%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN984^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:42:04 AM UTC 2026
% Result : Theorem 0.22s 0.34s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN984^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.19 % Computer : n017.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 16:15:07 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.23 Running first-order model finding
% 0.11/0.23 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
% 0.22/0.33 % (528004)Will run a generic schedule for satisfiability detection.
% 0.22/0.33 % (528026)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=260904245:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.33 % (528026)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.33 % (528026)Refutation not found, incomplete strategy
% 0.22/0.33 % (528026)------------------------------
% 0.22/0.33 % (528026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (528026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (528026)CaDiCaL version: 2.1.3
% 0.22/0.33 % (528026)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (528026)Time elapsed: 0.001 s
% 0.22/0.33 % (528026)Peak memory usage: 12 MB
% 0.22/0.33 % (528026)Instructions burned: 1 (million)
% 0.22/0.33 % (528026)------------------------------
% 0.22/0.33 % (528026)------------------------------
% 0.22/0.33 % (528023)% WARNING: option uhcvi not known.
% 0.22/0.33 % (528022)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2261328077_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.33 % (528023)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1422049019:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.33 % (528025)dis+10_1_sil=32000:sp=arity:random_seed=3236995028:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.33 % (528024)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3561970567:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.33 % (528023)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.33 % Exception at run slice level
% 0.22/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.33 % (528023)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.33 % (528028)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3363698895:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.33 % (528027)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=338738976:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.33 % (528023)Refutation not found, incomplete strategy
% 0.22/0.33 % (528023)------------------------------
% 0.22/0.33 % (528023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (528023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (528025)Refutation not found, incomplete strategy
% 0.22/0.33 % (528025)------------------------------
% 0.22/0.33 % (528025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (528023)CaDiCaL version: 2.1.3
% 0.22/0.33 % (528025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (528023)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (528023)Time elapsed: 0.002 s
% 0.22/0.33 % (528023)Peak memory usage: 12 MB
% 0.22/0.33 % (528025)CaDiCaL version: 2.1.3
% 0.22/0.33 % (528023)Instructions burned: 1 (million)
% 0.22/0.33 % (528025)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (528025)Time elapsed: 0.001 s
% 0.22/0.33 % (528025)Peak memory usage: 12 MB
% 0.22/0.33 % (528025)Instructions burned: 1 (million)
% 0.22/0.33 % (528028)Refutation not found, incomplete strategy
% 0.22/0.33 % (528028)------------------------------
% 0.22/0.33 % (528028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (528028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (528028)CaDiCaL version: 2.1.3
% 0.22/0.33 % (528028)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (528028)Time elapsed: 0.001 s
% 0.22/0.33 % (528028)Peak memory usage: 12 MB
% 0.22/0.33 % (528028)Instructions burned: 1 (million)
% 0.22/0.33 % (528027)Refutation not found, incomplete strategy
% 0.22/0.33 % (528027)------------------------------
% 0.22/0.33 % (528027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (528027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (528027)CaDiCaL version: 2.1.3
% 0.22/0.33 % (528027)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.33 % (528027)Time elapsed: 0.001 s
% 0.22/0.33 % (528027)Peak memory usage: 12 MB
% 0.22/0.34 % (528027)Instructions burned: 1 (million)
% 0.22/0.34 % (528024)Refutation not found, incomplete strategy
% 0.22/0.34 % (528024)------------------------------
% 0.22/0.34 % (528024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (528024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (528024)CaDiCaL version: 2.1.3
% 0.22/0.34 % (528024)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.34 % (528024)Time elapsed: 0.002 s
% 0.22/0.34 % (528024)Peak memory usage: 12 MB
% 0.22/0.34 % (528024)Instructions burned: 1 (million)
% 0.22/0.34 % (528023)------------------------------
% 0.22/0.34 % (528023)------------------------------
% 0.22/0.34 % (528025)------------------------------
% 0.22/0.34 % (528025)------------------------------
