%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV508^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 08:39:37 AM UTC 2026
% Result : Theorem 5.74s 1.09s
% Output : Refutation 5.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV508^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:54:52 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 4.32/1.01 % (1469410)Will run a generic schedule for satisfiability detection.
% 4.32/1.01 % (1469417)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1233437817:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.32/1.01 % (1469416)% WARNING: option uhcvi not known.
% 4.32/1.01 % (1469416)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1753126807:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.32/1.01 % (1469415)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2621059836_2999 on theBenchmark for (2999ds/0Mi)
% 4.32/1.01 % (1469418)dis+10_1_sil=32000:sp=arity:random_seed=2280482108:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.32/1.01 % (1469416)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.32/1.01 % (1469419)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4009301885:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.32/1.01 % (1469416)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.32/1.01 % Exception at run slice level
% 4.32/1.01 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.32/1.01 % (1469419)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.32/1.01 % (1469421)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2763540611:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.32/1.01 % (1469427)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2881855458:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.32/1.01 % (1469420)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4221534188:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.32/1.01 % Exception at run slice level
% 4.32/1.01 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.32/1.01 % (1469431)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1074949331:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.32/1.01 % (1469418)Instruction limit reached!
% 4.32/1.01 % (1469418)------------------------------
% 4.32/1.01 % (1469418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.32/1.01 % (1469418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.01 % (1469418)CaDiCaL version: 2.1.3
% 4.32/1.01 % (1469418)Termination reason: Instruction limit
% 4.32/1.01 % (1469418)Termination phase: Saturation
% 4.32/1.01 % (1469418)Time elapsed: 0.053 s
% 4.32/1.01 % (1469418)Peak memory usage: 12 MB
% 4.32/1.01 % (1469418)Instructions burned: 104 (million)
% 4.32/1.01 % (1469419)Instruction limit reached!
% 4.32/1.01 % (1469419)------------------------------
% 4.32/1.01 % (1469419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.32/1.01 % (1469419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.01 % (1469419)CaDiCaL version: 2.1.3
% 4.32/1.01 % (1469419)Termination reason: Instruction limit
% 4.32/1.01 % (1469419)Termination phase: Saturation
% 4.32/1.01 % (1469419)Time elapsed: 0.061 s
% 4.32/1.01 % (1469419)Peak memory usage: 12 MB
% 4.32/1.01 % (1469419)Instructions burned: 118 (million)
% 4.32/1.01 % (1469433)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=2073061408:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.32/1.01 % (1469433)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.32/1.01 % (1469433)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.32/1.01 % (1469434)ott-21_1_sil=16000:fs=off:random_seed=2226121255:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 4.32/1.01 % (1469420)Instruction limit reached!
% 4.32/1.01 % (1469420)------------------------------
% 4.32/1.01 % (1469420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.32/1.01 % (1469420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.01 % (1469420)CaDiCaL version: 2.1.3
% 4.32/1.01 % (1469420)Termination reason: Instruction limit
% 4.32/1.01 % (1469420)Termination phase: Saturation
% 4.32/1.01 % (1469420)Time elapsed: 0.077 s
% 4.32/1.01 % (1469420)Peak memory usage: 13 MB
% 4.32/1.01 % (1469420)Instructions burned: 132 (million)
% 4.32/1.01 % (1469431)Instruction limit reached!
% 5.74/1.09 % (1469431)------------------------------
% 5.74/1.09 % (1469431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.74/1.09 % (1469431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.09 % (1469431)CaDiCaL version: 2.1.3
% 5.74/1.09 % (1469431)Termination reason: Instruction limit
% 5.74/1.09 % (1469431)Termination phase: Saturation
% 5.74/1.09 % (1469431)Time elapsed: 0.073 s
% 5.74/1.09 % (1469431)Peak memory usage: 12 MB
% 5.74/1.09 % (1469431)Instructions burned: 133 (million)
% 5.74/1.09 % (1469437)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=48411277:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.74/1.09 % (1469438)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2592747338:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.74/1.09 % Exception at run slice level
% 5.74/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.74/1.09 % (1469421)Instruction limit reached!
% 5.74/1.09 % (1469421)------------------------------
% 5.74/1.09 % (1469421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.74/1.09 % (1469421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.09 % (1469421)CaDiCaL version: 2.1.3
% 5.74/1.09 % (1469421)Termination reason: Instruction limit
% 5.74/1.09 % (1469421)Termination phase: Saturation
% 5.74/1.09 % (1469421)Time elapsed: 0.124 s
% 5.74/1.09 % (1469421)Peak memory usage: 13 MB
% 5.74/1.09 % (1469421)Instructions burned: 159 (million)
% 5.74/1.09 % (1469441)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=872108004:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.74/1.09 % (1469442)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4073504017:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 5.74/1.09 % Exception at run slice level
% 5.74/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.74/1.09 % (1469434)Instruction limit reached!
% 5.74/1.09 % (1469434)------------------------------
% 5.74/1.09 % (1469434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.74/1.09 % (1469434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.09 % (1469434)CaDiCaL version: 2.1.3
% 5.74/1.09 % (1469434)Termination reason: Instruction limit
% 5.74/1.09 % (1469434)Termination phase: Saturation
% 5.74/1.09 % (1469434)Time elapsed: 0.089 s
% 5.74/1.09 % (1469434)Peak memory usage: 12 MB
% 5.74/1.09 % (1469434)Instructions burned: 181 (million)
% 5.74/1.09 % (1469446)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=54308629:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 5.74/1.09 % (1469446)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.74/1.09 % (1469445)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=2311891334:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 5.74/1.09 % (1469445)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.74/1.09 % (1469433)Instruction limit reached!
