%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO354^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:49:46 AM UTC 2026
% Result : Theorem 3.57s 0.80s
% Output : Refutation 3.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO354^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n003.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 16:50:14 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 3.57/0.80 % (2741767)Will run a generic schedule for satisfiability detection.
% 3.57/0.80 % (2741776)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1323801344:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.57/0.80 % (2741775)% WARNING: option uhcvi not known.
% 3.57/0.80 % (2741775)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=655374460:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.57/0.80 % (2741778)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1068121526:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.57/0.80 % (2741775)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.57/0.80 % (2741778)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.57/0.80 % (2741775)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.57/0.80 % (2741780)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=335845144:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.57/0.80 % (2741779)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=653995203:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.57/0.80 % (2741774)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=797198664_2999 on theBenchmark for (2999ds/0Mi)
% 3.57/0.80 % Exception at run slice level
% 3.57/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.57/0.80 % (2741777)dis+10_1_sil=32000:sp=arity:random_seed=2190218095:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.57/0.80 % (2741789)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3269408945:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.57/0.80 % Exception at run slice level
% 3.57/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.57/0.80 % (2741801)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2459340114:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.57/0.80 % (2741778)Instruction limit reached!
% 3.57/0.80 % (2741778)------------------------------
% 3.57/0.80 % (2741778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.80 % (2741778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.80 % (2741778)CaDiCaL version: 2.1.3
% 3.57/0.80 % (2741778)Termination reason: Instruction limit
% 3.57/0.80 % (2741778)Termination phase: Saturation
% 3.57/0.80 % (2741778)Time elapsed: 0.059 s
% 3.57/0.80 % (2741778)Peak memory usage: 12 MB
% 3.57/0.80 % (2741778)Instructions burned: 116 (million)
% 3.57/0.80 % (2741779)Instruction limit reached!
% 3.57/0.80 % (2741779)------------------------------
% 3.57/0.80 % (2741779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.80 % (2741779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.80 % (2741779)CaDiCaL version: 2.1.3
% 3.57/0.80 % (2741779)Termination reason: Instruction limit
% 3.57/0.80 % (2741779)Termination phase: Saturation
% 3.57/0.80 % (2741779)Time elapsed: 0.063 s
% 3.57/0.80 % (2741779)Peak memory usage: 14 MB
% 3.57/0.80 % (2741779)Instructions burned: 131 (million)
% 3.57/0.80 % (2741803)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=2430127403:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.57/0.80 % (2741803)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.57/0.80 % (2741803)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.57/0.80 % (2741805)ott-21_1_sil=16000:fs=off:random_seed=3844109772:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.57/0.80 % (2741780)Instruction limit reached!
% 3.57/0.80 % (2741780)------------------------------
% 3.57/0.80 % (2741780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.80 % (2741780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.80 % (2741780)CaDiCaL version: 2.1.3
% 3.57/0.80 % (2741780)Termination reason: Instruction limit
% 3.57/0.80 % (2741780)Termination phase: Saturation
% 3.57/0.80 % (2741780)Time elapsed: 0.087 s
% 3.57/0.80 % (2741780)Peak memory usage: 14 MB
% 3.57/0.80 % (2741780)Instructions burned: 161 (million)
% 3.57/0.80 % (2741777)Instruction limit reached!
% 3.57/0.80 % (2741777)------------------------------
% 3.57/0.80 % (2741777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.80 % (2741777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.80 % (2741777)CaDiCaL version: 2.1.3
% 3.57/0.80 % (2741777)Termination reason: Instruction limit
% 3.57/0.80 % (2741777)Termination phase: Saturation
% 3.57/0.80 % (2741777)Time elapsed: 0.084 s
% 3.57/0.80 % (2741777)Peak memory usage: 13 MB
% 3.57/0.80 % (2741777)Instructions burned: 104 (million)
% 3.57/0.80 % (2741809)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=992062764:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.57/0.80 % Exception at run slice level
% 3.57/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.57/0.80 % (2741808)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2070667749:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.57/0.80 % (2741811)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=406809512:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.57/0.80 % (2741801)Instruction limit reached!
