%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO559^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:50:25 AM UTC 2026
% Result : Theorem 3.59s 0.82s
% Output : Refutation 3.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO559^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.19 % Computer : n006.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Sep 29 17:14:54 UTC 2026
% 0.13/0.19 % CPUTime :
% 0.13/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.23 Running first-order model finding
% 0.13/0.23 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
% 3.59/0.82 % (1042718)Will run a generic schedule for satisfiability detection.
% 3.59/0.82 % (1042724)% WARNING: option uhcvi not known.
% 3.59/0.82 % (1042726)dis+10_1_sil=32000:sp=arity:random_seed=2566920451:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.59/0.82 % (1042724)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3055964326:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.59/0.82 % (1042723)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2011408942_2999 on theBenchmark for (2999ds/0Mi)
% 3.59/0.82 % (1042724)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.59/0.82 % (1042724)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.59/0.82 % Exception at run slice level
% 3.59/0.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.59/0.82 % (1042725)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2865467227:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.59/0.82 % (1042728)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3525550567:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.59/0.82 % (1042727)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2250041074:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.59/0.82 % (1042729)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=845288940:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.59/0.82 % (1042733)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=251939155:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.59/0.82 % Exception at run slice level
% 3.59/0.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.59/0.82 % (1042727)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.59/0.82 % (1042739)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1546571699:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.59/0.82 % (1042726)Instruction limit reached!
% 3.59/0.82 % (1042726)------------------------------
% 3.59/0.82 % (1042726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.59/0.82 % (1042726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/0.82 % (1042726)CaDiCaL version: 2.1.3
% 3.59/0.82 % (1042726)Termination reason: Instruction limit
% 3.59/0.82 % (1042726)Termination phase: Saturation
% 3.59/0.82 % (1042726)Time elapsed: 0.056 s
% 3.59/0.82 % (1042726)Peak memory usage: 12 MB
% 3.59/0.82 % (1042726)Instructions burned: 104 (million)
% 3.59/0.82 % (1042741)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=4197504903:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.59/0.82 % (1042741)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.59/0.82 % (1042741)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.59/0.82 % (1042727)Instruction limit reached!
% 3.59/0.82 % (1042727)------------------------------
% 3.59/0.82 % (1042727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.59/0.82 % (1042727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/0.82 % (1042727)CaDiCaL version: 2.1.3
% 3.59/0.82 % (1042727)Termination reason: Instruction limit
% 3.59/0.82 % (1042727)Termination phase: Saturation
% 3.59/0.82 % (1042727)Time elapsed: 0.066 s
% 3.59/0.82 % (1042727)Peak memory usage: 13 MB
% 3.59/0.82 % (1042727)Instructions burned: 118 (million)
% 3.59/0.82 % (1042728)Instruction limit reached!
% 3.59/0.82 % (1042728)------------------------------
% 3.59/0.82 % (1042728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.59/0.82 % (1042728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/0.82 % (1042728)CaDiCaL version: 2.1.3
% 3.59/0.82 % (1042728)Termination reason: Instruction limit
% 3.59/0.82 % (1042728)Termination phase: Saturation
% 3.59/0.82 % (1042728)Time elapsed: 0.076 s
% 3.59/0.82 % (1042728)Peak memory usage: 13 MB
% 3.59/0.82 % (1042728)Instructions burned: 132 (million)
% 3.59/0.82 % (1042743)ott-21_1_sil=16000:fs=off:random_seed=3161030459:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.59/0.82 % (1042744)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=36256110:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.59/0.82 % (1042739)Instruction limit reached!
% 3.59/0.82 % (1042739)------------------------------
% 3.59/0.82 % (1042739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.59/0.82 % (1042739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/0.82 % (1042739)CaDiCaL version: 2.1.3
% 3.59/0.82 % (1042739)Termination reason: Instruction limit
% 3.59/0.82 % (1042739)Termination phase: Saturation
% 3.59/0.82 % (1042739)Time elapsed: 0.074 s
% 3.59/0.82 % (1042739)Peak memory usage: 13 MB
% 3.59/0.82 % (1042739)Instructions burned: 131 (million)
% 3.59/0.82 % (1042729)Instruction limit reached!