% 5.74/1.09 % (1469433)------------------------------
% 5.74/1.09 % (1469433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.74/1.09 % (1469433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.09 % (1469433)CaDiCaL version: 2.1.3
% 5.74/1.09 % (1469433)Termination reason: Instruction limit
% 5.74/1.09 % (1469433)Termination phase: Saturation
% 5.74/1.09 % (1469433)Time elapsed: 0.331 s
% 5.74/1.09 % (1469433)Peak memory usage: 14 MB
% 5.74/1.09 % (1469433)Instructions burned: 685 (million)
% 5.74/1.09 % (1469437)Instruction limit reached!
% 5.74/1.09 % (1469437)------------------------------
% 5.74/1.09 % (1469437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.74/1.09 % (1469437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.09 % (1469437)CaDiCaL version: 2.1.3
% 5.74/1.09 % (1469437)Termination reason: Instruction limit
% 5.74/1.09 % (1469437)Termination phase: Saturation
% 5.74/1.09 % (1469437)Time elapsed: 0.296 s
% 5.74/1.09 % (1469437)Peak memory usage: 14 MB
% 5.74/1.09 % (1469437)Instructions burned: 479 (million)
% 5.74/1.09 % (1469449)fmb+10_1_sil=64000:random_seed=2753965603:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 5.74/1.09 % (1469449)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.74/1.09 % Exception at run slice level
% 5.74/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.74/1.09 % (1469450)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3960647012:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 5.74/1.09 % Exception at run slice level
% 5.74/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.74/1.09 % (1469452)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2272104724:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 5.74/1.09 % Exception at run slice level
% 5.74/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.74/1.09 % (1469454)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3945089603:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 5.74/1.09 % (1469454)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.74/1.09 % (1469456)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3141891275:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 5.74/1.09 % (1469456)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.74/1.09 % (1469456)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.74/1.09 % (1469445)Instruction limit reached!
% 5.74/1.09 % (1469445)------------------------------
% 5.74/1.09 % (1469445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.74/1.09 % (1469445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.09 % (1469445)CaDiCaL version: 2.1.3
% 5.74/1.09 % (1469445)Termination reason: Instruction limit
% 5.74/1.09 % (1469445)Termination phase: Saturation
% 5.74/1.09 % (1469445)Time elapsed: 0.404 s
% 5.74/1.09 % (1469445)Peak memory usage: 20 MB
% 5.74/1.09 % (1469445)Instructions burned: 692 (million)
% 5.74/1.09 % (1469459)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=170782400:i=6324_2993 on theBenchmark for (2993ds/6324Mi)
% 5.74/1.09 % Exception at run slice level
% 5.74/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.74/1.09 % (1469461)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3298581163:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 5.74/1.09 % Exception at run slice level
% 5.74/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.74/1.09 % (1469463)ott-2_1_sil=16000:newcnf=on:random_seed=2867760537:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 5.74/1.09 % (1469463)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.74/1.09 % (1469446)Instruction limit reached!
% 5.74/1.09 % (1469446)------------------------------
% 5.74/1.09 % (1469446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.74/1.09 % (1469446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.09 % (1469446)CaDiCaL version: 2.1.3
% 5.74/1.09 % (1469446)Termination reason: Instruction limit
% 5.74/1.09 % (1469446)Termination phase: Saturation
% 5.74/1.09 % (1469446)Time elapsed: 0.494 s
% 5.74/1.09 % (1469446)Peak memory usage: 16 MB
% 5.74/1.09 % (1469446)Instructions burned: 880 (million)
% 5.74/1.09 % (1469465)ott+10_1_sil=32000:tgt=ground:random_seed=2043929141:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 5.74/1.09 % (1469441)Instruction limit reached!
% 5.74/1.09 % (1469441)------------------------------
% 5.74/1.09 % (1469441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.74/1.09 % (1469441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.09 % (1469441)CaDiCaL version: 2.1.3
% 5.74/1.09 % (1469441)Termination reason: Instruction limit
% 5.74/1.09 % (1469441)Termination phase: Saturation
% 5.74/1.09 % (1469441)Time elapsed: 0.578 s
% 5.74/1.09 % (1469441)Peak memory usage: 17 MB
% 5.74/1.09 % (1469441)Instructions burned: 1180 (million)
% 5.74/1.09 % (1469467)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=4109329927:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 5.74/1.09 % Exception at run slice level
% 5.74/1.09 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.74/1.09 % (1469469)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2408302135:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 5.74/1.09 % (1469469)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.74/1.09 % (1469454) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1469410-1469454"...
% 5.74/1.09 % (1469454)...printing done.
% 5.74/1.09 % (1469454)Refutation found. Thanks to Tanya!
% 5.74/1.09 % SZS status Theorem for theBenchmark
% 5.74/1.09 % SZS output start Proof for theBenchmark
% 5.74/1.09 thf(type_def_5, type, 'type/realax/real': $tType).
% 5.74/1.09 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 5.74/1.09 thf(type_def_7, type, sK1: $tType).
% 5.74/1.09 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 5.74/1.09 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 5.74/1.09 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.74/1.09 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 5.74/1.09 thf(func_def_4, type, 'const/realax/real_lt': ('type/realax/real' > 'type/realax/real' > $o)).
% 5.74/1.09 thf(func_def_5, type, 'const/realax/real_le': ('type/realax/real' > 'type/realax/real' > $o)).
