%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PLA032^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 08:20:26 AM UTC 2026
% Result : Theorem 8.22s 1.41s
% Output : Refutation 8.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PLA032^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n006.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:20:09 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.29/1.00 % (695244)Will run a generic schedule for satisfiability detection.
% 4.29/1.00 % (695251)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3516223203:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.29/1.00 % (695250)% WARNING: option uhcvi not known.
% 4.29/1.00 % (695249)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3311877715_2999 on theBenchmark for (2999ds/0Mi)
% 4.29/1.00 % (695250)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3865312547:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.29/1.00 % (695253)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1125825686:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.29/1.00 % (695252)dis+10_1_sil=32000:sp=arity:random_seed=2786238154:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.29/1.00 % (695250)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.29/1.00 % (695253)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.29/1.00 % Exception at run slice level
% 4.29/1.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.29/1.00 % (695250)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.29/1.00 % (695255)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2753037012:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.29/1.00 % (695254)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1950717359:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.29/1.00 % (695261)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3810712715:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.29/1.00 % Exception at run slice level
% 4.29/1.00 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 4.29/1.00 % (695265)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=197763786:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.29/1.00 % (695253)Instruction limit reached!
% 4.29/1.00 % (695253)------------------------------
% 4.29/1.00 % (695253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.00 % (695253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.00 % (695253)CaDiCaL version: 2.1.3
% 4.29/1.00 % (695253)Termination reason: Instruction limit
% 4.29/1.00 % (695253)Termination phase: Saturation
% 4.29/1.00 % (695253)Time elapsed: 0.059 s
% 4.29/1.00 % (695253)Peak memory usage: 12 MB
% 4.29/1.00 % (695253)Instructions burned: 118 (million)
% 4.29/1.00 % (695252)Instruction limit reached!
% 4.29/1.00 % (695252)------------------------------
% 4.29/1.00 % (695252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.00 % (695252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.00 % (695252)CaDiCaL version: 2.1.3
% 4.29/1.00 % (695252)Termination reason: Instruction limit
% 4.29/1.00 % (695252)Termination phase: Saturation
% 4.29/1.00 % (695252)Time elapsed: 0.067 s
% 4.29/1.00 % (695252)Peak memory usage: 12 MB
% 4.29/1.00 % (695252)Instructions burned: 104 (million)
% 4.29/1.00 % (695267)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=710262091:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 4.29/1.00 % (695267)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 4.29/1.00 % (695267)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 4.29/1.00 % (695268)ott-21_1_sil=16000:fs=off:random_seed=1927423750:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 4.29/1.00 % (695254)Instruction limit reached!
% 4.29/1.00 % (695254)------------------------------
% 4.29/1.00 % (695254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.00 % (695254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.00 % (695254)CaDiCaL version: 2.1.3
% 4.29/1.00 % (695254)Termination reason: Instruction limit
% 4.29/1.00 % (695254)Termination phase: Saturation
% 4.29/1.00 % (695254)Time elapsed: 0.071 s
% 4.29/1.00 % (695254)Peak memory usage: 12 MB
% 4.29/1.00 % (695254)Instructions burned: 132 (million)
% 4.29/1.00 % (695255)Instruction limit reached!
% 4.29/1.00 % (695255)------------------------------
% 8.22/1.41 % (695255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.41 % (695255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.41 % (695255)CaDiCaL version: 2.1.3
% 8.22/1.41 % (695255)Termination reason: Instruction limit
% 8.22/1.41 % (695255)Termination phase: Saturation
% 8.22/1.41 % (695255)Time elapsed: 0.085 s
% 8.22/1.41 % (695255)Peak memory usage: 12 MB
% 8.22/1.41 % (695255)Instructions burned: 160 (million)
% 8.22/1.41 % (695265)Instruction limit reached!
% 8.22/1.41 % (695265)------------------------------
% 8.22/1.41 % (695265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.41 % (695265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.41 % (695265)CaDiCaL version: 2.1.3
% 8.22/1.41 % (695265)Termination reason: Instruction limit
% 8.22/1.41 % (695265)Termination phase: Saturation
% 8.22/1.41 % (695265)Time elapsed: 0.070 s
% 8.22/1.41 % (695265)Peak memory usage: 12 MB
% 8.22/1.41 % (695265)Instructions burned: 135 (million)
% 8.22/1.41 % (695272)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2698200259:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 8.22/1.41 % Exception at run slice level
% 8.22/1.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.22/1.41 % (695271)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2886480255:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 8.22/1.41 % (695273)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1824010514:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 8.22/1.41 % (695275)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4176256347:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 8.22/1.41 % Exception at run slice level
% 8.22/1.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.22/1.41 % (695279)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=4166924799: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)
% 8.22/1.41 % (695279)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.22/1.41 % (695268)Instruction limit reached!
% 8.22/1.41 % (695268)------------------------------
% 8.22/1.41 % (695268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.41 % (695268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.41 % (695268)CaDiCaL version: 2.1.3
% 8.22/1.41 % (695268)Termination reason: Instruction limit
% 8.22/1.41 % (695268)Termination phase: Saturation
% 8.22/1.41 % (695268)Time elapsed: 0.091 s
% 8.22/1.41 % (695268)Peak memory usage: 12 MB
% 8.22/1.41 % (695268)Instructions burned: 180 (million)
% 8.22/1.41 % (695281)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4033728929:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 8.22/1.41 % (695281)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.22/1.41 % (695267)Instruction limit reached!
% 8.22/1.41 % (695267)------------------------------
% 8.22/1.41 % (695267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.41 % (695267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.41 % (695267)CaDiCaL version: 2.1.3
% 8.22/1.41 % (695267)Termination reason: Instruction limit
% 8.22/1.41 % (695267)Termination phase: Saturation
% 8.22/1.41 % (695267)Time elapsed: 0.276 s
% 8.22/1.41 % (695267)Peak memory usage: 13 MB
% 8.22/1.41 % (695267)Instructions burned: 686 (million)
% 8.22/1.41 % (695283)fmb+10_1_sil=64000:random_seed=1906646741:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 8.22/1.41 % (695283)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.22/1.41 % Exception at run slice level
% 8.22/1.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.22/1.41 % (695285)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3420476825:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 8.22/1.41 % Exception at run slice level
% 8.22/1.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.22/1.41 % (695287)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1726735343:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 8.22/1.41 % Exception at run slice level
% 8.22/1.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.22/1.41 % (695289)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=115232831:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 8.22/1.41 % (695289)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.22/1.41 % (695279)Instruction limit reached!
% 8.22/1.41 % (695279)------------------------------
% 8.22/1.41 % (695279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.41 % (695279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.41 % (695279)CaDiCaL version: 2.1.3
% 8.22/1.41 % (695279)Termination reason: Instruction limit
% 8.22/1.41 % (695279)Termination phase: Saturation
% 8.22/1.41 % (695279)Time elapsed: 0.290 s
% 8.22/1.41 % (695279)Peak memory usage: 13 MB
% 8.22/1.41 % (695279)Instructions burned: 694 (million)
% 8.22/1.41 % (695291)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=4161703269:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 8.22/1.41 % (695291)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.22/1.41 % (695291)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.22/1.41 % (695271)Instruction limit reached!
% 8.22/1.41 % (695271)------------------------------
% 8.22/1.41 % (695271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.41 % (695271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.41 % (695271)CaDiCaL version: 2.1.3
% 8.22/1.41 % (695271)Termination reason: Instruction limit
% 8.22/1.41 % (695271)Termination phase: Saturation
% 8.22/1.41 % (695271)Time elapsed: 0.372 s
% 8.22/1.41 % (695271)Peak memory usage: 13 MB
% 8.22/1.41 % (695271)Instructions burned: 477 (million)
% 8.22/1.41 % (695293)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3684350446:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 8.22/1.41 % Exception at run slice level
% 8.22/1.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.22/1.41 % (695295)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=821958891:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 8.22/1.41 % Exception at run slice level
% 8.22/1.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.22/1.41 % (695297)ott-2_1_sil=16000:newcnf=on:random_seed=1134469122:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 8.22/1.41 % (695297)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.22/1.41 % (695281)Instruction limit reached!