% 3.57/0.80 % (2741801)------------------------------
% 3.57/0.80 % (2741801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.80 % (2741801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.80 % (2741801)CaDiCaL version: 2.1.3
% 3.57/0.80 % (2741801)Termination reason: Instruction limit
% 3.57/0.80 % (2741801)Termination phase: Saturation
% 3.57/0.80 % (2741801)Time elapsed: 0.082 s
% 3.57/0.80 % (2741801)Peak memory usage: 14 MB
% 3.57/0.80 % (2741801)Instructions burned: 132 (million)
% 3.57/0.80 % (2741814)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=464855344:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.57/0.80 % Exception at run slice level
% 3.57/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.57/0.80 % (2741816)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=1566330392: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)
% 3.57/0.80 % (2741816)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.57/0.80 % (2741805)Instruction limit reached!
% 3.57/0.80 % (2741805)------------------------------
% 3.57/0.80 % (2741805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.80 % (2741805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.80 % (2741805)CaDiCaL version: 2.1.3
% 3.57/0.80 % (2741805)Termination reason: Instruction limit
% 3.57/0.80 % (2741805)Termination phase: Saturation
% 3.57/0.80 % (2741805)Time elapsed: 0.108 s
% 3.57/0.80 % (2741805)Peak memory usage: 12 MB
% 3.57/0.80 % (2741805)Instructions burned: 180 (million)
% 3.57/0.80 % (2741818)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=888017848:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.57/0.80 % (2741818)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.57/0.80 % (2741803)Instruction limit reached!
% 3.57/0.80 % (2741803)------------------------------
% 3.57/0.80 % (2741803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.80 % (2741803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.80 % (2741803)CaDiCaL version: 2.1.3
% 3.57/0.80 % (2741803)Termination reason: Instruction limit
% 3.57/0.80 % (2741803)Termination phase: Saturation
% 3.57/0.80 % (2741803)Time elapsed: 0.314 s
% 3.57/0.80 % (2741803)Peak memory usage: 20 MB
% 3.57/0.80 % (2741803)Instructions burned: 685 (million)
% 3.57/0.80 % (2741820)fmb+10_1_sil=64000:random_seed=20076785:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 3.57/0.80 % (2741820)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.57/0.80 % Exception at run slice level
% 3.57/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.57/0.80 % (2741822)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1790417856:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 3.57/0.80 % Exception at run slice level
% 3.57/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.57/0.80 % (2741808)Instruction limit reached!
% 3.57/0.80 % (2741808)------------------------------
% 3.57/0.80 % (2741808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.80 % (2741808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.80 % (2741808)CaDiCaL version: 2.1.3
% 3.57/0.80 % (2741808)Termination reason: Instruction limit
% 3.57/0.80 % (2741808)Termination phase: Saturation
% 3.57/0.80 % (2741808)Time elapsed: 0.327 s
% 3.57/0.80 % (2741808)Peak memory usage: 16 MB
% 3.57/0.80 % (2741808)Instructions burned: 478 (million)
% 3.57/0.80 % (2741824)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=4273583385:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 3.57/0.80 % Exception at run slice level
% 3.57/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.57/0.80 % (2741825)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2219178232:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 3.57/0.80 % (2741825)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.57/0.80 % (2741827)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2506915660:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 3.57/0.80 % (2741827)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.57/0.80 % (2741827)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.57/0.80 % (2741816)Instruction limit reached!
% 3.57/0.80 % (2741816)------------------------------
% 3.57/0.80 % (2741816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.80 % (2741816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.80 % (2741816)CaDiCaL version: 2.1.3
% 3.57/0.80 % (2741816)Termination reason: Instruction limit
% 3.57/0.80 % (2741816)Termination phase: Saturation
% 3.57/0.80 % (2741816)Time elapsed: 0.350 s
% 3.57/0.80 % (2741816)Peak memory usage: 18 MB
% 3.57/0.80 % (2741816)Instructions burned: 692 (million)
% 3.57/0.80 % (2741827) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2741767-2741827"...