% 5.74/1.09 thf(func_def_6, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 5.74/1.09 thf(func_def_10, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.74/1.09 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 5.74/1.09 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.74/1.09 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.74/1.09 thf(func_def_14, type, vNOT: ($o > $o)).
% 5.74/1.09 thf(func_def_15, type, sK0: !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > (X0 > 'type/realax/real') > X0))).
% 5.74/1.09 thf(func_def_16, type, sK2: (sK1 > 'type/realax/real')).
% 5.74/1.09 thf(func_def_17, type, sK3: (sK1 > 'type/realax/real')).
% 5.74/1.09 thf(func_def_18, type, sK4: (sK1 > $o)).
% 5.74/1.09 thf(func_def_19, type, sK5: !>[X0: $tType]:(((X0 > $o) > X0))).
% 5.74/1.09 thf(func_def_20, type, sK6: sK1).
% 5.74/1.09 thf(func_def_22, type, sK8: !>[X0: $tType]:(((X0 > $o) > X0))).
% 5.74/1.09 thf(func_def_23, type, db1: !>[X0: $tType]:(X0)).
% 5.74/1.09 thf(f2,axiom,(
% 5.74/1.09 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : ((? [X4 : X0] : (('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) & ('const/sets/IN' @ X0 @ X4 @ X3)) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_le' @ (X1 @ X4) @ (X2 @ X4))) & ('const/sets/FINITE' @ X0 @ X3)) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 5.74/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_LT_')).
% 5.74/1.09 thf(f3,axiom,(
% 5.74/1.09 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_lt' @ X0 @ X1) => ('const/realax/real_le' @ X0 @ X1))),
% 5.74/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realarith/REAL_LT_IMP_LE_')).
% 5.74/1.09 thf(f4,axiom,(
% 5.74/1.09 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 5.74/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_')).
% 5.74/1.09 thf(f5,conjecture,(
% 5.74/1.09 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) & (X3 != 'const/sets/EMPTY' @ X0) & ('const/sets/FINITE' @ X0 @ X3)) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 5.74/1.09 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_LT_ALL_')).
% 5.74/1.09 thf(f6,negated_conjecture,(
% 5.74/1.09 ~ ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) & (X3 != 'const/sets/EMPTY' @ X0) & ('const/sets/FINITE' @ X0 @ X3)) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 5.74/1.09 inference(negated_conjecture,[status(cth)],[f5])).
% 5.74/1.09 thf(f7,plain,(
% 5.74/1.09 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : ((? [X4 : X0] : (('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4)) & ('const/sets/IN' @ X0 @ X4 @ X3)) & ! [X5 : X0] : (('const/sets/IN' @ X0 @ X5 @ X3) => ('const/realax/real_le' @ (X1 @ X5) @ (X2 @ X5))) & ('const/sets/FINITE' @ X0 @ X3)) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 5.74/1.09 inference(rectify,[],[f2])).
% 5.74/1.09 thf(f8,plain,(
% 5.74/1.09 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : ((? [X4 : X0] : (((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) = $true) & ((('const/sets/IN' @ X0 @ X4 @ X3)) = $true)) & ! [X5 : X0] : (((('const/sets/IN' @ X0 @ X5 @ X3)) = $true) => ((('const/realax/real_le' @ (X1 @ X5) @ (X2 @ X5))) = $true)) & ((('const/sets/FINITE' @ X0 @ X3)) = $true)) => ((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true))),
% 5.74/1.09 inference(fool_elimination,[],[f7])).
% 5.74/1.09 thf(f9,plain,(
% 5.74/1.09 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (('const/realax/real_lt' @ X0 @ X1) => ('const/realax/real_le' @ X0 @ X1))),
% 5.74/1.09 inference(rectify,[],[f3])).
% 5.74/1.09 thf(f10,plain,(
% 5.74/1.09 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ X0 @ X1)) = $true) => ((('const/realax/real_le' @ X0 @ X1)) = $true))),
% 5.74/1.09 inference(fool_elimination,[],[f9])).
% 5.74/1.09 thf(f11,plain,(
% 5.74/1.09 ! [X0 : $tType,X1 : (X0 > $o)] : (? [X2 : X0] : ('const/sets/IN' @ X0 @ X2 @ X1) = (X1 != 'const/sets/EMPTY' @ X0))),
% 5.74/1.09 inference(rectify,[],[f4])).
% 5.74/1.09 thf(f12,plain,(
% 5.74/1.09 ! [X0 : $tType,X1 : (X0 > $o)] : (((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = ((~ ('const/sets/EMPTY' @ X0 = X1))))),
% 5.74/1.09 inference(fool_elimination,[],[f11])).
% 5.74/1.09 thf(f13,plain,(
% 5.74/1.09 ~ ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : ((! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X3) => ('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) & (X3 != 'const/sets/EMPTY' @ X0) & ('const/sets/FINITE' @ X0 @ X3)) => ('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2)))),
% 5.74/1.09 inference(rectify,[],[f6])).
% 5.74/1.09 thf(f14,plain,(
% 5.74/1.09 ~ ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : ((! [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X3)) = $true) => ((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) = $true)) & ('const/sets/EMPTY' @ X0 != X3) & ((('const/sets/FINITE' @ X0 @ X3)) = $true)) => ((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true))),
% 5.74/1.09 inference(fool_elimination,[],[f13])).