% 8.22/1.41 % (695281)------------------------------
% 8.22/1.41 % (695281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.41 % (695281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.41 % (695281)CaDiCaL version: 2.1.3
% 8.22/1.41 % (695281)Termination reason: Instruction limit
% 8.22/1.41 % (695281)Termination phase: Saturation
% 8.22/1.41 % (695281)Time elapsed: 0.464 s
% 8.22/1.41 % (695281)Peak memory usage: 13 MB
% 8.22/1.41 % (695281)Instructions burned: 881 (million)
% 8.22/1.41 % (695299)ott+10_1_sil=32000:tgt=ground:random_seed=2593266240:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 8.22/1.41 % (695273)Instruction limit reached!
% 8.22/1.41 % (695273)------------------------------
% 8.22/1.41 % (695273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.41 % (695273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.41 % (695273)CaDiCaL version: 2.1.3
% 8.22/1.41 % (695273)Termination reason: Instruction limit
% 8.22/1.41 % (695273)Termination phase: Saturation
% 8.22/1.41 % (695273)Time elapsed: 0.559 s
% 8.22/1.41 % (695273)Peak memory usage: 13 MB
% 8.22/1.41 % (695273)Instructions burned: 1179 (million)
% 8.22/1.41 % (695301)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3875522291:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 8.22/1.41 % Exception at run slice level
% 8.22/1.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.22/1.41 % (695303)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1913414530:i=3512:aac=none_2992 on theBenchmark for (2992ds/3512Mi)
% 8.22/1.41 % (695303)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.22/1.41 % (695297)Instruction limit reached!
% 8.22/1.41 % (695297)------------------------------
% 8.22/1.41 % (695297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.41 % (695297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.41 % (695297)CaDiCaL version: 2.1.3
% 8.22/1.41 % (695297)Termination reason: Instruction limit
% 8.22/1.41 % (695297)Termination phase: Saturation
% 8.22/1.41 % (695297)Time elapsed: 0.451 s
% 8.22/1.41 % (695297)Peak memory usage: 13 MB
% 8.22/1.41 % (695297)Instructions burned: 870 (million)
% 8.22/1.41 % (695306)dis+21_1_sil=32000:sas=cadical:random_seed=3976851265:i=3773:amm=off_2989 on theBenchmark for (2989ds/3773Mi)
% 8.22/1.41 % (695303) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-695244-695303"...
% 8.22/1.41 % (695303)...printing done.
% 8.22/1.41 % (695303)Refutation found. Thanks to Tanya!
% 8.22/1.41 % SZS status Theorem for theBenchmark
% 8.22/1.41 % SZS output start Proof for theBenchmark
% 8.22/1.41 thf(type_def_5, type, mu: $tType).
% 8.22/1.41 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 8.22/1.41 thf(func_def_0, type, qmltpeq: (mu > mu > $i > $o)).
% 8.22/1.41 thf(func_def_1, type, meq_prop: (($i > $o) > ($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_3, type, mnot: (($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_4, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_5, type, mbox: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_6, type, mforall_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_7, type, mtrue: ($i > $o)).
% 8.22/1.41 thf(func_def_8, type, mfalse: ($i > $o)).
% 8.22/1.41 thf(func_def_9, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_10, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_11, type, mimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_12, type, mequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_13, type, mxor: (($i > $o) > ($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_14, type, mdia: (($i > $i > $o) > ($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_15, type, exists_in_world: (mu > $i > $o)).
% 8.22/1.41 thf(func_def_16, type, mforall_ind: ((mu > $i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_17, type, mexists_ind: ((mu > $i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_18, type, mexists_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_19, type, mreflexive: (($i > $i > $o) > $o)).
% 8.22/1.41 thf(func_def_20, type, msymmetric: (($i > $i > $o) > $o)).
% 8.22/1.41 thf(func_def_21, type, mserial: (($i > $i > $o) > $o)).
% 8.22/1.41 thf(func_def_22, type, mtransitive: (($i > $i > $o) > $o)).
% 8.22/1.41 thf(func_def_23, type, meuclidean: (($i > $i > $o) > $o)).
% 8.22/1.41 thf(func_def_24, type, mpartially_functional: (($i > $i > $o) > $o)).
% 8.22/1.41 thf(func_def_25, type, mfunctional: (($i > $i > $o) > $o)).
% 8.22/1.41 thf(func_def_26, type, mweakly_dense: (($i > $i > $o) > $o)).
% 8.22/1.41 thf(func_def_27, type, mweakly_connected: (($i > $i > $o) > $o)).
% 8.22/1.41 thf(func_def_28, type, mweakly_directed: (($i > $i > $o) > $o)).
% 8.22/1.41 thf(func_def_29, type, mvalid: (($i > $o) > $o)).
% 8.22/1.41 thf(func_def_30, type, msatisfiable: (($i > $o) > $o)).
% 8.22/1.41 thf(func_def_31, type, mcountersatisfiable: (($i > $o) > $o)).
% 8.22/1.41 thf(func_def_32, type, minvalid: (($i > $o) > $o)).
% 8.22/1.41 thf(func_def_33, type, rel_s4: ($i > $i > $o)).
% 8.22/1.41 thf(func_def_34, type, mbox_s4: (($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_35, type, mdia_s4: (($i > $o) > $i > $o)).
% 8.22/1.41 thf(func_def_36, type, defused: (mu > $i > $o)).
% 8.22/1.41 thf(func_def_37, type, h: (mu > $i > $o)).
% 8.22/1.41 thf(func_def_38, type, bomb: (mu > $i > $o)).
% 8.22/1.41 thf(func_def_39, type, db2: !>[X0: $tType]:(X0)).
% 8.22/1.41 thf(func_def_40, type, db0: !>[X0: $tType]:(X0)).
% 8.22/1.41 thf(func_def_41, type, db1: !>[X0: $tType]:(X0)).
% 8.22/1.41 thf(func_def_42, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 8.22/1.41 thf(func_def_43, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 8.22/1.41 thf(func_def_44, type, vNOT: ($o > $o)).
% 8.22/1.41 thf(func_def_45, type, vOR: ($o > $o > $o)).
% 8.22/1.41 thf(func_def_46, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 8.22/1.41 thf(func_def_47, type, db3: !>[X0: $tType]:(X0)).
% 8.22/1.41 thf(func_def_50, type, vIMP: ($o > $o > $o)).
% 8.22/1.41 thf(func_def_51, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 8.22/1.41 thf(func_def_52, type, vAND: ($o > $o > $o)).
% 8.22/1.41 thf(func_def_53, type, db4: !>[X0: $tType]:(X0)).
% 8.22/1.41 thf(func_def_54, type, sK0: ($i > mu)).
% 8.22/1.41 thf(func_def_57, type, sK3: mu).
% 8.22/1.41 thf(func_def_58, type, sK4: (mu > $i > mu)).
% 8.22/1.41 thf(func_def_59, type, sK5: ($i > mu)).
% 8.22/1.41 thf(func_def_60, type, sK6: ($i > mu)).
% 8.22/1.41 thf(f2,axiom,(
% 8.22/1.41 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot)).
% 8.22/1.41 thf(f3,axiom,(
% 8.22/1.41 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor)).
% 8.22/1.41 thf(f8,axiom,(
% 8.22/1.41 (mand = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mnot @ (mor @ (mnot @ X0) @ (mnot @ X1))))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mand)).
% 8.22/1.41 thf(f9,axiom,(
% 8.22/1.41 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies)).
% 8.22/1.41 thf(f15,axiom,(
% 8.22/1.41 (mforall_ind = (^[X0 : (mu > $i > $o), X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind)).
% 8.22/1.41 thf(f16,axiom,(
% 8.22/1.41 (mexists_ind = (^[X0 : (mu > $i > $o)] : ((mnot @ (mforall_ind @ (^[X1 : mu] : ((mnot @ (X0 @ X1)))))))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mexists_ind)).
% 8.22/1.41 thf(f18,axiom,(
% 8.22/1.41 (mreflexive = (^[X0 : ($i > $i > $o)] : (! [X1 : $i] : (X0 @ X1 @ X1))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mreflexive)).
% 8.22/1.41 thf(f21,axiom,(
% 8.22/1.41 (mtransitive = (^[X0 : ($i > $i > $o)] : (! [X1 : $i,X2 : $i,X3 : $i] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mtransitive)).
% 8.22/1.41 thf(f28,axiom,(
% 8.22/1.41 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid)).
% 8.22/1.41 thf(f32,axiom,(
% 8.22/1.41 (mbox_s4 = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4)).