% 3.57/0.80 % (2741827)...printing done.
% 3.57/0.80 % (2741827)Refutation found. Thanks to Tanya!
% 3.57/0.80 % SZS status Theorem for theBenchmark
% 3.57/0.80 % SZS output start Proof for theBenchmark
% 3.57/0.80 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 3.57/0.80 thf(func_def_0, type, n: ($i > $i)).
% 3.57/0.80 thf(func_def_1, type, m: ($i > $i)).
% 3.57/0.80 thf(func_def_5, type, db0: !>[X0: $tType]:(X0)).
% 3.57/0.80 thf(func_def_6, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.57/0.80 thf(func_def_7, type, sK0: (($i > $i) > $o)).
% 3.57/0.80 thf(func_def_8, type, sP1: ($o > $o)).
% 3.57/0.80 thf(func_def_9, type, vNOT: ($o > $o)).
% 3.57/0.80 thf(func_def_10, type, sF2: !>[X0: $tType]:(($i > ($i > X0) > X0))).
% 3.57/0.80 thf(func_def_11, type, sF3: !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 3.57/0.80 thf(func_def_12, type, sF4: !>[X0: $tType, X1: $tType]:(((($i > X0) > X1) > ($i > X0) > X1))).
% 3.57/0.80 thf(func_def_13, type, sF5: ($o > $o)).
% 3.57/0.80 thf(func_def_14, type, sF6: (($o > $o) > $o > $o)).
% 3.57/0.80 thf(func_def_15, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.57/0.80 thf(func_def_16, type, db1: !>[X0: $tType]:(X0)).
% 3.57/0.80 thf(func_def_17, type, sF7: ($i > $i > $i)).
% 3.57/0.80 thf(func_def_18, type, sF8: (($i > $i) > $i > $o)).
% 3.57/0.80 thf(func_def_20, type, sF10: ($i > $i)).
% 3.57/0.80 thf(func_def_21, type, sF11: (($i > $i) > $i > $i)).
% 3.57/0.80 thf(func_def_22, type, sF12: (($i > $i) > $i > $i > $i)).
% 3.57/0.80 thf(func_def_23, type, sF13: !>[X0: $tType]:(($i > ($i > $i) > (($i > $i) > $i > X0) > X0))).
% 3.57/0.80 thf(func_def_24, type, sF14: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > ((X0 > X2) > X1) > X1))).
% 3.57/0.80 thf(func_def_25, type, sF15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ($i > X1) > $i > (X0 > $o) > $o))).
% 3.57/0.80 thf(func_def_26, type, sK16: ($i > $i)).
% 3.57/0.80 thf(func_def_27, type, sF17: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > (X1 > X0) > X1 > X2))).
% 3.57/0.80 thf(func_def_28, type, sF18: !>[X0: $tType]:((($i > X0) > $i > X0))).
% 3.57/0.80 thf(func_def_29, type, sF19: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > (X1 > X2) > X2) > X0 > (X1 > X2) > X2))).
% 3.57/0.80 thf(func_def_30, type, sF20: ($i > $i > $i)).
% 3.57/0.80 thf(func_def_31, type, sK21: ($i > ($i > $i > $i) > $i)).
% 3.57/0.80 thf(func_def_32, type, sF22: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > X0 > X1 > X2))).
% 3.57/0.80 thf(func_def_33, type, sF23: !>[X0: $tType]:((X0 > (X0 > $i) > $i))).
% 3.57/0.80 thf(func_def_34, type, sF24: !>[X0: $tType, X1: $tType]:((X1 > (X1 > X0) > (X0 > $o) > $o))).
% 3.57/0.80 thf(func_def_35, type, sF25: (($i > $i > $i) > $i > $i > $i)).
% 3.57/0.80 thf(func_def_36, type, sF26: ($i > $i > $i)).
% 3.57/0.80 thf(func_def_37, type, sK27: ($i > $i)).