% 5.74/1.09 thf(f15,plain,(
% 5.74/1.09 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : (((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true) | (! [X4 : X0] : (((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X3)) != $true)) | ? [X5 : X0] : (((('const/realax/real_le' @ (X1 @ X5) @ (X2 @ X5))) != $true) & ((('const/sets/IN' @ X0 @ X5 @ X3)) = $true)) | ((('const/sets/FINITE' @ X0 @ X3)) != $true)))),
% 5.74/1.09 inference(ennf_transformation,[],[f8])).
% 5.74/1.09 thf(f16,plain,(
% 5.74/1.09 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : (((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true) | ! [X4 : X0] : (((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X3)) != $true)) | ? [X5 : X0] : (((('const/realax/real_le' @ (X1 @ X5) @ (X2 @ X5))) != $true) & ((('const/sets/IN' @ X0 @ X5 @ X3)) = $true)) | ((('const/sets/FINITE' @ X0 @ X3)) != $true))),
% 5.74/1.09 inference(flattening,[],[f15])).
% 5.74/1.09 thf(f17,plain,(
% 5.74/1.09 ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_le' @ X0 @ X1)) = $true) | ((('const/realax/real_lt' @ X0 @ X1)) != $true))),
% 5.74/1.09 inference(ennf_transformation,[],[f10])).
% 5.74/1.09 thf(f18,plain,(
% 5.74/1.09 ? [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : (((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) != $true) & (! [X4 : X0] : (((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) = $true) | ((('const/sets/IN' @ X0 @ X4 @ X3)) != $true)) & ('const/sets/EMPTY' @ X0 != X3) & ((('const/sets/FINITE' @ X0 @ X3)) = $true)))),
% 5.74/1.09 inference(ennf_transformation,[],[f14])).
% 5.74/1.09 thf(f19,plain,(
% 5.74/1.09 ? [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : (((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) != $true) & ! [X4 : X0] : (((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) = $true) | ((('const/sets/IN' @ X0 @ X4 @ X3)) != $true)) & ('const/sets/EMPTY' @ X0 != X3) & ((('const/sets/FINITE' @ X0 @ X3)) = $true))),
% 5.74/1.09 inference(flattening,[],[f18])).
% 5.74/1.09 thf(f20,plain,(
% 5.74/1.09 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o)] : (((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true) | ! [X4 : X0] : (((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X3)) != $true)) | (($true != (('const/realax/real_le' @ (X1 @ (sK0 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK0 @ X0 @ X3 @ X2 @ X1))))) & ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X3 @ X2 @ X1) @ X3)))) | ((('const/sets/FINITE' @ X0 @ X3)) != $true))),
% 5.74/1.09 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X5,sK0 @ X0 @ X3 @ X2 @ X1)],[f16])).
% 5.74/1.09 thf(f21,plain,(
% 5.74/1.09 ($true != (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ sK2) @ ('const/iterate/sum' @ sK1 @ sK4 @ sK3)))) & ! [X4 : sK1] : (($true = (('const/realax/real_lt' @ (sK2 @ X4) @ (sK3 @ X4)))) | ($true != (('const/sets/IN' @ sK1 @ X4 @ sK4)))) & (sK4 != 'const/sets/EMPTY' @ sK1) & ($true = (('const/sets/FINITE' @ sK1 @ sK4)))),
% 5.74/1.09 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f19])).
% 5.74/1.09 thf(f23,plain,(
% 5.74/1.09 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o),X1 : (X0 > 'type/realax/real'),X4 : X0] : (((('const/sets/FINITE' @ X0 @ X3)) != $true) | ((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X3)) != $true) | ($true = (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X3 @ X2 @ X1) @ X3))) | ((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true)) )),
% 5.74/1.09 inference(cnf_transformation,[],[f20])).
% 5.74/1.09 thf(f24,plain,(
% 5.74/1.09 ( ! [X0 : $tType,X2 : (X0 > 'type/realax/real'),X3 : (X0 > $o),X1 : (X0 > 'type/realax/real'),X4 : X0] : (((('const/sets/FINITE' @ X0 @ X3)) != $true) | ((('const/realax/real_lt' @ (X1 @ X4) @ (X2 @ X4))) != $true) | ((('const/sets/IN' @ X0 @ X4 @ X3)) != $true) | ($true != (('const/realax/real_le' @ (X1 @ (sK0 @ X0 @ X3 @ X2 @ X1)) @ (X2 @ (sK0 @ X0 @ X3 @ X2 @ X1))))) | ((('const/realax/real_lt' @ ('const/iterate/sum' @ X0 @ X3 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X2))) = $true)) )),
% 5.74/1.09 inference(cnf_transformation,[],[f20])).
% 5.74/1.09 thf(f25,plain,(
% 5.74/1.09 ( ! [X0 : 'type/realax/real',X1 : 'type/realax/real'] : (((('const/realax/real_lt' @ X0 @ X1)) != $true) | ((('const/realax/real_le' @ X0 @ X1)) = $true)) )),
% 5.74/1.09 inference(cnf_transformation,[],[f17])).
% 5.74/1.09 thf(f26,plain,(
% 5.74/1.09 ( ! [X0 : $tType,X1 : (X0 > $o)] : ((((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)))) = ((~ ('const/sets/EMPTY' @ X0 = X1))))) )),
% 5.74/1.09 inference(cnf_transformation,[],[f12])).
% 5.74/1.09 thf(f27,plain,(
% 5.74/1.09 ($true = (('const/sets/FINITE' @ sK1 @ sK4)))),
% 5.74/1.09 inference(cnf_transformation,[],[f21])).