% 8.22/1.41 thf(f34,axiom,(
% 8.22/1.41 (mreflexive @ rel_s4)),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1)).
% 8.22/1.41 thf(f35,axiom,(
% 8.22/1.41 (mtransitive @ rel_s4)),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a2)).
% 8.22/1.41 thf(f36,axiom,(
% 8.22/1.41 ! [X0 : mu,X1 : $i,X2 : $i] : (((rel_s4 @ X1 @ X2) & (exists_in_world @ X0 @ X1)) => (exists_in_world @ X0 @ X2))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/Axioms/LCL015^1.ax',cumulative_ax)).
% 8.22/1.41 thf(f39,axiom,(
% 8.22/1.41 (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : ((mexists_ind @ (^[X1 : mu] : ((mbox_s4 @ (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0)))))))))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3)).
% 8.22/1.41 thf(f40,conjecture,(
% 8.22/1.41 (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : ((mexists_ind @ (^[X1 : mu] : ((mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0))))))))))),
% 8.22/1.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 8.22/1.41 thf(f41,negated_conjecture,(
% 8.22/1.41 ~(mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : ((mexists_ind @ (^[X1 : mu] : ((mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0))))))))))),
% 8.22/1.41 inference(negated_conjecture,[status(cth)],[f40])).
% 8.22/1.41 thf(f43,plain,(
% 8.22/1.41 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 8.22/1.41 inference(rectify,[],[f2])).
% 8.22/1.41 thf(f44,plain,(
% 8.22/1.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 8.22/1.41 inference(fool_elimination,[],[f43])).
% 8.22/1.41 thf(f45,plain,(
% 8.22/1.41 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 8.22/1.41 inference(rectify,[],[f3])).
% 8.22/1.41 thf(f46,plain,(
% 8.22/1.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 8.22/1.41 inference(fool_elimination,[],[f45])).
% 8.22/1.41 thf(f52,plain,(
% 8.22/1.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 8.22/1.41 inference(fool_elimination,[],[f8])).
% 8.22/1.41 thf(f53,plain,(
% 8.22/1.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 8.22/1.41 inference(fool_elimination,[],[f9])).
% 8.22/1.41 thf(f60,plain,(
% 8.22/1.41 (mforall_ind = (^[X0 : (mu > $i > $o), X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 8.22/1.41 inference(rectify,[],[f15])).
% 8.22/1.41 thf(f61,plain,(
% 8.22/1.41 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 8.22/1.41 inference(fool_elimination,[],[f60])).
% 8.22/1.41 thf(f62,plain,(
% 8.22/1.41 (mexists_ind = (^[X0 : (mu > $i > $o)] : ((mnot @ (mforall_ind @ (^[X1 : mu] : ((mnot @ (X0 @ X1)))))))))),
% 8.22/1.41 inference(rectify,[],[f16])).
% 8.22/1.41 thf(f63,plain,(
% 8.22/1.41 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 8.22/1.41 inference(fool_elimination,[],[f62])).
% 8.22/1.41 thf(f66,plain,(
% 8.22/1.41 (mreflexive = (^[X0 : ($i > $i > $o)] : (! [X1 : $i] : (X0 @ X1 @ X1))))),
% 8.22/1.41 inference(rectify,[],[f18])).
% 8.22/1.41 thf(f67,plain,(
% 8.22/1.41 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 8.22/1.41 inference(fool_elimination,[],[f66])).
% 8.22/1.41 thf(f72,plain,(
% 8.22/1.41 (mtransitive = (^[X0 : ($i > $i > $o)] : (! [X1 : $i,X2 : $i,X3 : $i] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)))))),
% 8.22/1.41 inference(rectify,[],[f21])).
% 8.22/1.41 thf(f73,plain,(
% 8.22/1.41 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 8.22/1.41 inference(fool_elimination,[],[f72])).
% 8.22/1.41 thf(f86,plain,(
% 8.22/1.41 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 8.22/1.41 inference(rectify,[],[f28])).
% 8.22/1.41 thf(f87,plain,(
% 8.22/1.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 8.22/1.41 inference(fool_elimination,[],[f86])).
% 8.22/1.41 thf(f94,plain,(
% 8.22/1.41 (mbox_s4 = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))))),
% 8.22/1.41 inference(rectify,[],[f32])).
% 8.22/1.41 thf(f95,plain,(
% 8.22/1.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 8.22/1.41 inference(fool_elimination,[],[f94])).
% 8.22/1.41 thf(f97,plain,(
% 8.22/1.41 (mreflexive @ rel_s4)),
% 8.22/1.41 inference(rectify,[],[f34])).
% 8.22/1.41 thf(f98,plain,(
% 8.22/1.41 (((mreflexive @ rel_s4)) = $true)),
% 8.22/1.41 inference(fool_elimination,[],[f97])).
% 8.22/1.41 thf(f99,plain,(
% 8.22/1.41 (mtransitive @ rel_s4)),
% 8.22/1.41 inference(rectify,[],[f35])).
% 8.22/1.41 thf(f100,plain,(
% 8.22/1.41 (((mtransitive @ rel_s4)) = $true)),
% 8.22/1.41 inference(fool_elimination,[],[f99])).
% 8.22/1.41 thf(f101,plain,(
% 8.22/1.41 ! [X0 : mu,X1 : $i,X2 : $i] : (((rel_s4 @ X1 @ X2) & (exists_in_world @ X0 @ X1)) => (exists_in_world @ X0 @ X2))),
% 8.22/1.41 inference(rectify,[],[f36])).
% 8.22/1.41 thf(f102,plain,(
% 8.22/1.41 ! [X0 : mu,X1 : $i,X2 : $i] : (((((rel_s4 @ X1 @ X2)) = $true) & (((exists_in_world @ X0 @ X1)) = $true)) => (((exists_in_world @ X0 @ X2)) = $true))),
% 8.22/1.41 inference(fool_elimination,[],[f101])).
% 8.22/1.41 thf(f107,plain,(
% 8.22/1.41 (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : ((mexists_ind @ (^[X1 : mu] : ((mbox_s4 @ (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0)))))))))))),
% 8.22/1.41 inference(rectify,[],[f39])).
% 8.22/1.41 thf(f108,plain,(
% 8.22/1.41 ($true = ((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))))))),
% 8.22/1.41 inference(fool_elimination,[],[f107])).
% 8.22/1.41 thf(f109,plain,(
% 8.22/1.41 ~(mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : ((mexists_ind @ (^[X1 : mu] : ((mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0))))))))))),
% 8.22/1.41 inference(rectify,[],[f41])).
% 8.22/1.41 thf(f110,plain,(
% 8.22/1.41 ~ ($true = ((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 8.22/1.41 inference(fool_elimination,[],[f109])).
% 8.22/1.41 thf(f111,plain,(
% 8.22/1.41 ($true != ((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 8.22/1.41 inference(flattening,[],[f110])).
% 8.22/1.41 thf(f112,plain,(
% 8.22/1.41 ! [X0 : mu,X1 : $i,X2 : $i] : ((((exists_in_world @ X0 @ X2)) = $true) | ((((rel_s4 @ X1 @ X2)) != $true) | (((exists_in_world @ X0 @ X1)) != $true)))),
% 8.22/1.41 inference(ennf_transformation,[],[f102])).
% 8.22/1.41 thf(f113,plain,(
% 8.22/1.41 ! [X0 : mu,X1 : $i,X2 : $i] : ((((exists_in_world @ X0 @ X2)) = $true) | (((rel_s4 @ X1 @ X2)) != $true) | (((exists_in_world @ X0 @ X1)) != $true))),
% 8.22/1.41 inference(flattening,[],[f112])).
% 8.22/1.41 thf(f116,plain,(
% 8.22/1.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 8.22/1.41 inference(cnf_transformation,[],[f44])).
% 8.22/1.41 thf(f117,plain,(
% 8.22/1.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 8.22/1.41 inference(cnf_transformation,[],[f46])).
% 8.22/1.41 thf(f122,plain,(
% 8.22/1.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 8.22/1.41 inference(cnf_transformation,[],[f52])).
% 8.22/1.41 thf(f123,plain,(
% 8.22/1.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 8.22/1.41 inference(cnf_transformation,[],[f53])).
% 8.22/1.41 thf(f129,plain,(
% 8.22/1.41 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 8.22/1.41 inference(cnf_transformation,[],[f61])).