% 3.59/0.82 % (1042729)------------------------------
% 3.59/0.82 % (1042729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.59/0.82 % (1042729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/0.82 % (1042729)CaDiCaL version: 2.1.3
% 3.59/0.82 % (1042729)Termination reason: Instruction limit
% 3.59/0.82 % (1042729)Termination phase: Saturation
% 3.59/0.82 % (1042729)Time elapsed: 0.097 s
% 3.59/0.82 % (1042729)Peak memory usage: 12 MB
% 3.59/0.82 % (1042729)Instructions burned: 160 (million)
% 3.59/0.82 % (1042748)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1916475513:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.59/0.82 % (1042747)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1166782000:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.59/0.82 % Exception at run slice level
% 3.59/0.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.59/0.82 % (1042751)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4063115201:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.59/0.82 % Exception at run slice level
% 3.59/0.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.59/0.82 % (1042753)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=461424235:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 3.59/0.82 % (1042743)Instruction limit reached!
% 3.59/0.82 % (1042743)------------------------------
% 3.59/0.82 % (1042743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.59/0.82 % (1042743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/0.82 % (1042743)CaDiCaL version: 2.1.3
% 3.59/0.82 % (1042743)Termination reason: Instruction limit
% 3.59/0.82 % (1042743)Termination phase: Saturation
% 3.59/0.82 % (1042743)Time elapsed: 0.084 s
% 3.59/0.82 % (1042743)Peak memory usage: 12 MB
% 3.59/0.82 % (1042743)Instructions burned: 182 (million)
% 3.59/0.82 % (1042753)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.59/0.82 % (1042755)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=482032031:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.59/0.82 % (1042755)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.59/0.82 % (1042744)Instruction limit reached!
% 3.59/0.82 % (1042744)------------------------------
% 3.59/0.82 % (1042744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.59/0.82 % (1042744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/0.82 % (1042744)CaDiCaL version: 2.1.3
% 3.59/0.82 % (1042744)Termination reason: Instruction limit
% 3.59/0.82 % (1042744)Termination phase: Saturation
% 3.59/0.82 % (1042744)Time elapsed: 0.263 s
% 3.59/0.82 % (1042744)Peak memory usage: 14 MB
% 3.59/0.82 % (1042744)Instructions burned: 477 (million)
% 3.59/0.82 % (1042741)Instruction limit reached!
% 3.59/0.82 % (1042741)------------------------------
% 3.59/0.82 % (1042741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.59/0.82 % (1042741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/0.82 % (1042741)CaDiCaL version: 2.1.3
% 3.59/0.82 % (1042741)Termination reason: Instruction limit
% 3.59/0.82 % (1042741)Termination phase: Saturation
% 3.59/0.82 % (1042741)Time elapsed: 0.297 s
% 3.59/0.82 % (1042741)Peak memory usage: 16 MB
% 3.59/0.82 % (1042741)Instructions burned: 685 (million)
% 3.59/0.82 % (1042759)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3293581074:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 3.59/0.82 % Exception at run slice level
% 3.59/0.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.59/0.82 % (1042758)fmb+10_1_sil=64000:random_seed=2498648720:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 3.59/0.82 % (1042758)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.59/0.82 % Exception at run slice level
% 3.59/0.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.59/0.82 % (1042761)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2550214774:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 3.59/0.82 % Exception at run slice level
% 3.59/0.82 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.59/0.82 % (1042763)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2199647841:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 3.59/0.82 % (1042763)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.59/0.82 % (1042765)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=12669217:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 3.59/0.82 % (1042765)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.59/0.82 % (1042765)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.59/0.82 % (1042763) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1042718-1042763"...
% 3.59/0.82 % (1042763)...printing done.
% 3.59/0.82 % (1042763)Refutation found. Thanks to Tanya!
% 3.59/0.82 % SZS status Theorem for theBenchmark
% 3.59/0.82 % SZS output start Proof for theBenchmark
% 3.59/0.82 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 3.59/0.82 thf(func_def_0, type, epso: (($o > $o) > $o)).
% 3.59/0.82 thf(func_def_2, type, epsoo: ((($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_5, type, vNOT: ($o > $o)).
% 3.59/0.82 thf(func_def_6, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.59/0.82 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 3.59/0.82 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.59/0.82 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 3.59/0.82 thf(func_def_11, type, sK1: ((($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_12, type, sK2: ($o > ($o > ($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_13, type, db2: !>[X0: $tType]:(X0)).