% 5.74/1.09 thf(f28,plain,(
% 5.74/1.09 (sK4 != 'const/sets/EMPTY' @ sK1)),
% 5.74/1.09 inference(cnf_transformation,[],[f21])).
% 5.74/1.09 thf(f29,plain,(
% 5.74/1.09 ( ! [X4 : sK1] : (($true != (('const/sets/IN' @ sK1 @ X4 @ sK4))) | ($true = (('const/realax/real_lt' @ (sK2 @ X4) @ (sK3 @ X4))))) )),
% 5.74/1.09 inference(cnf_transformation,[],[f21])).
% 5.74/1.09 thf(f30,plain,(
% 5.74/1.09 ($true != (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ sK2) @ ('const/iterate/sum' @ sK1 @ sK4 @ sK3))))),
% 5.74/1.09 inference(cnf_transformation,[],[f21])).
% 5.74/1.09 thf(f32,definition,(
% 5.74/1.09 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 5.74/1.09 introduced(theory,[fool_exhaustiveness_axiom])).
% 5.74/1.09 thf(f33,plain,(
% 5.74/1.09 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = ((?? @ X0 @ (^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1))))) | (((~ ('const/sets/EMPTY' @ X0 = X1))) = $false)) )),
% 5.74/1.09 inference(iff_proxy_clausification,[],[f26])).
% 5.74/1.09 thf(f39,plain,(
% 5.74/1.09 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ (sK5 @ X0 @ X1)))) | (((~ ('const/sets/EMPTY' @ X0 = X1))) = $false)) )),
% 5.74/1.09 inference(sigma_proxy_clausification,[],[f33])).
% 5.74/1.09 thf(f40,plain,(
% 5.74/1.09 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ (sK5 @ X0 @ X1)))) | ($true = (('const/sets/EMPTY' @ X0 = X1)))) )),
% 5.74/1.09 inference(not_proxy_clausification,[],[f39])).
% 5.74/1.09 thf(f41,plain,(
% 5.74/1.09 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (((^[Y0 : X0]: ('const/sets/IN' @ X0 @ Y0 @ X1)) @ (sK5 @ X0 @ X1)))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 5.74/1.09 inference(equality_proxy_clausification,[],[f40])).
% 5.74/1.09 thf(f42,plain,(
% 5.74/1.09 ( ! [X0 : $tType,X1 : (X0 > $o)] : (($true = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1) @ X1))) | ('const/sets/EMPTY' @ X0 = X1)) )),
% 5.74/1.09 inference(beta-eta_normalization,[],[f41])).
% 5.74/1.09 thf(f59,plain,(
% 5.74/1.09 ( ! [X0 : sK1] : (($true != $true) | ($true = (('const/realax/real_lt' @ (sK2 @ X0) @ (sK3 @ X0)))) | ($false = (('const/sets/IN' @ sK1 @ X0 @ sK4)))) )),
% 5.74/1.09 inference(constrained_superposition,[],[f29,f32])).
% 5.74/1.09 thf(f65,plain,(
% 5.74/1.09 ( ! [X0 : sK1] : (($true = (('const/realax/real_lt' @ (sK2 @ X0) @ (sK3 @ X0)))) | ($false = (('const/sets/IN' @ sK1 @ X0 @ sK4)))) )),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f59])).
% 5.74/1.09 thf(f80,plain,(
% 5.74/1.09 ( ! [X2 : (sK1 > 'type/realax/real'),X0 : (sK1 > 'type/realax/real'),X1 : sK1] : (($true != $true) | ($true != (('const/realax/real_lt' @ (X0 @ X1) @ (X2 @ X1)))) | ($true != (('const/sets/IN' @ sK1 @ X1 @ sK4))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ X2 @ X0) @ sK4))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ X0) @ ('const/iterate/sum' @ sK1 @ sK4 @ X2))))) )),
% 5.74/1.09 inference(constrained_superposition,[],[f23,f27])).
% 5.74/1.09 thf(f83,plain,(
% 5.74/1.09 ( ! [X2 : (sK1 > 'type/realax/real'),X0 : (sK1 > 'type/realax/real'),X1 : sK1] : (($true != (('const/sets/IN' @ sK1 @ X1 @ sK4))) | ($true != (('const/realax/real_lt' @ (X0 @ X1) @ (X2 @ X1)))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ X2 @ X0) @ sK4))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ X0) @ ('const/iterate/sum' @ sK1 @ sK4 @ X2))))) )),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f80])).
% 5.74/1.09 thf(f88,plain,(
% 5.74/1.09 ( ! [X2 : (sK1 > 'type/realax/real'),X0 : (sK1 > 'type/realax/real'),X1 : sK1] : (($true != $true) | ($true != (('const/realax/real_lt' @ (X0 @ X1) @ (X2 @ X1)))) | ($true != (('const/sets/IN' @ sK1 @ X1 @ sK4))) | ($true != (('const/realax/real_le' @ (X0 @ (sK0 @ sK1 @ sK4 @ X2 @ X0)) @ (X2 @ (sK0 @ sK1 @ sK4 @ X2 @ X0))))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ X0) @ ('const/iterate/sum' @ sK1 @ sK4 @ X2))))) )),
% 5.74/1.09 inference(constrained_superposition,[],[f24,f27])).