% 0.22/0.34 % (528028)------------------------------
% 0.22/0.34 % (528028)------------------------------
% 0.22/0.34 % (528027)------------------------------
% 0.22/0.34 % (528027)------------------------------
% 0.22/0.34 % (528024)------------------------------
% 0.22/0.34 % (528024)------------------------------
% 0.22/0.34 % (528039)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2567985820:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.34 % Exception at run slice level
% 0.22/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.34 % (528058)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1127043259:i=889:ins=1_2999 on theBenchmark for (2999ds/889Mi)
% 0.22/0.34 % Exception at run slice level
% 0.22/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.34 % (528049)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1262634144:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.34 % (528049)Refutation not found, incomplete strategy
% 0.22/0.34 % (528049)------------------------------
% 0.22/0.34 % (528049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (528049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (528049)CaDiCaL version: 2.1.3
% 0.22/0.34 % (528049)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.34 % (528049)Time elapsed: 0.002 s
% 0.22/0.34 % (528049)Peak memory usage: 12 MB
% 0.22/0.34 % (528049)Instructions burned: 1 (million)
% 0.22/0.34 % (528052)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=2051242713:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.22/0.34 % (528053)ott-21_1_sil=16000:fs=off:random_seed=2080031850:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.22/0.34 % (528054)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4186425690:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.22/0.34 % (528056)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=121630658:i=1179_2999 on theBenchmark for (2999ds/1179Mi)
% 0.22/0.34 % (528052)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.34 % (528055)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1368168870:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 0.22/0.34 % (528052)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.34 % (528049)------------------------------
% 0.22/0.34 % (528049)------------------------------
% 0.22/0.34 % Exception at run slice level
% 0.22/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.34 % (528052)Refutation not found, incomplete strategy
% 0.22/0.34 % (528052)------------------------------
% 0.22/0.34 % (528052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (528052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (528052)CaDiCaL version: 2.1.3
% 0.22/0.34 % (528052)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.34 % (528052)Time elapsed: 0.002 s
% 0.22/0.34 % (528052)Peak memory usage: 12 MB
% 0.22/0.34 % (528052)Instructions burned: 1 (million)
% 0.22/0.34 % (528052)------------------------------
% 0.22/0.34 % (528052)------------------------------
% 0.22/0.34 % (528056)Refutation not found, incomplete strategy
% 0.22/0.34 % (528056)------------------------------
% 0.22/0.34 % (528056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (528056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (528056)CaDiCaL version: 2.1.3
% 0.22/0.34 % (528056)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.34 % (528056)Time elapsed: 0.002 s
% 0.22/0.34 % (528056)Peak memory usage: 12 MB
% 0.22/0.34 % (528056)Instructions burned: 2 (million)
% 0.22/0.34 % (528054)Refutation not found, incomplete strategy
% 0.22/0.34 % (528054)------------------------------
% 0.22/0.34 % (528054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (528054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (528054)CaDiCaL version: 2.1.3
% 0.22/0.34 % (528054)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.34 % (528054)Time elapsed: 0.003 s
% 0.22/0.34 % (528054)Peak memory usage: 12 MB
% 0.22/0.34 % (528054)Instructions burned: 3 (million)
% 0.22/0.34 % (528056)------------------------------
% 0.22/0.34 % (528056)------------------------------
% 0.22/0.34 % (528054)------------------------------
% 0.22/0.34 % (528054)------------------------------
% 0.22/0.34 % (528062)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=1914966762:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2999 on theBenchmark for (2999ds/692Mi)
% 0.22/0.34 % (528062)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.34 % (528062)Refutation not found, incomplete strategy
% 0.22/0.34 % (528062)------------------------------
% 0.22/0.34 % (528062)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (528062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (528062)CaDiCaL version: 2.1.3
% 0.22/0.34 % (528062)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.34 % (528062)Time elapsed: 0.001 s
% 0.22/0.34 % (528062)Peak memory usage: 12 MB
% 0.22/0.34 % (528062)Instructions burned: 1 (million)
% 0.22/0.34 % (528062)------------------------------
% 0.22/0.34 % (528062)------------------------------
% 0.22/0.34 % (528072)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=112141916:i=879:kws=inv_precedence:fsr=off_2999 on theBenchmark for (2999ds/879Mi)