% 3.59/0.82 thf(func_def_14, type, db3: !>[X0: $tType]:(X0)).
% 3.59/0.82 thf(func_def_15, type, sK3: ($o > $o)).
% 3.59/0.82 thf(func_def_16, type, sK4: ((($o > $o) > ($o > $o) > $o) > ($o > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_17, type, sK5: ($o > ($o > ($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_18, type, sK6: (($o > ($o > $o) > $o) > (($o > $o) > $o) > ($o > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_19, type, sK7: (($o > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_20, type, sK8: (($o > $o) > $o)).
% 3.59/0.82 thf(func_def_21, type, sK9: ((($o > $o) > ($o > $o) > $o) > ($o > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_22, type, sK10: (($o > ($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_23, type, sK11: (($o > ($o > $o) > $o) > $o > $o > $o)).
% 3.59/0.82 thf(func_def_24, type, sK12: (($o > ($o > $o) > $o > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_25, type, sK13: (($o > ($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_26, type, sK14: (($o > ($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_27, type, sK15: ($o > ($o > ($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_28, type, sK16: ((($o > $o) > ($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_29, type, sK17: ((($o > $o) > ($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_30, type, sK18: ((($o > $o) > ($o > $o) > $o) > ($o > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_31, type, sK19: ($o > $o)).
% 3.59/0.82 thf(func_def_32, type, sK20: ($o > ($o > ($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_33, type, sK21: ((($o > $o) > ($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_34, type, sK22: ((($o > $o) > ($o > $o) > $o) > $o > $o)).
% 3.59/0.82 thf(func_def_35, type, sK23: ((($o > $o) > $o > $o) > ($o > $o) > $o)).
% 3.59/0.82 thf(f1,axiom,(
% 3.59/0.82 ! [X0 : ($o > $o)] : (? [X1 : $o] : (X0 @ X1) => (X0 @ (epso @ X0)))),
% 3.59/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceaxo)).
% 3.59/0.82 thf(f2,axiom,(
% 3.59/0.82 ! [X0 : (($o > $o) > $o)] : (? [X1 : ($o > $o)] : (X0 @ X1) => (X0 @ (epsoo @ X0)))),
% 3.59/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceaxoo)).
% 3.59/0.82 thf(f3,conjecture,(
% 3.59/0.82 (epsoo @ epso @ $false) => (epsoo @ epso @ $true)),
% 3.59/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c)).
% 3.59/0.82 thf(f4,negated_conjecture,(
% 3.59/0.82 ~((epsoo @ epso @ $false) => (epsoo @ epso @ $true))),
% 3.59/0.82 inference(negated_conjecture,[status(cth)],[f3])).
% 3.59/0.82 thf(f5,plain,(
% 3.59/0.82 ! [X0 : ($o > $o)] : (? [X1 : $o] : (X0 @ X1) => (X0 @ (epso @ X0)))),
% 3.59/0.82 inference(rectify,[],[f1])).
% 3.59/0.82 thf(f6,plain,(
% 3.59/0.82 ! [X0 : ($o > $o)] : (? [X1 : $o] : (((X0 @ X1)) = $true) => (((X0 @ (epso @ X0))) = $true))),
% 3.59/0.82 inference(fool_elimination,[],[f5])).
% 3.59/0.82 thf(f7,plain,(
% 3.59/0.82 ! [X0 : (($o > $o) > $o)] : (? [X1 : ($o > $o)] : (X0 @ X1) => (X0 @ (epsoo @ X0)))),
% 3.59/0.82 inference(rectify,[],[f2])).
% 3.59/0.82 thf(f8,plain,(
% 3.59/0.82 ! [X0 : (($o > $o) > $o)] : (? [X1 : ($o > $o)] : (((X0 @ X1)) = $true) => (((X0 @ (epsoo @ X0))) = $true))),
% 3.59/0.82 inference(fool_elimination,[],[f7])).
% 3.59/0.82 thf(f9,plain,(
% 3.59/0.82 ~((epsoo @ epso @ $false) => (epsoo @ epso @ $true))),
% 3.59/0.82 inference(rectify,[],[f4])).