% 8.22/1.41 thf(f130,plain,(
% 8.22/1.41 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 8.22/1.41 inference(cnf_transformation,[],[f63])).
% 8.22/1.41 thf(f132,plain,(
% 8.22/1.41 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 8.22/1.41 inference(cnf_transformation,[],[f67])).
% 8.22/1.41 thf(f135,plain,(
% 8.22/1.41 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 8.22/1.41 inference(cnf_transformation,[],[f73])).
% 8.22/1.41 thf(f142,plain,(
% 8.22/1.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 8.22/1.41 inference(cnf_transformation,[],[f87])).
% 8.22/1.41 thf(f146,plain,(
% 8.22/1.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 8.22/1.41 inference(cnf_transformation,[],[f95])).
% 8.22/1.41 thf(f148,plain,(
% 8.22/1.41 (((mreflexive @ rel_s4)) = $true)),
% 8.22/1.41 inference(cnf_transformation,[],[f98])).
% 8.22/1.41 thf(f149,plain,(
% 8.22/1.41 (((mtransitive @ rel_s4)) = $true)),
% 8.22/1.41 inference(cnf_transformation,[],[f100])).
% 8.22/1.41 thf(f150,plain,(
% 8.22/1.41 ( ! [X2 : $i,X0 : mu,X1 : $i] : ((((exists_in_world @ X0 @ X1)) != $true) | (((rel_s4 @ X1 @ X2)) != $true) | (((exists_in_world @ X0 @ X2)) = $true)) )),
% 8.22/1.41 inference(cnf_transformation,[],[f113])).
% 8.22/1.41 thf(f153,plain,(
% 8.22/1.41 ($true = ((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))))))),
% 8.22/1.41 inference(cnf_transformation,[],[f108])).
% 8.22/1.41 thf(f154,plain,(
% 8.22/1.41 ($true != ((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 8.22/1.41 inference(cnf_transformation,[],[f111])).
% 8.22/1.41 thf(f156,definition,(
% 8.22/1.41 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 8.22/1.41 introduced(theory,[fool_exhaustiveness_axiom])).
% 8.22/1.41 thf(f158,plain,(
% 8.22/1.41 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 8.22/1.41 inference(definition_unfolding,[],[f122,f116,f117,f116,f116])).
% 8.22/1.41 thf(f159,plain,(
% 8.22/1.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 8.22/1.41 inference(definition_unfolding,[],[f123,f117,f116])).
% 8.22/1.41 thf(f164,plain,(
% 8.22/1.41 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))))),
% 8.22/1.41 inference(definition_unfolding,[],[f130,f116,f129,f116])).
% 8.22/1.41 thf(f167,plain,(
% 8.22/1.41 ($true = (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4)))),
% 8.22/1.41 inference(definition_unfolding,[],[f148,f132])).
% 8.22/1.41 thf(f168,plain,(
% 8.22/1.41 ($true = (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) @ rel_s4)))),
% 8.22/1.41 inference(definition_unfolding,[],[f149,f135])).
% 8.22/1.41 thf(f171,plain,(
% 8.22/1.41 ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ (Y1 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))))))),
% 8.22/1.41 inference(definition_unfolding,[],[f153,f142,f146,f129,f164,f146,f159,f158])).
% 8.22/1.41 thf(f172,plain,(
% 8.22/1.41 ($true != (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ (Y1 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 8.22/1.41 inference(definition_unfolding,[],[f154,f142,f146,f129,f164,f159,f158])).
% 8.22/1.41 thf(f173,plain,(
% 8.22/1.41 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ ((~ (~ ((~ (bomb @ Y2 @ Y1)) | (~ (h @ Y3 @ Y1))))) | (defused @ Y2 @ Y1)))))))))))))))))),
% 8.22/1.41 inference(beta-eta_normalization,[],[f172])).
% 8.22/1.41 thf(f174,plain,(
% 8.22/1.41 ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ ((~ (~ ((~ (bomb @ Y2 @ Y1)) | (~ (h @ Y3 @ Y1))))) | (defused @ Y2 @ Y1)))))))))))))) @ sK1)))),
% 8.22/1.41 inference(sigma_proxy_clausification,[],[f173])).
% 8.22/1.41 thf(f175,plain,(
% 8.22/1.41 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ ((~ (~ ((~ (bomb @ Y1 @ Y0)) | (~ (h @ Y2 @ Y0))))) | (defused @ Y1 @ Y0)))))))))))))))),
% 8.22/1.41 inference(beta-eta_normalization,[],[f174])).
% 8.22/1.41 thf(f176,plain,(
% 8.22/1.41 ($false = (((^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ ((~ (~ ((~ (bomb @ Y1 @ Y0)) | (~ (h @ Y2 @ Y0))))) | (defused @ Y1 @ Y0)))))))))))) @ sK2)))),
% 8.22/1.41 inference(sigma_proxy_clausification,[],[f175])).
% 8.22/1.41 thf(f177,plain,(
% 8.22/1.41 ($false = (((~ (rel_s4 @ sK1 @ sK2)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK2) => (~ ((~ (~ ((~ (bomb @ Y0 @ sK2)) | (~ (h @ Y1 @ sK2))))) | (defused @ Y0 @ sK2)))))))))))))),
% 8.22/1.41 inference(beta-eta_normalization,[],[f176])).
% 8.22/1.41 thf(f178,plain,(
% 8.22/1.41 ($false = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK2) => (~ ((~ (~ ((~ (bomb @ Y0 @ sK2)) | (~ (h @ Y1 @ sK2))))) | (defused @ Y0 @ sK2))))))))))))),
% 8.22/1.41 inference(or_proxy_clausification,[],[f177])).
% 8.22/1.41 thf(f179,plain,(
% 8.22/1.41 ($false = ((~ (rel_s4 @ sK1 @ sK2))))),
% 8.22/1.41 inference(or_proxy_clausification,[],[f177])).
% 8.22/1.41 thf(f180,plain,(
% 8.22/1.41 ($true = ((rel_s4 @ sK1 @ sK2)))),
% 8.22/1.41 inference(not_proxy_clausification,[],[f179])).
% 8.22/1.41 thf(f181,plain,(
% 8.22/1.41 ($false = (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK2) => (~ ((~ (~ ((~ (bomb @ Y0 @ sK2)) | (~ (h @ Y1 @ sK2))))) | (defused @ Y0 @ sK2))))))))) @ sK3)))),
% 8.22/1.41 inference(sigma_proxy_clausification,[],[f178])).
% 8.22/1.41 thf(f182,plain,(
% 8.22/1.41 ($false = (((exists_in_world @ sK3 @ sK2) => (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (~ ((~ (~ ((~ (bomb @ sK3 @ sK2)) | (~ (h @ Y0 @ sK2))))) | (defused @ sK3 @ sK2))))))))))),
% 8.22/1.41 inference(beta-eta_normalization,[],[f181])).
% 8.22/1.41 thf(f183,plain,(
% 8.22/1.41 ($false = ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (~ ((~ (~ ((~ (bomb @ sK3 @ sK2)) | (~ (h @ Y0 @ sK2))))) | (defused @ sK3 @ sK2)))))))))),
% 8.22/1.41 inference(imp_proxy_clausification,[],[f182])).
% 8.22/1.41 thf(f184,plain,(
% 8.22/1.41 ($true = ((exists_in_world @ sK3 @ sK2)))),
% 8.22/1.41 inference(imp_proxy_clausification,[],[f182])).
% 8.22/1.41 thf(f185,plain,(
% 8.22/1.41 ($true = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (~ ((~ (~ ((~ (bomb @ sK3 @ sK2)) | (~ (h @ Y0 @ sK2))))) | (defused @ sK3 @ sK2))))))))),
% 8.22/1.41 inference(not_proxy_clausification,[],[f183])).
% 8.22/1.41 thf(f186,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($true = (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK2) => (~ ((~ (~ ((~ (bomb @ sK3 @ sK2)) | (~ (h @ Y0 @ sK2))))) | (defused @ sK3 @ sK2))))) @ X1)))) )),
% 8.22/1.41 inference(pi_proxy_clausification,[],[f185])).
% 8.22/1.41 thf(f187,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($true = (((exists_in_world @ X1 @ sK2) => (~ ((~ (~ ((~ (bomb @ sK3 @ sK2)) | (~ (h @ X1 @ sK2))))) | (defused @ sK3 @ sK2))))))) )),
% 8.22/1.41 inference(beta-eta_normalization,[],[f186])).