% 0.22/0.34 % (528074)fmb+10_1_sil=64000:random_seed=3024405921:i=22061:nm=2:gsp=on_2999 on theBenchmark for (2999ds/22061Mi)
% 0.22/0.34 % (528072)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.34 % (528074)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.34 % Exception at run slice level
% 0.22/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.34 % (528075)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3542953108:i=9515:nm=5_2999 on theBenchmark for (2999ds/9515Mi)
% 0.22/0.34 % (528072)Refutation not found, incomplete strategy
% 0.22/0.34 % (528072)------------------------------
% 0.22/0.34 % (528072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (528072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (528072)CaDiCaL version: 2.1.3
% 0.22/0.34 % (528072)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.34 % (528072)Time elapsed: 0.002 s
% 0.22/0.34 % (528072)Peak memory usage: 12 MB
% 0.22/0.34 % (528072)Instructions burned: 1 (million)
% 0.22/0.34 % Exception at run slice level
% 0.22/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.34 % (528077)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1544717200:fmbsr=1.7:i=920_2999 on theBenchmark for (2999ds/920Mi)
% 0.22/0.34 % (528072)------------------------------
% 0.22/0.34 % (528072)------------------------------
% 0.22/0.34 % Exception at run slice level
% 0.22/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.34 % (528078)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1175256783:i=5131_2999 on theBenchmark for (2999ds/5131Mi)
% 0.22/0.34 % (528078)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.34 % (528078)Refutation not found, incomplete strategy
% 0.22/0.34 % (528078)------------------------------
% 0.22/0.34 % (528078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (528078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (528078)CaDiCaL version: 2.1.3
% 0.22/0.34 % (528078)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.34 % (528078)Time elapsed: 0.001 s
% 0.22/0.34 % (528078)Peak memory usage: 12 MB
% 0.22/0.34 % (528078)Instructions burned: 1 (million)
% 0.22/0.34 % (528082)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=782460568:i=1472:ins=7:fdi=8:gsp=on_2999 on theBenchmark for (2999ds/1472Mi)
% 0.22/0.34 % (528078)------------------------------
% 0.22/0.34 % (528078)------------------------------
% 0.22/0.34 % (528082)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.34 % (528082)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.34 % (528082) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-528004-528082"...
% 0.22/0.34 % (528090)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3554689349:i=6324_2999 on theBenchmark for (2999ds/6324Mi)
% 0.22/0.34 % Exception at run slice level
% 0.22/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.34 % (528082)...printing done.
% 0.22/0.34 % (528082)Refutation found. Thanks to Tanya!
% 0.22/0.34 % SZS status Theorem for theBenchmark
% 0.22/0.34 % SZS output start Proof for theBenchmark
% 0.22/0.34 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.34 thf(func_def_0, type, a: $o).
% 0.22/0.34 thf(func_def_1, type, b: $o).
% 0.22/0.34 thf(func_def_2, type, p: (($i > $o) > $o)).
% 0.22/0.34 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.34 thf(func_def_7, type, vAND: ($o > $o > $o)).
% 0.22/0.34 thf(func_def_8, type, sP0: ($o > $o)).
% 0.22/0.34 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.22/0.34 thf(func_def_10, type, sF1: !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.22/0.34 thf(func_def_11, type, sF2: ($o > $i > $o)).
% 0.22/0.34 thf(func_def_12, type, sF3: ($o > $o)).
% 0.22/0.34 thf(func_def_13, type, sF4: !>[X0: $tType]:(($o > ($o > X0) > X0))).
% 0.22/0.34 thf(func_def_14, type, sF5: !>[X0: $tType, X1: $tType]:((((X0 > X1) > X1) > (X0 > X1) > X1))).
% 0.22/0.34 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.34 thf(func_def_16, type, sK6: ($o > $i)).
% 0.22/0.34 thf(func_def_17, type, sF7: (($o > $o) > $o > $o)).
% 0.22/0.34 thf(func_def_19, type, sF9: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > X0 > X1 > X2))).
% 0.22/0.34 thf(func_def_20, type, sF10: ($o > $o)).
% 0.22/0.34 thf(func_def_21, type, sF11: (($o > $o) > $o)).
% 0.22/0.34 thf(func_def_22, type, sF12: $o).
% 0.22/0.34 thf(f1,conjecture,(
% 0.22/0.34 ((p @ (^[X0 : $i] : (b))) & (p @ (^[X0 : $i] : (a)))) => (p @ (^[X0 : $i] : (b & a)))),
% 0.22/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm)).
% 0.22/0.34 thf(f2,negated_conjecture,(
% 0.22/0.34 ~(((p @ (^[X0 : $i] : (b))) & (p @ (^[X0 : $i] : (a)))) => (p @ (^[X0 : $i] : (b & a))))),
% 0.22/0.34 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.34 thf(f3,plain,(
% 0.22/0.34 ~(((p @ (^[X0 : $i] : (b))) & (p @ (^[X1 : $i] : (a)))) => (p @ (^[X2 : $i] : (b & a))))),
% 0.22/0.34 inference(rectify,[],[f2])).
% 0.22/0.34 thf(f4,plain,(
% 0.22/0.34 ~((($true = ((p @ (^[Y0 : $i]: (b))))) & (((p @ (^[Y0 : $i]: (a)))) = $true)) => ($true = ((p @ (^[Y0 : $i]: (a & b))))))),
% 0.22/0.34 inference(fool_elimination,[],[f3])).