% 3.59/0.82 thf(f10,plain,(
% 3.59/0.82 ~(($true = ((epsoo @ epso @ $false))) => ($true = ((epsoo @ epso @ $true))))),
% 3.59/0.82 inference(fool_elimination,[],[f9])).
% 3.59/0.82 thf(f11,plain,(
% 3.59/0.82 ! [X0 : ($o > $o)] : ((((X0 @ (epso @ X0))) = $true) | ! [X1 : $o] : (((X0 @ X1)) != $true))),
% 3.59/0.82 inference(ennf_transformation,[],[f6])).
% 3.59/0.82 thf(f12,plain,(
% 3.59/0.82 ! [X0 : (($o > $o) > $o)] : ((((X0 @ (epsoo @ X0))) = $true) | ! [X1 : ($o > $o)] : (((X0 @ X1)) != $true))),
% 3.59/0.82 inference(ennf_transformation,[],[f8])).
% 3.59/0.82 thf(f13,plain,(
% 3.59/0.82 ($true != ((epsoo @ epso @ $true))) & ($true = ((epsoo @ epso @ $false)))),
% 3.59/0.82 inference(ennf_transformation,[],[f10])).
% 3.59/0.82 thf(f14,plain,(
% 3.59/0.82 ( ! [X0 : ($o > $o),X1 : $o] : ((((X0 @ X1)) != $true) | (((X0 @ (epso @ X0))) = $true)) )),
% 3.59/0.82 inference(cnf_transformation,[],[f11])).
% 3.59/0.82 thf(f15,plain,(
% 3.59/0.82 ( ! [X0 : (($o > $o) > $o),X1 : ($o > $o)] : ((((X0 @ X1)) != $true) | (((X0 @ (epsoo @ X0))) = $true)) )),
% 3.59/0.82 inference(cnf_transformation,[],[f12])).
% 3.59/0.82 thf(f16,plain,(
% 3.59/0.82 ($true = ((epsoo @ epso @ $false)))),
% 3.59/0.82 inference(cnf_transformation,[],[f13])).
% 3.59/0.82 thf(f17,plain,(
% 3.59/0.82 ($true != ((epsoo @ epso @ $true)))),
% 3.59/0.82 inference(cnf_transformation,[],[f13])).
% 3.59/0.82 thf(f19,definition,(
% 3.59/0.82 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.59/0.82 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.59/0.82 thf(f42,plain,(
% 3.59/0.82 ( ! [X0 : (($o > $o) > $o),X1 : $o] : (($true != $true) | ($true = (((^[Y0 : $o]: (Y0)) @ (epso @ (^[Y0 : $o]: (Y0)))))) | (epso != X0) | ($false != X1)) )),
% 3.59/0.82 inference(constrained_superposition,[],[f14,f16])).
% 3.59/0.82 thf(f50,plain,(
% 3.59/0.82 ( ! [X0 : ($o > $o),X1 : $o] : (($true != $true) | (((X0 @ (epso @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 3.59/0.82 inference(constrained_superposition,[],[f14,f19])).
% 3.59/0.82 thf(f55,plain,(
% 3.59/0.82 ( ! [X0 : ($o > $o),X1 : $o] : ((((X0 @ (epso @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 3.59/0.82 inference(trivial_inequality_removal,[],[f50])).
% 3.59/0.82 thf(f65,plain,(
% 3.59/0.82 ( ! [X0 : (($o > $o) > $o),X1 : $o] : (($true = (((^[Y0 : $o]: (Y0)) @ (epso @ (^[Y0 : $o]: (Y0)))))) | (epso != X0) | ($false != X1)) )),
% 3.59/0.82 inference(trivial_inequality_removal,[],[f42])).
% 3.59/0.82 thf(f66,plain,(
% 3.59/0.82 ( ! [X0 : (($o > $o) > $o),X1 : $o] : (($true = ((epso @ (^[Y0 : $o]: (Y0))))) | (epso != X0) | ($false != X1)) )),
% 3.59/0.83 inference(beta-eta_normalization,[],[f65])).