% 8.22/1.41 thf(f188,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($false = ((exists_in_world @ X1 @ sK2))) | ($true = ((~ ((~ (~ ((~ (bomb @ sK3 @ sK2)) | (~ (h @ X1 @ sK2))))) | (defused @ sK3 @ sK2)))))) )),
% 8.22/1.41 inference(imp_proxy_clausification,[],[f187])).
% 8.22/1.41 thf(f189,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($false = ((exists_in_world @ X1 @ sK2))) | ($false = (((~ (~ ((~ (bomb @ sK3 @ sK2)) | (~ (h @ X1 @ sK2))))) | (defused @ sK3 @ sK2))))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f188])).
% 8.22/1.41 thf(f190,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($false = ((exists_in_world @ X1 @ sK2))) | ($false = ((defused @ sK3 @ sK2)))) )),
% 8.22/1.41 inference(or_proxy_clausification,[],[f189])).
% 8.22/1.41 thf(f191,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($false = ((exists_in_world @ X1 @ sK2))) | ($false = ((~ (~ ((~ (bomb @ sK3 @ sK2)) | (~ (h @ X1 @ sK2)))))))) )),
% 8.22/1.41 inference(or_proxy_clausification,[],[f189])).
% 8.22/1.41 thf(f192,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($false = ((exists_in_world @ X1 @ sK2))) | ($true = ((~ ((~ (bomb @ sK3 @ sK2)) | (~ (h @ X1 @ sK2))))))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f191])).
% 8.22/1.41 thf(f193,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($false = ((exists_in_world @ X1 @ sK2))) | ($false = (((~ (bomb @ sK3 @ sK2)) | (~ (h @ X1 @ sK2)))))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f192])).
% 8.22/1.41 thf(f194,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($false = ((exists_in_world @ X1 @ sK2))) | ($false = ((~ (h @ X1 @ sK2))))) )),
% 8.22/1.41 inference(or_proxy_clausification,[],[f193])).
% 8.22/1.41 thf(f195,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($false = ((exists_in_world @ X1 @ sK2))) | ($false = ((~ (bomb @ sK3 @ sK2))))) )),
% 8.22/1.41 inference(or_proxy_clausification,[],[f193])).
% 8.22/1.41 thf(f196,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($false = ((exists_in_world @ X1 @ sK2))) | ($true = ((bomb @ sK3 @ sK2)))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f195])).
% 8.22/1.41 thf(f197,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($false = ((exists_in_world @ X1 @ sK2))) | ($true = ((h @ X1 @ sK2)))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f194])).
% 8.22/1.41 thf(f198,plain,(
% 8.22/1.41 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y1 @ Y4)) | ((~ (~ ((~ (bomb @ Y2 @ Y4)) | (~ (h @ Y3 @ Y4))))) | (defused @ Y2 @ Y4))))))))))))))))))))),
% 8.22/1.41 inference(beta-eta_normalization,[],[f171])).
% 8.22/1.41 thf(f199,plain,(
% 8.22/1.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y1 @ Y4)) | ((~ (~ ((~ (bomb @ Y2 @ Y4)) | (~ (h @ Y3 @ Y4))))) | (defused @ Y2 @ Y4))))))))))))))))) @ X1)))) )),
% 8.22/1.41 inference(pi_proxy_clausification,[],[f198])).
% 8.22/1.41 thf(f200,plain,(
% 8.22/1.41 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y0 @ Y3)) | ((~ (~ ((~ (bomb @ Y1 @ Y3)) | (~ (h @ Y2 @ Y3))))) | (defused @ Y1 @ Y3))))))))))))))))))) )),
% 8.22/1.41 inference(beta-eta_normalization,[],[f199])).
% 8.22/1.41 thf(f201,plain,(
% 8.22/1.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y0 @ Y3)) | ((~ (~ ((~ (bomb @ Y1 @ Y3)) | (~ (h @ Y2 @ Y3))))) | (defused @ Y1 @ Y3))))))))))))))) @ X2)))) )),
% 8.22/1.41 inference(pi_proxy_clausification,[],[f200])).
% 8.22/1.41 thf(f202,plain,(
% 8.22/1.41 ( ! [X2 : $i,X1 : $i] : (($true = (((~ (rel_s4 @ X1 @ X2)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ X2 @ Y2)) | ((~ (~ ((~ (bomb @ Y0 @ Y2)) | (~ (h @ Y1 @ Y2))))) | (defused @ Y0 @ Y2))))))))))))))))) )),
% 8.22/1.41 inference(beta-eta_normalization,[],[f201])).
% 8.22/1.41 thf(f203,plain,(
% 8.22/1.41 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ X2 @ Y2)) | ((~ (~ ((~ (bomb @ Y0 @ Y2)) | (~ (h @ Y1 @ Y2))))) | (defused @ Y0 @ Y2))))))))))))))) | ($true = ((~ (rel_s4 @ X1 @ X2))))) )),
% 8.22/1.41 inference(or_proxy_clausification,[],[f202])).
% 8.22/1.41 thf(f204,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i] : (($true = (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ X2 @ Y2)) | ((~ (~ ((~ (bomb @ Y0 @ Y2)) | (~ (h @ Y1 @ Y2))))) | (defused @ Y0 @ Y2)))))))))))) @ X3))) | ($true = ((~ (rel_s4 @ X1 @ X2))))) )),
% 8.22/1.41 inference(pi_proxy_clausification,[],[f203])).
% 8.22/1.41 thf(f205,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i] : (($true = (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X2) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ X2 @ Y2)) | ((~ (~ ((~ (bomb @ Y0 @ Y2)) | (~ (h @ Y1 @ Y2))))) | (defused @ Y0 @ Y2)))))))))))) @ X3))) | (((rel_s4 @ X1 @ X2)) = $false)) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f204])).
% 8.22/1.41 thf(f206,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i] : (($true = (((exists_in_world @ X3 @ X2) => (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | ((~ (~ ((~ (bomb @ X3 @ Y1)) | (~ (h @ Y0 @ Y1))))) | (defused @ X3 @ Y1))))))))))))) | (((rel_s4 @ X1 @ X2)) = $false)) )),
% 8.22/1.41 inference(beta-eta_normalization,[],[f205])).
% 8.22/1.41 thf(f207,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = ((~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | ((~ (~ ((~ (bomb @ X3 @ Y1)) | (~ (h @ Y0 @ Y1))))) | (defused @ X3 @ Y1))))))))))))) )),
% 8.22/1.41 inference(imp_proxy_clausification,[],[f206])).
% 8.22/1.41 thf(f208,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($false = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | ((~ (~ ((~ (bomb @ X3 @ Y1)) | (~ (h @ Y0 @ Y1))))) | (defused @ X3 @ Y1)))))))))))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f207])).
% 8.22/1.41 thf(f209,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($false = (((^[Y0 : mu]: ((exists_in_world @ Y0 @ X2) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X2 @ Y1)) | ((~ (~ ((~ (bomb @ X3 @ Y1)) | (~ (h @ Y0 @ Y1))))) | (defused @ X3 @ Y1)))))))) @ (sK4 @ X3 @ X2))))) )),
% 8.22/1.41 inference(sigma_proxy_clausification,[],[f208])).
% 8.22/1.41 thf(f210,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($false = (((exists_in_world @ (sK4 @ X3 @ X2) @ X2) => (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | ((~ (~ ((~ (bomb @ X3 @ Y0)) | (~ (h @ (sK4 @ X3 @ X2) @ Y0))))) | (defused @ X3 @ Y0)))))))))) )),
% 8.22/1.41 inference(beta-eta_normalization,[],[f209])).
% 8.22/1.41 thf(f211,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | ((~ (~ ((~ (bomb @ X3 @ Y0)) | (~ (h @ (sK4 @ X3 @ X2) @ Y0))))) | (defused @ X3 @ Y0))))))))) )),
% 8.22/1.41 inference(imp_proxy_clausification,[],[f210])).
% 8.22/1.41 thf(f212,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i] : (($true = ((exists_in_world @ (sK4 @ X3 @ X2) @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($false = ((exists_in_world @ X3 @ X2)))) )),
% 8.22/1.41 inference(imp_proxy_clausification,[],[f210])).
