false),
% 6.49/1.14 inference(avatar_sat_refutation,[],[s17])).
% 6.49/1.14 % SZS output end Proof for theBenchmark
% 6.49/1.14 % (49961)------------------------------
% 6.49/1.14 % (49961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.49/1.14 % (49961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.49/1.14 % (49961)CaDiCaL version: 2.1.3
% 6.49/1.14 % (49961)Termination reason: Refutation
% 6.49/1.14 % (49961)Time elapsed: 0.491 s
% 6.49/1.14 % (49961)Peak memory usage: 16 MB
% 6.49/1.14 % (49961)Instructions burned: 1109 (million)
% 6.49/1.14 % (49916)Success in time 0.928 s
% 6.49/1.14 % Vampire exiting
%------------------------------------------------------------------------------