% 3.57/0.80 thf(func_def_38, type, sF28: !>[X0: $tType]:(($i > ($i > X0) > (X0 > $o) > $o))).
% 3.57/0.80 thf(func_def_39, type, sF29: !>[X0: $tType]:((X0 > (X0 > X0) > X0))).
% 3.57/0.80 thf(func_def_40, type, sK30: ($i > $i)).
% 3.57/0.80 thf(func_def_41, type, sF31: !>[X0: $tType, X1: $tType]:(((X0 > X0) > ((X0 > X0) > X1) > X1))).
% 3.57/0.80 thf(func_def_42, type, sK32: ($i > $i)).
% 3.57/0.80 thf(func_def_43, type, sF33: !>[X0: $tType, X1: $tType]:(($i > ($i > X0) > (X0 > X1) > X1))).
% 3.57/0.80 thf(func_def_44, type, sK34: ($i > $i)).
% 3.57/0.80 thf(func_def_45, type, sK35: (($i > $i > $i) > $i > $i)).
% 3.57/0.80 thf(func_def_46, type, sF36: (($i > $i) > $i > $o)).
% 3.57/0.80 thf(func_def_47, type, sF37: ($i > ($i > $i > $i) > ($i > $i > $i) > $o)).
% 3.57/0.80 thf(func_def_48, type, sF38: ($i > ($i > $i > $i) > $i)).
% 3.57/0.80 thf(func_def_49, type, sF39: ($i > ($i > $i > $i) > ($i > $i) > $i > $i)).
% 3.57/0.80 thf(func_def_50, type, sK40: ($i > ($i > $i > $i) > $i)).
% 3.57/0.80 thf(func_def_51, type, sF41: !>[X0: $tType]:((($i > $i) > (($i > $i) > X0) > X0))).
% 3.57/0.80 thf(func_def_52, type, sF42: !>[X0: $tType, X1: $tType]:((X0 > X1 > (X1 > X0 > $i) > $i))).
% 3.57/0.80 thf(func_def_53, type, sF43: !>[X0: $tType]:((($i > X0) > (($i > X0) > $o) > $o))).
% 3.57/0.80 thf(func_def_54, type, sF44: (($i > $i) > $i > $i > $i)).
% 3.57/0.80 thf(func_def_55, type, sF45: ($i > $o)).
% 3.57/0.80 thf(func_def_56, type, sF46: (($i > $i > $i) > $i > $i)).
% 3.57/0.80 thf(func_def_57, type, sF47: (($i > $i) > $o)).
% 3.57/0.80 thf(func_def_58, type, sK48: ($i > $i)).
% 3.57/0.80 thf(func_def_59, type, sF49: ((($i > $i) > $o) > ($i > $i) > $o)).
% 3.57/0.80 thf(func_def_60, type, sF50: ($i > ($i > $i) > ($i > $i) > $i > $i)).
% 3.57/0.80 thf(func_def_61, type, sF51: !>[X0: $tType, X1: $tType]:((((X0 > X1) > $o) > (X0 > X1) > $o))).
% 3.57/0.80 thf(func_def_62, type, sK52: (($i > $i > $i) > $i > $i)).
% 3.57/0.80 thf(func_def_63, type, sF53: ($i > $o)).
% 3.57/0.80 thf(func_def_64, type, sF54: ($i > ($i > $i > $i) > $i)).
% 3.57/0.80 thf(func_def_65, type, sK55: ($i > $i)).
% 3.57/0.80 thf(func_def_66, type, sF56: ($i > $i > $i)).
% 3.57/0.80 thf(func_def_67, type, sK57: ($i > $i)).
% 3.57/0.80 thf(func_def_68, type, sK58: ($i > $i)).
% 3.57/0.80 thf(func_def_69, type, sF59: (($i > $i) > $i > $o)).
% 3.57/0.80 thf(func_def_70, type, sF60: ($i > $i > $i)).
% 3.57/0.80 thf(func_def_71, type, sF61: (($i > $i) > $i > $o)).