% 8.22/1.41 thf(f213,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | ((~ (~ ((~ (bomb @ X3 @ Y0)) | (~ (h @ (sK4 @ X3 @ X2) @ Y0))))) | (defused @ X3 @ Y0)))))))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f211])).
% 8.22/1.41 thf(f214,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = (((^[Y0 : $i]: ((~ (rel_s4 @ X2 @ Y0)) | ((~ (~ ((~ (bomb @ X3 @ Y0)) | (~ (h @ (sK4 @ X3 @ X2) @ Y0))))) | (defused @ X3 @ Y0)))) @ X4)))) )),
% 8.22/1.41 inference(pi_proxy_clausification,[],[f213])).
% 8.22/1.41 thf(f215,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = (((~ (rel_s4 @ X2 @ X4)) | ((~ (~ ((~ (bomb @ X3 @ X4)) | (~ (h @ (sK4 @ X3 @ X2) @ X4))))) | (defused @ X3 @ X4)))))) )),
% 8.22/1.41 inference(beta-eta_normalization,[],[f214])).
% 8.22/1.41 thf(f216,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = (((~ (~ ((~ (bomb @ X3 @ X4)) | (~ (h @ (sK4 @ X3 @ X2) @ X4))))) | (defused @ X3 @ X4)))) | ($true = ((~ (rel_s4 @ X2 @ X4))))) )),
% 8.22/1.41 inference(or_proxy_clausification,[],[f215])).
% 8.22/1.41 thf(f217,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = ((defused @ X3 @ X4))) | ($true = ((~ (rel_s4 @ X2 @ X4)))) | ($true = ((~ (~ ((~ (bomb @ X3 @ X4)) | (~ (h @ (sK4 @ X3 @ X2) @ X4)))))))) )),
% 8.22/1.41 inference(or_proxy_clausification,[],[f216])).
% 8.22/1.41 thf(f218,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = ((defused @ X3 @ X4))) | ($false = ((rel_s4 @ X2 @ X4))) | ($true = ((~ (~ ((~ (bomb @ X3 @ X4)) | (~ (h @ (sK4 @ X3 @ X2) @ X4)))))))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f217])).
% 8.22/1.41 thf(f219,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = ((defused @ X3 @ X4))) | ($false = ((rel_s4 @ X2 @ X4))) | ($false = ((~ ((~ (bomb @ X3 @ X4)) | (~ (h @ (sK4 @ X3 @ X2) @ X4))))))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f218])).
% 8.22/1.41 thf(f220,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = ((defused @ X3 @ X4))) | ($false = ((rel_s4 @ X2 @ X4))) | ($true = (((~ (bomb @ X3 @ X4)) | (~ (h @ (sK4 @ X3 @ X2) @ X4)))))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f219])).
% 8.22/1.41 thf(f221,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = ((defused @ X3 @ X4))) | ($false = ((rel_s4 @ X2 @ X4))) | ($true = ((~ (h @ (sK4 @ X3 @ X2) @ X4)))) | ($true = ((~ (bomb @ X3 @ X4))))) )),
% 8.22/1.41 inference(or_proxy_clausification,[],[f220])).
% 8.22/1.41 thf(f222,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : $i] : (($false = ((exists_in_world @ X3 @ X2))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = ((defused @ X3 @ X4))) | ($false = ((rel_s4 @ X2 @ X4))) | ($false = ((h @ (sK4 @ X3 @ X2) @ X4))) | ($true = ((~ (bomb @ X3 @ X4))))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f221])).
% 8.22/1.41 thf(f223,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : mu,X1 : $i,X4 : $i] : (($false = ((h @ (sK4 @ X3 @ X2) @ X4))) | (((rel_s4 @ X1 @ X2)) = $false) | ($true = ((defused @ X3 @ X4))) | ($false = ((rel_s4 @ X2 @ X4))) | ($false = ((exists_in_world @ X3 @ X2))) | ($false = ((bomb @ X3 @ X4)))) )),
% 8.22/1.41 inference(not_proxy_clausification,[],[f222])).
% 8.22/1.41 thf(f263,plain,(
% 8.22/1.41 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y1) & (rel_s4 @ Y1 @ Y0)) => (rel_s4 @ Y2 @ Y0))))))))))),
% 8.22/1.41 inference(beta-eta_normalization,[],[f168])).
% 8.22/1.41 thf(f264,plain,(
% 8.22/1.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y1) & (rel_s4 @ Y1 @ Y0)) => (rel_s4 @ Y2 @ Y0))))))) @ X1)))) )),
% 8.22/1.41 inference(pi_proxy_clausification,[],[f263])).
% 8.22/1.41 thf(f265,plain,(
% 8.22/1.41 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ Y0) & (rel_s4 @ Y0 @ X1)) => (rel_s4 @ Y1 @ X1))))))))) )),
% 8.22/1.41 inference(beta-eta_normalization,[],[f264])).
% 8.22/1.41 thf(f266,plain,(
% 8.22/1.41 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ Y0) & (rel_s4 @ Y0 @ X1)) => (rel_s4 @ Y1 @ X1))))) @ X2)))) )),
% 8.22/1.41 inference(pi_proxy_clausification,[],[f265])).
% 8.22/1.41 thf(f267,plain,(
% 8.22/1.41 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ Y0 @ X2) & (rel_s4 @ X2 @ X1)) => (rel_s4 @ Y0 @ X1))))))) )),
% 8.22/1.41 inference(beta-eta_normalization,[],[f266])).
% 8.22/1.41 thf(f268,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (((rel_s4 @ Y0 @ X2) & (rel_s4 @ X2 @ X1)) => (rel_s4 @ Y0 @ X1))) @ X3)))) )),
% 8.22/1.41 inference(pi_proxy_clausification,[],[f267])).
% 8.22/1.41 thf(f269,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((((rel_s4 @ X3 @ X2) & (rel_s4 @ X2 @ X1)) => (rel_s4 @ X3 @ X1))))) )),
% 8.22/1.41 inference(beta-eta_normalization,[],[f268])).
% 8.22/1.41 thf(f270,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (((rel_s4 @ X3 @ X2) & (rel_s4 @ X2 @ X1)))) | ($true = ((rel_s4 @ X3 @ X1)))) )),
% 8.22/1.41 inference(imp_proxy_clausification,[],[f269])).
% 8.22/1.41 thf(f271,plain,(
% 8.22/1.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((rel_s4 @ X2 @ X1))) | ($true = ((rel_s4 @ X3 @ X1))) | ($false = ((rel_s4 @ X3 @ X2)))) )),
% 8.22/1.41 inference(and_proxy_clausification,[],[f270])).
% 8.22/1.41 thf(f272,plain,(
% 8.22/1.41 ($true = ((!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)))))),
% 8.22/1.41 inference(beta-eta_normalization,[],[f167])).
% 8.22/1.41 thf(f273,plain,(
% 8.22/1.41 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1)))) )),
% 8.22/1.41 inference(pi_proxy_clausification,[],[f272])).
% 8.22/1.41 thf(f274,plain,(
% 8.22/1.41 ( ! [X1 : $i] : (($true = ((rel_s4 @ X1 @ X1)))) )),
% 8.22/1.41 inference(beta-eta_normalization,[],[f273])).
% 8.22/1.41 thf(f276,definition,(
% 8.22/1.41 spl7_1 <=> ($true = ((bomb @ sK3 @ sK2)))),
% 8.22/1.41 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 8.22/1.41 thf(f277,plain,(
% 8.22/1.41 ($true = ((bomb @ sK3 @ sK2))) | ~spl7_1),
% 8.22/1.41 inference(avatar_component_clause,[],[f276])).
% 8.22/1.41 thf(f279,definition,(
% 8.22/1.41 spl7_2 <=> ! [X1 : mu] : ($false = ((exists_in_world @ X1 @ sK2)))),
% 8.22/1.41 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 8.22/1.41 thf(f280,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($false = ((exists_in_world @ X1 @ sK2)))) ) | ~spl7_2),
% 8.22/1.41 inference(avatar_component_clause,[],[f279])).
% 8.22/1.41 thf(f281,plain,(
% 8.22/1.41 spl7_1 | spl7_2),
% 8.22/1.41 inference(avatar_split_clause,[],[f196,f279,f276])).