% 0.22/0.34 thf(f5,plain,(
% 0.22/0.34 ($true != ((p @ (^[Y0 : $i]: (a & b))))) & (($true = ((p @ (^[Y0 : $i]: (b))))) & (((p @ (^[Y0 : $i]: (a)))) = $true))),
% 0.22/0.34 inference(ennf_transformation,[],[f4])).
% 0.22/0.34 thf(f6,plain,(
% 0.22/0.34 ($true != ((p @ (^[Y0 : $i]: (a & b))))) & ($true = ((p @ (^[Y0 : $i]: (b))))) & (((p @ (^[Y0 : $i]: (a)))) = $true)),
% 0.22/0.34 inference(flattening,[],[f5])).
% 0.22/0.34 thf(f7,plain,(
% 0.22/0.34 (((p @ (^[Y0 : $i]: (a)))) = $true)),
% 0.22/0.34 inference(cnf_transformation,[],[f6])).
% 0.22/0.34 thf(f8,plain,(
% 0.22/0.34 ($true = ((p @ (^[Y0 : $i]: (b)))))),
% 0.22/0.34 inference(cnf_transformation,[],[f6])).
% 0.22/0.34 thf(f9,plain,(
% 0.22/0.34 ($true != ((p @ (^[Y0 : $i]: (a & b)))))),
% 0.22/0.34 inference(cnf_transformation,[],[f6])).
% 0.22/0.34 thf(f11,definition,(
% 0.22/0.34 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.22/0.34 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.22/0.34 thf(f12,definition,(
% 0.22/0.34 ($false = ((sP0 @ (p @ (^[Y0 : $i]: (a & b))))))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction])).
% 0.22/0.34 thf(f13,plain,(
% 0.22/0.34 ($true = ((sP0 @ $true)))),
% 0.22/0.34 inference(inequality_splitting,[],[f9,f12])).
% 0.22/0.34 thf(f18,definition,(
% 0.22/0.34 ( ! [X0 : $o] : ((((sF3 @ X0)) = ((p @ (^[Y0 : $i]: (X0)))))) )),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 0.22/0.34 thf(f19,plain,(
% 0.22/0.34 ( ! [X0 : $o] : ((((p @ (^[Y0 : $i]: (X0)))) = ((sF3 @ X0)))) )),
% 0.22/0.34 inference(reorient_equations,[],[f18])).
% 0.22/0.34 thf(f20,plain,(
% 0.22/0.34 ( ! [X0 : $o] : (($true = ((p @ (^[Y0 : $i]: (X0))))) | ($false = ((sF3 @ X0)))) )),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f19])).
% 0.22/0.34 thf(f21,plain,(
% 0.22/0.34 ( ! [X0 : $o] : (($false = ((p @ (^[Y0 : $i]: (X0))))) | ($true = ((sF3 @ X0)))) )),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f19])).
% 0.22/0.34 thf(f28,plain,(
% 0.22/0.34 ( ! [X0 : $o] : ((((sP0 @ X0)) = X0) | ($false = X0)) )),
% 0.22/0.34 inference(constrained_superposition,[],[f13,f11])).
% 0.22/0.34 thf(f30,plain,(
% 0.22/0.34 ( ! [X0 : $o] : (($true = ((sP0 @ X0))) | ($false = X0) | ($false = X0)) )),
% 0.22/0.34 inference(iff_proxy_clausification,[],[f28])).
% 0.22/0.34 thf(f32,plain,(
% 0.22/0.34 ( ! [X0 : $o] : (($true = ((sP0 @ X0))) | ($false = X0)) )),
% 0.22/0.34 inference(duplicate_literal_removal,[],[f30])).
% 0.22/0.34 thf(f40,plain,(
% 0.22/0.34 ($true = $false) | (((p @ (^[Y0 : $i]: (a & b)))) = $false)),
% 0.22/0.34 inference(constrained_superposition,[],[f32,f12])).
% 0.22/0.34 thf(f41,plain,(
% 0.22/0.34 (((p @ (^[Y0 : $i]: (a & b)))) = $false)),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f40])).
% 0.22/0.34 thf(f63,plain,(
% 0.22/0.34 ( ! [X0 : $o] : (($true = $false) | ($false = ((sF3 @ (X0 & b)))) | ((^[Y0 : $i]: (a)) != (^[Y0 : $i]: (X0)))) )),
% 0.22/0.34 inference(constrained_superposition,[],[f41,f20])).