% 5.74/1.09 thf(f91,plain,(
% 5.74/1.09 ( ! [X2 : (sK1 > 'type/realax/real'),X0 : (sK1 > 'type/realax/real'),X1 : sK1] : (($true != (('const/sets/IN' @ sK1 @ X1 @ sK4))) | ($true != (('const/realax/real_lt' @ (X0 @ X1) @ (X2 @ X1)))) | ($true != (('const/realax/real_le' @ (X0 @ (sK0 @ sK1 @ sK4 @ X2 @ X0)) @ (X2 @ (sK0 @ sK1 @ sK4 @ X2 @ X0))))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ X0) @ ('const/iterate/sum' @ sK1 @ sK4 @ X2))))) )),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f88])).
% 5.74/1.09 thf(f150,plain,(
% 5.74/1.09 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true != $true) | ($true != (('const/realax/real_lt' @ (X0 @ (sK5 @ sK1 @ sK4)) @ (X1 @ (sK5 @ sK1 @ sK4))))) | ($true != (('const/realax/real_le' @ (X0 @ (sK0 @ sK1 @ sK4 @ X1 @ X0)) @ (X1 @ (sK0 @ sK1 @ sK4 @ X1 @ X0))))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ X0) @ ('const/iterate/sum' @ sK1 @ sK4 @ X1)))) | (sK4 = 'const/sets/EMPTY' @ sK1)) )),
% 5.74/1.09 inference(constrained_superposition,[],[f91,f42])).
% 5.74/1.09 thf(f151,plain,(
% 5.74/1.09 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true != $true) | ($true != (('const/realax/real_lt' @ (X0 @ (sK5 @ sK1 @ sK4)) @ (X1 @ (sK5 @ sK1 @ sK4))))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ X1 @ X0) @ sK4))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ X0) @ ('const/iterate/sum' @ sK1 @ sK4 @ X1)))) | (sK4 = 'const/sets/EMPTY' @ sK1)) )),
% 5.74/1.09 inference(constrained_superposition,[],[f83,f42])).
% 5.74/1.09 thf(f152,plain,(
% 5.74/1.09 ($true != $true) | ($true = (('const/realax/real_lt' @ (sK2 @ (sK5 @ sK1 @ sK4)) @ (sK3 @ (sK5 @ sK1 @ sK4))))) | (sK4 = 'const/sets/EMPTY' @ sK1)),
% 5.74/1.09 inference(constrained_superposition,[],[f29,f42])).
% 5.74/1.09 thf(f153,plain,(
% 5.74/1.09 ($true = (('const/realax/real_lt' @ (sK2 @ (sK5 @ sK1 @ sK4)) @ (sK3 @ (sK5 @ sK1 @ sK4))))) | (sK4 = 'const/sets/EMPTY' @ sK1)),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f152])).
% 5.74/1.09 thf(f154,plain,(
% 5.74/1.09 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true != (('const/realax/real_lt' @ (X0 @ (sK5 @ sK1 @ sK4)) @ (X1 @ (sK5 @ sK1 @ sK4))))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ X1 @ X0) @ sK4))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ X0) @ ('const/iterate/sum' @ sK1 @ sK4 @ X1)))) | (sK4 = 'const/sets/EMPTY' @ sK1)) )),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f151])).
% 5.74/1.09 thf(f155,plain,(
% 5.74/1.09 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true != (('const/realax/real_lt' @ (X0 @ (sK5 @ sK1 @ sK4)) @ (X1 @ (sK5 @ sK1 @ sK4))))) | ($true != (('const/realax/real_le' @ (X0 @ (sK0 @ sK1 @ sK4 @ X1 @ X0)) @ (X1 @ (sK0 @ sK1 @ sK4 @ X1 @ X0))))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ X0) @ ('const/iterate/sum' @ sK1 @ sK4 @ X1)))) | (sK4 = 'const/sets/EMPTY' @ sK1)) )),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f150])).
% 5.74/1.09 thf(f156,plain,(
% 5.74/1.09 ($true = (('const/realax/real_lt' @ (sK2 @ (sK5 @ sK1 @ sK4)) @ (sK3 @ (sK5 @ sK1 @ sK4)))))),
% 5.74/1.09 inference(forward_subsumption_resolution,[],[f153,f28])).
% 5.74/1.09 thf(f157,plain,(
% 5.74/1.09 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true != (('const/realax/real_lt' @ (X0 @ (sK5 @ sK1 @ sK4)) @ (X1 @ (sK5 @ sK1 @ sK4))))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ X1 @ X0) @ sK4))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ X0) @ ('const/iterate/sum' @ sK1 @ sK4 @ X1))))) )),
% 5.74/1.09 inference(forward_subsumption_resolution,[],[f154,f28])).
% 5.74/1.09 thf(f158,plain,(
% 5.74/1.09 ( ! [X0 : (sK1 > 'type/realax/real'),X1 : (sK1 > 'type/realax/real')] : (($true != (('const/realax/real_lt' @ (X0 @ (sK5 @ sK1 @ sK4)) @ (X1 @ (sK5 @ sK1 @ sK4))))) | ($true != (('const/realax/real_le' @ (X0 @ (sK0 @ sK1 @ sK4 @ X1 @ X0)) @ (X1 @ (sK0 @ sK1 @ sK4 @ X1 @ X0))))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ X0) @ ('const/iterate/sum' @ sK1 @ sK4 @ X1))))) )),
% 5.74/1.09 inference(forward_subsumption_resolution,[],[f155,f28])).