% 8.22/1.41 thf(f283,definition,(
% 8.22/1.41 spl7_3 <=> ($false = ((defused @ sK3 @ sK2)))),
% 8.22/1.41 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 8.22/1.41 thf(f284,plain,(
% 8.22/1.41 ($false = ((defused @ sK3 @ sK2))) | ~spl7_3),
% 8.22/1.41 inference(avatar_component_clause,[],[f283])).
% 8.22/1.41 thf(f285,plain,(
% 8.22/1.41 spl7_3 | spl7_2),
% 8.22/1.41 inference(avatar_split_clause,[],[f190,f279,f283])).
% 8.22/1.41 thf(f293,plain,(
% 8.22/1.41 ($true = $false) | ~spl7_2),
% 8.22/1.41 inference(constrained_superposition,[],[f280,f184])).
% 8.22/1.41 thf(f299,plain,(
% 8.22/1.41 $false | ~spl7_2),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f293])).
% 8.22/1.41 thf(f300,plain,(
% 8.22/1.41 ~spl7_2),
% 8.22/1.41 inference(avatar_contradiction_clause,[],[f299])).
% 8.22/1.41 thf(f305,plain,(
% 8.22/1.41 ( ! [X2 : $i,X0 : mu,X1 : $i] : (($true != $true) | (((rel_s4 @ X1 @ X2)) != $true) | (((exists_in_world @ X0 @ X2)) = $true) | (((exists_in_world @ X0 @ X1)) = $false)) )),
% 8.22/1.41 inference(constrained_superposition,[],[f150,f156])).
% 8.22/1.41 thf(f306,plain,(
% 8.22/1.41 ( ! [X2 : $i,X0 : mu,X1 : $i] : ((((rel_s4 @ X1 @ X2)) != $true) | (((exists_in_world @ X0 @ X2)) = $true) | (((exists_in_world @ X0 @ X1)) = $false)) )),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f305])).
% 8.22/1.41 thf(f322,plain,(
% 8.22/1.41 ( ! [X0 : $i] : (($true = $false) | ($true = ((rel_s4 @ X0 @ sK2))) | ($false = ((rel_s4 @ X0 @ sK1)))) )),
% 8.22/1.41 inference(constrained_superposition,[],[f180,f271])).
% 8.22/1.41 thf(f333,plain,(
% 8.22/1.41 ( ! [X0 : $i] : (($true = ((rel_s4 @ X0 @ sK2))) | ($false = ((rel_s4 @ X0 @ sK1)))) )),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f322])).
% 8.22/1.41 thf(f371,definition,(
% 8.22/1.41 spl7_5 <=> ! [X0 : $i] : ($false = ((rel_s4 @ X0 @ sK1)))),
% 8.22/1.41 introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition])).
% 8.22/1.41 thf(f372,plain,(
% 8.22/1.41 ( ! [X0 : $i] : (($false = ((rel_s4 @ X0 @ sK1)))) ) | ~spl7_5),
% 8.22/1.41 inference(avatar_component_clause,[],[f371])).
% 8.22/1.41 thf(f392,plain,(
% 8.22/1.41 ($true = $false) | ~spl7_5),
% 8.22/1.41 inference(constrained_superposition,[],[f372,f274])).
% 8.22/1.41 thf(f403,plain,(
% 8.22/1.41 $false | ~spl7_5),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f392])).
% 8.22/1.41 thf(f404,plain,(
% 8.22/1.41 ~spl7_5),
% 8.22/1.41 inference(avatar_contradiction_clause,[],[f403])).
% 8.22/1.41 thf(f429,plain,(
% 8.22/1.41 ( ! [X2 : mu,X0 : $i,X1 : $i] : (($true != $true) | (((exists_in_world @ X2 @ X1)) = $true) | ($false = ((exists_in_world @ X2 @ X0))) | ($false = ((rel_s4 @ X0 @ X1)))) )),
% 8.22/1.41 inference(constrained_superposition,[],[f306,f156])).
% 8.22/1.41 thf(f430,plain,(
% 8.22/1.41 ( ! [X2 : mu,X0 : $i,X1 : $i] : ((((exists_in_world @ X2 @ X1)) = $true) | ($false = ((exists_in_world @ X2 @ X0))) | ($false = ((rel_s4 @ X0 @ X1)))) )),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f429])).
% 8.22/1.41 thf(f436,plain,(
% 8.22/1.41 ( ! [X0 : $i,X1 : mu] : (($true = $false) | ($true = ((exists_in_world @ (sK4 @ X1 @ sK2) @ sK2))) | ($false = ((exists_in_world @ X1 @ sK2))) | ($false = ((rel_s4 @ X0 @ sK1)))) )),
% 8.22/1.41 inference(constrained_superposition,[],[f212,f333])).
% 8.22/1.41 thf(f447,plain,(
% 8.22/1.41 ( ! [X0 : $i,X1 : mu] : (($true = ((exists_in_world @ (sK4 @ X1 @ sK2) @ sK2))) | ($false = ((exists_in_world @ X1 @ sK2))) | ($false = ((rel_s4 @ X0 @ sK1)))) )),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f436])).
% 8.22/1.41 thf(f450,definition,(
% 8.22/1.41 spl7_7 <=> ! [X1 : mu] : (($true = ((exists_in_world @ (sK4 @ X1 @ sK2) @ sK2))) | ($false = ((exists_in_world @ X1 @ sK2))))),
% 8.22/1.41 introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition])).
% 8.22/1.41 thf(f451,plain,(
% 8.22/1.41 ( ! [X1 : mu] : (($true = ((exists_in_world @ (sK4 @ X1 @ sK2) @ sK2))) | ($false = ((exists_in_world @ X1 @ sK2)))) ) | ~spl7_7),
% 8.22/1.41 inference(avatar_component_clause,[],[f450])).
% 8.22/1.41 thf(f453,plain,(
% 8.22/1.41 spl7_5 | spl7_7),
% 8.22/1.41 inference(avatar_split_clause,[],[f447,f450,f371])).
% 8.22/1.41 thf(f596,definition,(
% 8.22/1.41 spl7_8 <=> ! [X0 : mu] : (($false = ((exists_in_world @ X0 @ sK2))) | ($true = ((h @ (sK4 @ X0 @ sK2) @ sK2))))),
% 8.22/1.41 introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition])).
% 8.22/1.41 thf(f597,plain,(
% 8.22/1.41 ( ! [X0 : mu] : (($true = ((h @ (sK4 @ X0 @ sK2) @ sK2))) | ($false = ((exists_in_world @ X0 @ sK2)))) ) | ~spl7_8),
% 8.22/1.41 inference(avatar_component_clause,[],[f596])).
% 8.22/1.41 thf(f689,plain,(
% 8.22/1.41 ( ! [X2 : $i,X0 : $i,X1 : mu] : (($true = $false) | ($false = ((h @ (sK4 @ X1 @ X0) @ X2))) | ($true = ((defused @ X1 @ X2))) | ($false = ((rel_s4 @ X0 @ X2))) | (((exists_in_world @ X1 @ X0)) = $false) | ($false = ((bomb @ X1 @ X2)))) )),
% 8.22/1.41 inference(constrained_superposition,[],[f274,f223])).
% 8.22/1.41 thf(f698,plain,(
% 8.22/1.41 ( ! [X2 : $i,X0 : $i,X1 : mu] : (($false = ((h @ (sK4 @ X1 @ X0) @ X2))) | ($true = ((defused @ X1 @ X2))) | ($false = ((rel_s4 @ X0 @ X2))) | (((exists_in_world @ X1 @ X0)) = $false) | ($false = ((bomb @ X1 @ X2)))) )),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f689])).
% 8.22/1.41 thf(f886,plain,(
% 8.22/1.41 ( ! [X0 : $i] : (($true = $false) | ($true = ((exists_in_world @ sK3 @ X0))) | ($false = ((rel_s4 @ sK2 @ X0)))) )),
% 8.22/1.41 inference(constrained_superposition,[],[f184,f430])).
% 8.22/1.41 thf(f909,plain,(
% 8.22/1.41 ( ! [X0 : $i] : (($true = ((exists_in_world @ sK3 @ X0))) | ($false = ((rel_s4 @ sK2 @ X0)))) )),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f886])).
% 8.22/1.41 thf(f3241,plain,(
% 8.22/1.41 ( ! [X0 : mu] : (($true = $false) | ($true = ((h @ (sK4 @ X0 @ sK2) @ sK2))) | ($false = ((exists_in_world @ X0 @ sK2)))) ) | ~spl7_7),
% 8.22/1.41 inference(constrained_superposition,[],[f197,f451])).