% 0.22/0.34 thf(f65,plain,(
% 0.22/0.34 ( ! [X0 : $o] : (((^[Y0 : $i]: (a)) != (^[Y0 : $i]: (X0))) | ($false = ((sF3 @ (X0 & b))))) )),
% 0.22/0.34 inference(trivial_inequality_removal,[],[f63])).
% 0.22/0.34 thf(f70,plain,(
% 0.22/0.34 ($false = ((sF3 @ (a & b))))),
% 0.22/0.34 inference(equality_resolution,[],[f65])).
% 0.22/0.34 thf(f81,definition,(
% 0.22/0.34 spl8_2 <=> (a = $false)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.22/0.34 thf(f83,plain,(
% 0.22/0.34 (a = $false) | ~spl8_2),
% 0.22/0.34 inference(avatar_component_clause,[],[f81])).
% 0.22/0.34 thf(f98,plain,(
% 0.22/0.34 ($false = ((sF3 @ $true))) | (((a & b)) = $false)),
% 0.22/0.34 inference(constrained_superposition,[],[f70,f11])).
% 0.22/0.34 thf(f101,plain,(
% 0.22/0.34 ($false = ((sF3 @ $true))) | (b = $false) | (a = $false)),
% 0.22/0.34 inference(and_proxy_clausification,[],[f98])).
% 0.22/0.34 thf(f109,definition,(
% 0.22/0.34 spl8_5 <=> (b = $false)),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition])).
% 0.22/0.34 thf(f110,plain,(
% 0.22/0.34 (b != $false) | spl8_5),
% 0.22/0.34 inference(avatar_component_clause,[],[f109])).
% 0.22/0.34 thf(f111,plain,(
% 0.22/0.34 (b = $false) | ~spl8_5),
% 0.22/0.34 inference(avatar_component_clause,[],[f109])).
% 0.22/0.34 thf(f113,definition,(
% 0.22/0.34 spl8_6 <=> ($false = ((sF3 @ $true)))),
% 0.22/0.34 introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition])).
% 0.22/0.34 thf(f115,plain,(
% 0.22/0.34 ($false = ((sF3 @ $true))) | ~spl8_6),
% 0.22/0.34 inference(avatar_component_clause,[],[f113])).
% 0.22/0.34 thf(f119,plain,(
% 0.22/0.34 ($false = ((sF3 @ (a & $false)))) | ~spl8_5),
% 0.22/0.34 inference(constrained_superposition,[],[f70,f111])).
% 0.22/0.34 thf(f120,plain,(
% 0.22/0.34 ($false = ((sF3 @ $false))) | ~spl8_5),
% 0.22/0.34 inference(boolean_simplification,[],[f119])).
% 0.22/0.34 thf(f145,plain,(
% 0.22/0.34 ($true = $false) | ($true = ((sF3 @ b)))),
% 0.22/0.34 inference(constrained_superposition,[],[f21,f8])).
% 0.22/0.34 thf(f147,plain,(
% 0.22/0.35 ($true = $false) | ($true = ((sF3 @ a)))),
% 0.22/0.35 inference(constrained_superposition,[],[f7,f21])).
% 0.22/0.35 thf(f148,plain,(
% 0.22/0.35 ($true = $false) | ($true = ((sF3 @ b)))),
% 0.22/0.35 inference(constrained_superposition,[],[f8,f21])).
% 0.22/0.35 thf(f150,plain,(
% 0.22/0.35 ($true = ((sF3 @ b)))),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f148])).
% 0.22/0.35 thf(f151,plain,(
% 0.22/0.35 ($true = ((sF3 @ a)))),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f147])).
% 0.22/0.35 thf(f153,plain,(
% 0.22/0.35 ($true = ((sF3 @ b)))),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f145])).
% 0.22/0.35 thf(f171,plain,(
% 0.22/0.35 ($true = ((sF3 @ $false))) | ~spl8_5),
% 0.22/0.35 inference(forward_demodulation,[],[f153,f111])).
% 0.22/0.35 thf(f175,plain,(
% 0.22/0.35 ($true = $false) | ~spl8_5),
% 0.22/0.35 inference(forward_demodulation,[],[f171,f120])).
% 0.22/0.35 thf(f176,plain,(
% 0.22/0.35 $false | ~spl8_5),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f175])).
% 0.22/0.35 thf(f177,plain,(
% 0.22/0.35 ~spl8_5),
% 0.22/0.35 inference(avatar_contradiction_clause,[],[f176])).