% 3.57/0.80 thf(func_def_72, type, sK62: ($i > $i)).
% 3.57/0.80 thf(func_def_73, type, sK63: ($i > $i)).
% 3.57/0.80 thf(func_def_74, type, sF64: (($i > $i > $i) > $i > $o)).
% 3.57/0.80 thf(func_def_75, type, sK65: ($i > $i)).
% 3.57/0.80 thf(func_def_76, type, sK66: ($i > ($i > $i) > $i)).
% 3.57/0.80 thf(func_def_77, type, sF67: (($i > $i) > $o)).
% 3.57/0.80 thf(func_def_78, type, sK68: ($i > ($i > $i) > $i)).
% 3.57/0.80 thf(func_def_79, type, sK69: (($i > $i) > $i > $i)).
% 3.57/0.80 thf(func_def_80, type, sF70: ($i > $i)).
% 3.57/0.80 thf(func_def_81, type, sF71: ($i > $i > $i)).
% 3.57/0.80 thf(func_def_82, type, sK72: (($i > $i) > $i)).
% 3.57/0.80 thf(func_def_83, type, sF73: (($i > $i > $i) > $i > $i)).
% 3.57/0.80 thf(f1,conjecture,(
% 3.57/0.80 ! [X0 : $i,X1 : ($i > $o)] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : (($i > $i) > $o)] : ((X2 @ (^[X0 : $i] : ((m @ X0)))) => (X2 @ (^[X0 : $i] : ((n @ X0)))))),
% 3.57/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE4EXT)).
% 3.57/0.80 thf(f2,negated_conjecture,(
% 3.57/0.80 ~(! [X0 : $i,X1 : ($i > $o)] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : (($i > $i) > $o)] : ((X2 @ (^[X0 : $i] : ((m @ X0)))) => (X2 @ (^[X0 : $i] : ((n @ X0))))))),
% 3.57/0.80 inference(negated_conjecture,[status(cth)],[f1])).
% 3.57/0.80 thf(f3,plain,(
% 3.57/0.80 ~(! [X0 : $i,X1 : ($i > $o)] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : (($i > $i) > $o)] : ((X2 @ (^[X3 : $i] : ((m @ X3)))) => (X2 @ (^[X4 : $i] : ((n @ X4))))))),
% 3.57/0.80 inference(rectify,[],[f2])).
% 3.57/0.80 thf(f4,plain,(
% 3.57/0.80 ~(! [X0 : $i,X1 : ($i > $o)] : ((((X1 @ (m @ X0))) = $true) => (((X1 @ (n @ X0))) = $true)) => ! [X2 : (($i > $i) > $o)] : (($true = ((X2 @ (^[Y0 : $i]: (m @ Y0))))) => ($true = ((X2 @ (^[Y0 : $i]: (n @ Y0)))))))),
% 3.57/0.80 inference(fool_elimination,[],[f3])).
% 3.57/0.80 thf(f5,plain,(
% 3.57/0.80 ? [X2 : (($i > $i) > $o)] : (($true != ((X2 @ (^[Y0 : $i]: (n @ Y0))))) & ($true = ((X2 @ (^[Y0 : $i]: (m @ Y0)))))) & ! [X0 : $i,X1 : ($i > $o)] : ((((X1 @ (n @ X0))) = $true) | (((X1 @ (m @ X0))) != $true))),
% 3.57/0.80 inference(ennf_transformation,[],[f4])).
% 3.57/0.80 thf(f6,plain,(
% 3.57/0.80 ? [X0 : (($i > $i) > $o)] : (($true != ((X0 @ (^[Y0 : $i]: (n @ Y0))))) & ($true = ((X0 @ (^[Y0 : $i]: (m @ Y0)))))) & ! [X1 : $i,X2 : ($i > $o)] : (($true = ((X2 @ (n @ X1)))) | ($true != ((X2 @ (m @ X1)))))),
% 3.57/0.80 inference(rectify,[],[f5])).