% 8.22/1.41 thf(f3242,plain,(
% 8.22/1.41 ( ! [X0 : mu] : (($true = ((h @ (sK4 @ X0 @ sK2) @ sK2))) | ($false = ((exists_in_world @ X0 @ sK2)))) ) | ~spl7_7),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f3241])).
% 8.22/1.41 thf(f3257,plain,(
% 8.22/1.41 spl7_8 | ~spl7_7),
% 8.22/1.41 inference(avatar_split_clause,[],[f3242,f450,f596])).
% 8.22/1.41 thf(f4298,plain,(
% 8.22/1.41 ( ! [X0 : mu] : (($true = $false) | ($true = ((defused @ X0 @ sK2))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((exists_in_world @ X0 @ sK2))) | ($false = ((bomb @ X0 @ sK2))) | ($false = ((exists_in_world @ X0 @ sK2)))) ) | ~spl7_8),
% 8.22/1.41 inference(constrained_superposition,[],[f698,f597])).
% 8.22/1.41 thf(f4302,plain,(
% 8.22/1.41 ( ! [X0 : mu] : (($true = $false) | ($true = ((defused @ X0 @ sK2))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((exists_in_world @ X0 @ sK2))) | ($false = ((bomb @ X0 @ sK2)))) ) | ~spl7_8),
% 8.22/1.41 inference(duplicate_literal_removal,[],[f4298])).
% 8.22/1.41 thf(f4303,plain,(
% 8.22/1.41 ( ! [X0 : mu] : (($true = ((defused @ X0 @ sK2))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ($false = ((exists_in_world @ X0 @ sK2))) | ($false = ((bomb @ X0 @ sK2)))) ) | ~spl7_8),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f4302])).
% 8.22/1.41 thf(f4310,plain,(
% 8.22/1.41 ( ! [X0 : mu] : (($true = $false) | ($true = ((defused @ X0 @ sK2))) | ($false = ((exists_in_world @ X0 @ sK2))) | ($false = ((bomb @ X0 @ sK2)))) ) | ~spl7_8),
% 8.22/1.41 inference(forward_demodulation,[],[f4303,f274])).
% 8.22/1.41 thf(f4311,plain,(
% 8.22/1.41 ( ! [X0 : mu] : (($true = ((defused @ X0 @ sK2))) | ($false = ((exists_in_world @ X0 @ sK2))) | ($false = ((bomb @ X0 @ sK2)))) ) | ~spl7_8),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f4310])).
% 8.22/1.41 thf(f4317,definition,(
% 8.22/1.41 spl7_70 <=> ! [X0 : mu] : (($true = ((defused @ X0 @ sK2))) | ($false = ((bomb @ X0 @ sK2))) | ($false = ((exists_in_world @ X0 @ sK2))))),
% 8.22/1.41 introduced(definition,[new_symbols(definition,[spl7_70])],[avatar_definition])).
% 8.22/1.41 thf(f4318,plain,(
% 8.22/1.41 ( ! [X0 : mu] : (($false = ((exists_in_world @ X0 @ sK2))) | ($false = ((bomb @ X0 @ sK2))) | ($true = ((defused @ X0 @ sK2)))) ) | ~spl7_70),
% 8.22/1.41 inference(avatar_component_clause,[],[f4317])).
% 8.22/1.41 thf(f4320,plain,(
% 8.22/1.41 spl7_70 | ~spl7_8),
% 8.22/1.41 inference(avatar_split_clause,[],[f4311,f596,f4317])).
% 8.22/1.41 thf(f6628,plain,(
% 8.22/1.41 ($true = $false) | ($false = ((bomb @ sK3 @ sK2))) | ($true = ((defused @ sK3 @ sK2))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ~spl7_70),
% 8.22/1.41 inference(constrained_superposition,[],[f4318,f909])).
% 8.22/1.41 thf(f6748,plain,(
% 8.22/1.41 ($false = ((bomb @ sK3 @ sK2))) | ($true = ((defused @ sK3 @ sK2))) | ($false = ((rel_s4 @ sK2 @ sK2))) | ~spl7_70),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f6628])).
% 8.22/1.41 thf(f6803,plain,(
% 8.22/1.41 ($true = $false) | ($true = ((defused @ sK3 @ sK2))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl7_1 | ~spl7_70)),
% 8.22/1.41 inference(forward_demodulation,[],[f6748,f277])).
% 8.22/1.41 thf(f6804,plain,(
% 8.22/1.41 ($true = ((defused @ sK3 @ sK2))) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl7_1 | ~spl7_70)),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f6803])).
% 8.22/1.41 thf(f6836,plain,(
% 8.22/1.41 ($true = $false) | ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl7_1 | ~spl7_3 | ~spl7_70)),
% 8.22/1.41 inference(forward_demodulation,[],[f6804,f284])).
% 8.22/1.41 thf(f6837,plain,(
% 8.22/1.41 ($false = ((rel_s4 @ sK2 @ sK2))) | (~spl7_1 | ~spl7_3 | ~spl7_70)),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f6836])).
% 8.22/1.41 thf(f6849,plain,(
% 8.22/1.41 ($true = $false) | (~spl7_1 | ~spl7_3 | ~spl7_70)),
% 8.22/1.41 inference(forward_demodulation,[],[f6837,f274])).
% 8.22/1.41 thf(f6850,plain,(
% 8.22/1.41 $false | (~spl7_1 | ~spl7_3 | ~spl7_70)),
% 8.22/1.41 inference(trivial_inequality_removal,[],[f6849])).
% 8.22/1.41 thf(f6851,plain,(
% 8.22/1.41 ~spl7_1 | ~spl7_3 | ~spl7_70),
% 8.22/1.41 inference(avatar_contradiction_clause,[],[f6850])).
% 8.22/1.41 cnf(s1, plain, spl7_1 | spl7_2, inference(sat_conversion,[],[f281])).
% 8.22/1.41 cnf(s2, plain, spl7_2 | spl7_3, inference(sat_conversion,[],[f285])).
% 8.22/1.41 cnf(s4, plain, ~spl7_2, inference(sat_conversion,[],[f300])).
% 8.22/1.41 cnf(s10, plain, ~spl7_5, inference(sat_conversion,[],[f404])).
% 8.22/1.41 cnf(s12, plain, spl7_5 | spl7_7, inference(sat_conversion,[],[f453])).
% 8.22/1.41 cnf(s87, plain, ~spl7_7 | spl7_8, inference(sat_conversion,[],[f3257])).
% 8.22/1.41 cnf(s145, plain, ~spl7_8 | spl7_70, inference(sat_conversion,[],[f4320])).
% 8.22/1.41 cnf(s229, plain, ~spl7_1 | ~spl7_3 | ~spl7_70, inference(sat_conversion,[],[f6851])).
% 8.22/1.41 cnf(s283, plain, spl7_7, inference(rat,[],[s12,s10])).
% 8.22/1.41 cnf(s289, plain, spl7_8, inference(rat,[],[s87,s283])).
% 8.22/1.41 cnf(s290, plain, spl7_70, inference(rat,[],[s145,s289])).
% 8.22/1.41 cnf(s299, plain, spl7_3, inference(rat,[],[s2,s4])).
% 8.22/1.41 cnf(s300, plain, ~spl7_1, inference(rat,[],[s229,s290,s299])).
% 8.22/1.41 cnf(s301, plain, $false, inference(rat,[],[s1,s4,s300])).
% 8.22/1.41 thf(f6852,plain,(
% 8.22/1.41 $false),
% 8.22/1.41 inference(avatar_sat_refutation,[],[s301])).
% 8.22/1.41 % SZS output end Proof for theBenchmark
% 8.22/1.41 % (695303)------------------------------
% 8.22/1.41 % (695303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.22/1.41 % (695303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/1.41 % (695303)CaDiCaL version: 2.1.3
% 8.22/1.41 % (695303)Termination reason: Refutation
% 8.22/1.41 % (695303)Time elapsed: 0.406 s
% 8.22/1.41 % (695303)Peak memory usage: 14 MB
% 8.22/1.41 % (695303)Instructions burned: 778 (million)
% 8.22/1.41 % (695244)Success in time 1.192 s
% 8.22/1.41 % Vampire exiting
%------------------------------------------------------------------------------