% 3.59/0.83 thf(f175,definition,(
% 3.59/0.83 spl0_1 <=> ! [X1 : $o] : ($false != X1)),
% 3.59/0.83 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 3.59/0.83 thf(f176,plain,(
% 3.59/0.83 ( ! [X1 : $o] : (($false != X1)) ) | ~spl0_1),
% 3.59/0.83 inference(avatar_component_clause,[],[f175])).
% 3.59/0.83 thf(f178,definition,(
% 3.59/0.83 spl0_2 <=> ! [X0 : (($o > $o) > $o)] : (epso != X0)),
% 3.59/0.83 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 3.59/0.83 thf(f179,plain,(
% 3.59/0.83 ( ! [X0 : (($o > $o) > $o)] : ((epso != X0)) ) | ~spl0_2),
% 3.59/0.83 inference(avatar_component_clause,[],[f178])).
% 3.59/0.83 thf(f181,definition,(
% 3.59/0.83 spl0_3 <=> ($true = ((epso @ (^[Y0 : $o]: (Y0)))))),
% 3.59/0.83 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 3.59/0.83 thf(f183,plain,(
% 3.59/0.83 ($true = ((epso @ (^[Y0 : $o]: (Y0))))) | ~spl0_3),
% 3.59/0.83 inference(avatar_component_clause,[],[f181])).
% 3.59/0.83 thf(f184,plain,(
% 3.59/0.83 spl0_1 | spl0_2 | spl0_3),
% 3.59/0.83 inference(avatar_split_clause,[],[f66,f181,f178,f175])).
% 3.59/0.83 thf(f186,plain,(
% 3.59/0.83 $false | ~spl0_2),
% 3.59/0.83 inference(equality_resolution,[],[f179])).
% 3.59/0.83 thf(f187,plain,(
% 3.59/0.83 ~spl0_2),
% 3.59/0.83 inference(avatar_contradiction_clause,[],[f186])).
% 3.59/0.83 thf(f2194,plain,(
% 3.59/0.83 $false | ~spl0_1),
% 3.59/0.83 inference(equality_resolution,[],[f176])).
% 3.59/0.83 thf(f2195,plain,(
% 3.59/0.83 ~spl0_1),
% 3.59/0.83 inference(avatar_contradiction_clause,[],[f2194])).
% 3.59/0.83 thf(f2217,plain,(
% 3.59/0.83 ( ! [X2 : ($o > $o),X1 : (($o > $o) > $o > $o)] : (($true != $true) | ($true = (((^[Y0 : $o > $o]: (epso @ ((^[Y1 : $o > $o]: ((^[Y2 : $o]: (Y1 @ (X1 @ Y1 @ Y2))))) @ Y0))) @ (epsoo @ (^[Y0 : $o > $o]: (epso @ ((^[Y1 : $o > $o]: ((^[Y2 : $o]: (Y1 @ (X1 @ Y1 @ Y2))))) @ Y0))))))) | ((^[Y0 : $o]: (Y0)) != (^[Y0 : $o]: (X2 @ (X1 @ X2 @ Y0))))) ) | ~spl0_3),
% 3.59/0.83 inference(constrained_superposition,[],[f15,f183])).
% 3.59/0.83 thf(f2228,plain,(
% 3.59/0.83 ( ! [X2 : ($o > $o),X1 : (($o > $o) > $o > $o)] : (($true = (((^[Y0 : $o > $o]: (epso @ ((^[Y1 : $o > $o]: ((^[Y2 : $o]: (Y1 @ (X1 @ Y1 @ Y2))))) @ Y0))) @ (epsoo @ (^[Y0 : $o > $o]: (epso @ ((^[Y1 : $o > $o]: ((^[Y2 : $o]: (Y1 @ (X1 @ Y1 @ Y2))))) @ Y0))))))) | ((^[Y0 : $o]: (Y0)) != (^[Y0 : $o]: (X2 @ (X1 @ X2 @ Y0))))) ) | ~spl0_3),
% 3.59/0.83 inference(trivial_inequality_removal,[],[f2217])).