% 0.22/0.35 thf(f180,plain,(
% 0.22/0.35 ($false = ((sF3 @ $true))) | (a = $false) | spl8_5),
% 0.22/0.35 inference(forward_subsumption_resolution,[],[f101,f110])).
% 0.22/0.35 thf(f193,plain,(
% 0.22/0.35 spl8_2 | spl8_6 | spl8_5),
% 0.22/0.35 inference(avatar_split_clause,[],[f180,f109,f113,f81])).
% 0.22/0.35 thf(f195,plain,(
% 0.22/0.35 ($false = ((sF3 @ ($false & b)))) | ~spl8_2),
% 0.22/0.35 inference(constrained_superposition,[],[f70,f83])).
% 0.22/0.35 thf(f200,plain,(
% 0.22/0.35 ($false = ((sF3 @ $false))) | ~spl8_2),
% 0.22/0.35 inference(boolean_simplification,[],[f195])).
% 0.22/0.35 thf(f206,plain,(
% 0.22/0.35 ($true = ((sF3 @ $true))) | (b = $false)),
% 0.22/0.35 inference(constrained_superposition,[],[f150,f11])).
% 0.22/0.35 thf(f207,plain,(
% 0.22/0.35 ($true = ((sF3 @ $true))) | spl8_5),
% 0.22/0.35 inference(forward_subsumption_resolution,[],[f206,f110])).
% 0.22/0.35 thf(f208,plain,(
% 0.22/0.35 ($true = $false) | (spl8_5 | ~spl8_6)),
% 0.22/0.35 inference(forward_demodulation,[],[f207,f115])).
% 0.22/0.35 thf(f209,plain,(
% 0.22/0.35 $false | (spl8_5 | ~spl8_6)),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f208])).
% 0.22/0.35 thf(f210,plain,(
% 0.22/0.35 spl8_5 | ~spl8_6),
% 0.22/0.35 inference(avatar_contradiction_clause,[],[f209])).
% 0.22/0.35 thf(f214,plain,(
% 0.22/0.35 ($true = ((sF3 @ $false))) | ~spl8_2),
% 0.22/0.35 inference(constrained_superposition,[],[f151,f83])).
% 0.22/0.35 thf(f218,plain,(
% 0.22/0.35 ($true = $false) | ~spl8_2),
% 0.22/0.35 inference(forward_demodulation,[],[f214,f200])).
% 0.22/0.35 thf(f219,plain,(
% 0.22/0.35 $false | ~spl8_2),
% 0.22/0.35 inference(trivial_inequality_removal,[],[f218])).
% 0.22/0.35 thf(f220,plain,(
% 0.22/0.35 ~spl8_2),
% 0.22/0.35 inference(avatar_contradiction_clause,[],[f219])).
% 0.22/0.35 cnf(s8, plain, ~spl8_5, inference(sat_conversion,[],[f177])).
% 0.22/0.35 cnf(s11, plain, spl8_2 | spl8_5 | spl8_6, inference(sat_conversion,[],[f193])).
% 0.22/0.35 cnf(s12, plain, spl8_5 | ~spl8_6, inference(sat_conversion,[],[f210])).
% 0.22/0.35 cnf(s13, plain, ~spl8_2, inference(sat_conversion,[],[f220])).
% 0.22/0.35 cnf(s14, plain, spl8_5 | spl8_6, inference(rat,[],[s11,s13])).
% 0.22/0.35 cnf(s16, plain, ~spl8_6, inference(rat,[],[s12,s8])).
% 0.22/0.35 cnf(s17, plain, $false, inference(rat,[],[s14,s16,s8])).
% 0.22/0.35 thf(f221,plain,(
% 0.22/0.35 $false),
% 0.22/0.35 inference(avatar_sat_refutation,[],[s17])).
% 0.22/0.35 % SZS output end Proof for theBenchmark
% 0.22/0.35 % (528082)------------------------------
% 0.22/0.35 % (528082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (528082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (528082)CaDiCaL version: 2.1.3
% 0.22/0.35 % (528082)Termination reason: Refutation
% 0.22/0.35 % (528082)Time elapsed: 0.011 s
% 0.22/0.35 % (528082)Peak memory usage: 13 MB
% 0.22/0.35 % (528082)Instructions burned: 15 (million)
% 0.22/0.35 % (528004)Success in time 0.108 s
% 0.22/0.35 % Vampire exiting
%------------------------------------------------------------------------------