% 3.57/0.80 thf(f7,plain,(
% 3.57/0.80 (($true != ((sK0 @ (^[Y0 : $i]: (n @ Y0))))) & ($true = ((sK0 @ (^[Y0 : $i]: (m @ Y0)))))) & ! [X1 : $i,X2 : ($i > $o)] : (($true = ((X2 @ (n @ X1)))) | ($true != ((X2 @ (m @ X1)))))),
% 3.57/0.80 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6])).
% 3.57/0.80 thf(f8,plain,(
% 3.57/0.80 ( ! [X2 : ($i > $o),X1 : $i] : (($true != ((X2 @ (m @ X1)))) | ($true = ((X2 @ (n @ X1))))) )),
% 3.57/0.80 inference(cnf_transformation,[],[f7])).
% 3.57/0.80 thf(f9,plain,(
% 3.57/0.80 ($true = ((sK0 @ (^[Y0 : $i]: (m @ Y0)))))),
% 3.57/0.80 inference(cnf_transformation,[],[f7])).
% 3.57/0.80 thf(f10,plain,(
% 3.57/0.80 ($true != ((sK0 @ (^[Y0 : $i]: (n @ Y0)))))),
% 3.57/0.80 inference(cnf_transformation,[],[f7])).
% 3.57/0.80 thf(f12,definition,(
% 3.57/0.80 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.57/0.80 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.57/0.80 thf(f13,definition,(
% 3.57/0.80 ($false = ((sP1 @ (sK0 @ (^[Y0 : $i]: (n @ Y0))))))),
% 3.57/0.80 introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction])).
% 3.57/0.80 thf(f14,plain,(
% 3.57/0.80 ($true = ((sP1 @ $true)))),
% 3.57/0.80 inference(inequality_splitting,[],[f10,f13])).
% 3.57/0.80 thf(f15,plain,(
% 3.57/0.80 ($false = ((sP1 @ (sK0 @ n))))),
% 3.57/0.80 inference(beta-eta_normalization,[],[f13])).
% 3.57/0.80 thf(f16,plain,(
% 3.57/0.80 ($true = ((sK0 @ m)))),
% 3.57/0.80 inference(beta-eta_normalization,[],[f9])).
% 3.57/0.80 thf(f27,plain,(
% 3.57/0.80 ($false = ((sP1 @ $true))) | ($false = ((sK0 @ n)))),
% 3.57/0.80 inference(constrained_superposition,[],[f15,f12])).
% 3.57/0.80 thf(f37,plain,(
% 3.57/0.80 ($true = $false) | ($false = ((sK0 @ n)))),
% 3.57/0.80 inference(forward_demodulation,[],[f27,f14])).
% 3.57/0.80 thf(f38,plain,(
% 3.57/0.80 ($false = ((sK0 @ n)))),
% 3.57/0.80 inference(trivial_inequality_removal,[],[f37])).
% 3.57/0.80 thf(f59,plain,(
% 3.57/0.80 ( ! [X0 : $i] : ((((m @ X0)) = ((n @ X0)))) )),
% 3.57/0.80 inference(leibniz_equality_elimination,[],[f8])).
% 3.57/0.80 thf(f62,plain,(
% 3.57/0.80 ( ! [X3 : ($i > $o),X1 : $i] : (($true != (((^[Y0 : $i]: (~ (X3 @ Y0))) @ (m @ X1)))) | ($true = (((^[Y0 : $i]: (~ (X3 @ Y0))) @ (n @ X1))))) )),
% 3.57/0.80 inference(primitive_instantiation,[],[f8])).
% 3.57/0.80 thf(f92,plain,(
% 3.57/0.80 ( ! [X3 : ($i > $o),X1 : $i] : (($true != ((~ (X3 @ (m @ X1))))) | ($true = ((~ (X3 @ (n @ X1)))))) )),
% 3.57/0.80 inference(beta-eta_normalization,[],[f62])).
% 3.57/0.80 thf(f93,plain,(
% 3.57/0.80 ( ! [X3 : ($i > $o),X1 : $i] : (($true = ((X3 @ (m @ X1)))) | ($true = ((~ (X3 @ (n @ X1)))))) )),
% 3.57/0.80 inference(not_proxy_clausification,[],[f92])).