% 3.59/0.83 thf(f2229,plain,(
% 3.59/0.83 ( ! [X2 : ($o > $o),X1 : (($o > $o) > $o > $o)] : (((^[Y0 : $o]: (Y0)) != (^[Y0 : $o]: (X2 @ (X1 @ X2 @ Y0)))) | ($true = ((epso @ (^[Y0 : $o]: (epsoo @ (^[Y1 : $o > $o]: (epso @ (^[Y2 : $o]: (Y1 @ (X1 @ Y1 @ Y2))))) @ (X1 @ (epsoo @ (^[Y1 : $o > $o]: (epso @ (^[Y2 : $o]: (Y1 @ (X1 @ Y1 @ Y2)))))) @ Y0))))))) ) | ~spl0_3),
% 3.59/0.83 inference(beta-eta_normalization,[],[f2228])).
% 3.59/0.83 thf(f3932,plain,(
% 3.59/0.83 ($true = ((epso @ (^[Y0 : $o]: (epsoo @ (^[Y1 : $o > $o]: (epso @ (^[Y2 : $o]: (Y1 @ ((^[Y3 : $o > $o]: ((^[Y4 : $o]: (Y4)))) @ Y1 @ Y2))))) @ ((^[Y1 : $o > $o]: ((^[Y2 : $o]: (Y2)))) @ (epsoo @ (^[Y1 : $o > $o]: (epso @ (^[Y2 : $o]: (Y1 @ ((^[Y3 : $o > $o]: ((^[Y4 : $o]: (Y4)))) @ Y1 @ Y2)))))) @ Y0)))))) | ~spl0_3),
% 3.59/0.83 inference(equality_resolution,[],[f2229])).
% 3.59/0.83 thf(f3933,plain,(
% 3.59/0.83 ($true = ((epso @ (epsoo @ epso)))) | ~spl0_3),
% 3.59/0.83 inference(beta-eta_normalization,[],[f3932])).
% 3.59/0.83 thf(f3956,plain,(
% 3.59/0.83 ( ! [X0 : $o] : (($true = ((epsoo @ epso @ $true))) | ($false = ((epsoo @ epso @ X0)))) ) | ~spl0_3),
% 3.59/0.83 inference(constrained_superposition,[],[f55,f3933])).
% 3.59/0.83 thf(f4021,plain,(
% 3.59/0.83 ( ! [X0 : $o] : (($false = ((epsoo @ epso @ X0)))) ) | ~spl0_3),
% 3.59/0.83 inference(forward_subsumption_resolution,[],[f3956,f17])).
% 3.59/0.83 thf(f4022,plain,(
% 3.59/0.83 ($true = $false) | ~spl0_3),
% 3.59/0.83 inference(constrained_superposition,[],[f4021,f16])).
% 3.59/0.83 thf(f4196,plain,(
% 3.59/0.83 $false | ~spl0_3),
% 3.59/0.83 inference(trivial_inequality_removal,[],[f4022])).
% 3.59/0.83 thf(f4197,plain,(
% 3.59/0.83 ~spl0_3),
% 3.59/0.83 inference(avatar_contradiction_clause,[],[f4196])).
% 3.59/0.83 cnf(s1, plain, spl0_1 | spl0_2 | spl0_3, inference(sat_conversion,[],[f184])).
% 3.59/0.83 cnf(s2, plain, ~spl0_2, inference(sat_conversion,[],[f187])).
% 3.59/0.83 cnf(s9, plain, ~spl0_1, inference(sat_conversion,[],[f2195])).
% 3.59/0.83 cnf(s17, plain, ~spl0_3, inference(sat_conversion,[],[f4197])).
% 3.59/0.83 cnf(s20, plain, $false, inference(rat,[],[s1,s17,s2,s9])).
% 3.59/0.83 thf(f4198,plain,(
% 3.59/0.83 $false),
% 3.59/0.83 inference(avatar_sat_refutation,[],[s20])).
% 3.59/0.83 % SZS output end Proof for theBenchmark
% 3.59/0.83 % (1042763)------------------------------
% 3.59/0.83 % (1042763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.59/0.83 % (1042763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/0.83 % (1042763)CaDiCaL version: 2.1.3
% 3.59/0.83 % (1042763)Termination reason: Refutation
% 3.59/0.83 % (1042763)Time elapsed: 0.121 s
% 3.59/0.83 % (1042763)Peak memory usage: 15 MB
% 3.59/0.83 % (1042763)Instructions burned: 380 (million)
% 3.59/0.83 % (1042718)Success in time 0.589 s
% 3.59/0.83 % Vampire exiting
%------------------------------------------------------------------------------