% 5.74/1.09 thf(f219,plain,(
% 5.74/1.09 ( ! [X0 : (sK1 > sK1),X1 : (sK1 > sK1)] : (($true != $true) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))) @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))) @ sK4))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))))))) | (((sK5 @ sK1 @ sK4)) != ((X1 @ (sK5 @ sK1 @ sK4)))) | (((sK5 @ sK1 @ sK4)) != ((X0 @ (sK5 @ sK1 @ sK4))))) )),
% 5.74/1.09 inference(constrained_superposition,[],[f157,f156])).
% 5.74/1.09 thf(f224,plain,(
% 5.74/1.09 ( ! [X0 : (sK1 > sK1),X1 : (sK1 > sK1)] : ((((sK5 @ sK1 @ sK4)) != ((X1 @ (sK5 @ sK1 @ sK4)))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))))))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))) @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))) @ sK4))) | (((sK5 @ sK1 @ sK4)) != ((X0 @ (sK5 @ sK1 @ sK4))))) )),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f219])).
% 5.74/1.09 thf(f230,plain,(
% 5.74/1.09 ( ! [X2 : sK1,X0 : (sK1 > sK1),X1 : (sK1 > sK1)] : (($true != $true) | ($true != (('const/realax/real_le' @ ((^[Y0 : sK1]: (sK2 @ (X0 @ Y0))) @ (sK0 @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))) @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0))))) @ ((^[Y0 : sK1]: (sK3 @ (X1 @ Y0))) @ (sK0 @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))) @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))))))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))))))) | ($false = (('const/sets/IN' @ sK1 @ X2 @ sK4))) | (((X1 @ (sK5 @ sK1 @ sK4))) != X2) | (((X0 @ (sK5 @ sK1 @ sK4))) != X2)) )),
% 5.74/1.09 inference(constrained_superposition,[],[f158,f65])).
% 5.74/1.09 thf(f239,plain,(
% 5.74/1.09 ( ! [X2 : sK1,X0 : (sK1 > sK1),X1 : (sK1 > sK1)] : (($true != (('const/realax/real_le' @ ((^[Y0 : sK1]: (sK2 @ (X0 @ Y0))) @ (sK0 @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))) @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0))))) @ ((^[Y0 : sK1]: (sK3 @ (X1 @ Y0))) @ (sK0 @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))) @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))))))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))))))) | ($false = (('const/sets/IN' @ sK1 @ X2 @ sK4))) | (((X1 @ (sK5 @ sK1 @ sK4))) != X2) | (((X0 @ (sK5 @ sK1 @ sK4))) != X2)) )),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f230])).
% 5.74/1.09 thf(f240,plain,(
% 5.74/1.09 ( ! [X2 : sK1,X0 : (sK1 > sK1),X1 : (sK1 > sK1)] : (($true != (('const/realax/real_le' @ (sK2 @ (X0 @ (sK0 @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))) @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))))) @ (sK3 @ (X1 @ (sK0 @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))) @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0))))))))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ (X1 @ Y0))))))) | ($false = (('const/sets/IN' @ sK1 @ X2 @ sK4))) | (((X1 @ (sK5 @ sK1 @ sK4))) != X2) | (((X0 @ (sK5 @ sK1 @ sK4))) != X2)) )),
% 5.74/1.09 inference(beta-eta_normalization,[],[f239])).
% 5.74/1.09 thf(f1035,plain,(
% 5.74/1.09 ( ! [X0 : (sK1 > sK1)] : (($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ ((^[Y1 : sK1]: (Y1)) @ Y0))))))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ ((^[Y1 : sK1]: (Y1)) @ Y0))) @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))) @ sK4))) | (((sK5 @ sK1 @ sK4)) != ((X0 @ (sK5 @ sK1 @ sK4))))) )),
% 5.74/1.09 inference(equality_resolution,[],[f224])).
% 5.74/1.09 thf(f1038,plain,(
% 5.74/1.09 ( ! [X0 : (sK1 > sK1)] : ((((sK5 @ sK1 @ sK4)) != ((X0 @ (sK5 @ sK1 @ sK4)))) | ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ sK3 @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))) @ sK4))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK2 @ (X0 @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK4 @ sK3))))) )),
% 5.74/1.09 inference(beta-eta_normalization,[],[f1035])).
% 5.74/1.09 thf(f1045,plain,(
% 5.74/1.09 ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ sK3 @ (^[Y0 : sK1]: (sK2 @ ((^[Y1 : sK1]: (Y1)) @ Y0)))) @ sK4))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK2 @ ((^[Y1 : sK1]: (Y1)) @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK4 @ sK3))))),
% 5.74/1.09 inference(equality_resolution,[],[f1038])).
% 5.74/1.09 thf(f1048,plain,(
% 5.74/1.09 ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ sK3 @ sK2) @ sK4))) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ sK2) @ ('const/iterate/sum' @ sK1 @ sK4 @ sK3))))),
% 5.74/1.09 inference(beta-eta_normalization,[],[f1045])).
% 5.74/1.09 thf(f1052,plain,(
% 5.74/1.09 ($true = (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK4 @ sK3 @ sK2) @ sK4)))),
% 5.74/1.09 inference(forward_subsumption_resolution,[],[f1048,f30])).
% 5.74/1.09 thf(f1081,plain,(
% 5.74/1.09 ($true != $true) | ($true = (('const/realax/real_lt' @ (sK2 @ (sK0 @ sK1 @ sK4 @ sK3 @ sK2)) @ (sK3 @ (sK0 @ sK1 @ sK4 @ sK3 @ sK2)))))),
% 5.74/1.09 inference(constrained_superposition,[],[f29,f1052])).