% 3.57/0.80 thf(f94,plain,(
% 3.57/0.80 ( ! [X3 : ($i > $o),X1 : $i] : (($true = ((X3 @ (m @ X1)))) | ($false = ((X3 @ (n @ X1))))) )),
% 3.57/0.80 inference(not_proxy_clausification,[],[f93])).
% 3.57/0.80 thf(f879,definition,(
% 3.57/0.80 ( ! [X0 : ($i > $i)] : ((((sF47 @ X0)) = ((sK0 @ X0)))) )),
% 3.57/0.80 introduced(definition,[new_symbols(definition,[sF47])],[function_definition])).
% 3.57/0.80 thf(f880,plain,(
% 3.57/0.80 ( ! [X0 : ($i > $i)] : ((((sK0 @ X0)) = ((sF47 @ X0)))) )),
% 3.57/0.80 inference(reorient_equations,[],[f879])).
% 3.57/0.80 thf(f883,plain,(
% 3.57/0.80 ( ! [X0 : ($i > $i)] : (($false = ((sF47 @ X0))) | ($true = ((sK0 @ X0)))) )),
% 3.57/0.80 inference(iff_proxy_clausification,[],[f880])).
% 3.57/0.80 thf(f884,plain,(
% 3.57/0.80 ( ! [X0 : ($i > $i)] : (($true = ((sF47 @ X0))) | ($false = ((sK0 @ X0)))) )),
% 3.57/0.80 inference(iff_proxy_clausification,[],[f880])).
% 3.57/0.80 thf(f980,plain,(
% 3.57/0.80 ( ! [X2 : ($i > $i),X0 : ($i > $i > $i),X1 : $i] : (($true = $false) | ($false = (((^[Y0 : $i]: (sF47 @ (X0 @ Y0))) @ (n @ X1)))) | ($true = ((sK0 @ X2))) | (((X0 @ (m @ X1))) != X2)) )),
% 3.57/0.80 inference(constrained_superposition,[],[f94,f883])).
% 3.57/0.80 thf(f983,plain,(
% 3.57/0.80 ( ! [X2 : ($i > $i),X0 : ($i > $i > $i),X1 : $i] : (($false = (((^[Y0 : $i]: (sF47 @ (X0 @ Y0))) @ (n @ X1)))) | ($true = ((sK0 @ X2))) | (((X0 @ (m @ X1))) != X2)) )),
% 3.57/0.80 inference(trivial_inequality_removal,[],[f980])).
% 3.57/0.80 thf(f984,plain,(
% 3.57/0.80 ( ! [X2 : ($i > $i),X0 : ($i > $i > $i),X1 : $i] : (($false = ((sF47 @ (X0 @ (n @ X1))))) | ($true = ((sK0 @ X2))) | (((X0 @ (m @ X1))) != X2)) )),
% 3.57/0.80 inference(beta-eta_normalization,[],[f983])).
% 3.57/0.80 thf(f988,plain,(
% 3.57/0.80 ( ! [X2 : ($i > $i),X0 : ($i > $i > $i),X1 : $i] : (($false = ((sF47 @ (X0 @ (n @ X1))))) | ($true = ((sK0 @ X2))) | (((X0 @ (n @ X1))) != X2)) )),
% 3.57/0.80 inference(forward_demodulation,[],[f984,f59])).
% 3.57/0.80 thf(f1056,plain,(
% 3.57/0.80 ( ! [X2 : ($i > $i),X0 : ($i > $i > $i),X1 : $i] : (($true = $false) | ($true = ((sK0 @ X2))) | (((X0 @ (n @ X1))) != X2) | ($false = ((sK0 @ (X0 @ (n @ X1)))))) )),
% 3.57/0.80 inference(constrained_superposition,[],[f988,f884])).
% 3.57/0.80 thf(f1062,plain,(
% 3.57/0.80 ( ! [X2 : ($i > $i),X0 : ($i > $i > $i),X1 : $i] : (($true = ((sK0 @ X2))) | ($false = ((sK0 @ (X0 @ (n @ X1))))) | (((X0 @ (n @ X1))) != X2)) )),
% 3.57/0.80 inference(trivial_inequality_removal,[],[f1056])).
% 3.57/0.80 thf(f1141,plain,(
% 3.57/0.80 ( ! [X0 : $i,X1 : ($i > $i)] : (($true = $false) | ($true = ((sK0 @ X1))) | ((((^[Y0 : $i]: ((^[Y1 : $i]: (m @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ (n @ X0))) != X1)) )),
% 3.57/0.80 inference(constrained_superposition,[],[f16,f1062])).
% 3.57/0.80 thf(f1149,plain,(
% 3.57/0.80 ( ! [X0 : $i,X1 : ($i > $i)] : (($true = ((sK0 @ X1))) | ((((^[Y0 : $i]: ((^[Y1 : $i]: (m @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ (n @ X0))) != X1)) )),
% 3.57/0.80 inference(trivial_inequality_removal,[],[f1141])).
% 3.57/0.80 thf(f1150,plain,(
% 3.57/0.80 ( ! [X1 : ($i > $i)] : ((m != X1) | ($true = ((sK0 @ X1)))) )),
% 3.57/0.80 inference(beta-eta_normalization,[],[f1149])).
% 3.57/0.80 thf(f1173,plain,(
% 3.57/0.80 ( ! [X1 : ($i > $i)] : ((((m @ (sK72 @ X1))) != ((X1 @ (sK72 @ X1)))) | ($true = ((sK0 @ X1)))) )),
% 3.57/0.80 inference(negative_extensionality,[],[f1150])).
% 3.57/0.80 thf(f1175,plain,(
% 3.57/0.80 ( ! [X1 : ($i > $i)] : ((((X1 @ (sK72 @ X1))) != ((n @ (sK72 @ X1)))) | ($true = ((sK0 @ X1)))) )),
% 3.57/0.80 inference(forward_demodulation,[],[f1173,f59])).
% 3.57/0.80 thf(f1184,plain,(
% 3.57/0.80 ($true = ((sK0 @ (^[Y0 : $i]: (n @ ((^[Y1 : $i]: (Y1)) @ Y0)))))) | (n != (^[Y0 : $i]: (n @ ((^[Y1 : $i]: (Y1)) @ Y0))))),
% 3.57/0.80 inference(equality_resolution,[],[f1175])).
% 3.57/0.80 thf(f1187,plain,(
% 3.57/0.80 ($true = ((sK0 @ n))) | (n != n)),
% 3.57/0.80 inference(beta-eta_normalization,[],[f1184])).
% 3.57/0.80 thf(f1188,plain,(
% 3.57/0.80 ($true = ((sK0 @ n)))),
% 3.57/0.80 inference(trivial_inequality_removal,[],[f1187])).
% 3.57/0.80 thf(f1191,plain,(
% 3.57/0.80 ($true = $false)),
% 3.57/0.80 inference(forward_demodulation,[],[f1188,f38])).
% 3.57/0.80 thf(f1192,plain,(
% 3.57/0.80 $false),
% 3.57/0.80 inference(trivial_inequality_removal,[],[f1191])).
% 3.57/0.80 % SZS output end Proof for theBenchmark
% 3.57/0.80 % (2741827)------------------------------
% 3.57/0.80 % (2741827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.57/0.80 % (2741827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/0.80 % (2741827)CaDiCaL version: 2.1.3
% 3.57/0.80 % (2741827)Termination reason: Refutation
% 3.57/0.80 % (2741827)Time elapsed: 0.066 s
% 3.57/0.80 % (2741827)Peak memory usage: 13 MB
% 3.57/0.80 % (2741827)Instructions burned: 115 (million)
% 3.57/0.80 % (2741767)Success in time 0.584 s
% 3.57/0.80 % Vampire exiting
%------------------------------------------------------------------------------