% 5.74/1.09 thf(f1082,plain,(
% 5.74/1.09 ($true = (('const/realax/real_lt' @ (sK2 @ (sK0 @ sK1 @ sK4 @ sK3 @ sK2)) @ (sK3 @ (sK0 @ sK1 @ sK4 @ sK3 @ sK2)))))),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f1081])).
% 5.74/1.09 thf(f1150,plain,(
% 5.74/1.09 ($true != $true) | ($true = (('const/realax/real_le' @ (sK2 @ (sK0 @ sK1 @ sK4 @ sK3 @ sK2)) @ (sK3 @ (sK0 @ sK1 @ sK4 @ sK3 @ sK2)))))),
% 5.74/1.09 inference(constrained_superposition,[],[f25,f1082])).
% 5.74/1.09 thf(f1208,plain,(
% 5.74/1.09 ($true = (('const/realax/real_le' @ (sK2 @ (sK0 @ sK1 @ sK4 @ sK3 @ sK2)) @ (sK3 @ (sK0 @ sK1 @ sK4 @ sK3 @ sK2)))))),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f1150])).
% 5.74/1.09 thf(f2730,plain,(
% 5.74/1.09 ( ! [X0 : sK1] : (($true != $true) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK2 @ ((^[Y1 : sK1]: (Y1)) @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ ((^[Y1 : sK1]: (Y1)) @ Y0))))))) | ($false = (('const/sets/IN' @ sK1 @ X0 @ sK4))) | ((((^[Y0 : sK1]: (Y0)) @ (sK5 @ sK1 @ sK4))) != X0) | ((((^[Y0 : sK1]: (Y0)) @ (sK5 @ sK1 @ sK4))) != X0)) )),
% 5.74/1.09 inference(constrained_superposition,[],[f240,f1208])).
% 5.74/1.09 thf(f2744,plain,(
% 5.74/1.09 ( ! [X0 : sK1] : (($true != $true) | ($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK2 @ ((^[Y1 : sK1]: (Y1)) @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ ((^[Y1 : sK1]: (Y1)) @ Y0))))))) | ($false = (('const/sets/IN' @ sK1 @ X0 @ sK4))) | ((((^[Y0 : sK1]: (Y0)) @ (sK5 @ sK1 @ sK4))) != X0)) )),
% 5.74/1.09 inference(duplicate_literal_removal,[],[f2730])).
% 5.74/1.09 thf(f2745,plain,(
% 5.74/1.09 ( ! [X0 : sK1] : (($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK2 @ ((^[Y1 : sK1]: (Y1)) @ Y0)))) @ ('const/iterate/sum' @ sK1 @ sK4 @ (^[Y0 : sK1]: (sK3 @ ((^[Y1 : sK1]: (Y1)) @ Y0))))))) | ($false = (('const/sets/IN' @ sK1 @ X0 @ sK4))) | ((((^[Y0 : sK1]: (Y0)) @ (sK5 @ sK1 @ sK4))) != X0)) )),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f2744])).
% 5.74/1.09 thf(f2746,plain,(
% 5.74/1.09 ( ! [X0 : sK1] : (($true = (('const/realax/real_lt' @ ('const/iterate/sum' @ sK1 @ sK4 @ sK2) @ ('const/iterate/sum' @ sK1 @ sK4 @ sK3)))) | ($false = (('const/sets/IN' @ sK1 @ X0 @ sK4))) | (((sK5 @ sK1 @ sK4)) != X0)) )),
% 5.74/1.09 inference(beta-eta_normalization,[],[f2745])).
% 5.74/1.09 thf(f2758,plain,(
% 5.74/1.09 ( ! [X0 : sK1] : ((((sK5 @ sK1 @ sK4)) != X0) | ($false = (('const/sets/IN' @ sK1 @ X0 @ sK4)))) )),
% 5.74/1.09 inference(forward_subsumption_resolution,[],[f2746,f30])).
% 5.74/1.09 thf(f2765,plain,(
% 5.74/1.09 ($false = (('const/sets/IN' @ sK1 @ (sK5 @ sK1 @ sK4) @ sK4)))),
% 5.74/1.09 inference(equality_resolution,[],[f2758])).
% 5.74/1.09 thf(f2793,plain,(
% 5.74/1.09 ($true = $false) | (sK4 = 'const/sets/EMPTY' @ sK1)),
% 5.74/1.09 inference(constrained_superposition,[],[f42,f2765])).
% 5.74/1.09 thf(f2801,plain,(
% 5.74/1.09 (sK4 = 'const/sets/EMPTY' @ sK1)),
% 5.74/1.09 inference(trivial_inequality_removal,[],[f2793])).
% 5.74/1.09 thf(f2804,plain,(
% 5.74/1.09 $false),
% 5.74/1.09 inference(forward_subsumption_resolution,[],[f2801,f28])).
% 5.74/1.09 % SZS output end Proof for theBenchmark
% 5.74/1.09 % (1469454)------------------------------
% 5.74/1.09 % (1469454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.74/1.09 % (1469454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.74/1.09 % (1469454)CaDiCaL version: 2.1.3
% 5.74/1.09 % (1469454)Termination reason: Refutation
% 5.74/1.09 % (1469454)Time elapsed: 0.377 s
% 5.74/1.09 % (1469454)Peak memory usage: 14 MB
% 5.74/1.09 % (1469454)Instructions burned: 787 (million)
% 5.74/1.09 % (1469410)Success in time 0.876 s
% 5.74/1.09 % Vampire exiting
%------------------------------------------------------------------------------