%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO352^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 3.11s 0.73s
% Output : Refutation 3.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO352^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:48:18 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 3.11/0.73 % (1044580)Will run a generic schedule for satisfiability detection.
% 3.11/0.73 % (1044603)dis+10_1_sil=32000:sp=arity:random_seed=675718076:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.11/0.73 % (1044601)% WARNING: option uhcvi not known.
% 3.11/0.73 % (1044600)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2392335815_2999 on theBenchmark for (2999ds/0Mi)
% 3.11/0.73 % (1044601)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4090249093:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.11/0.73 % (1044602)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3227571061:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.11/0.73 % (1044604)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1994719225:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.11/0.73 % Exception at run slice level
% 3.11/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.11/0.73 % (1044601)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.11/0.73 % (1044604)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.11/0.73 % (1044601)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.11/0.73 % (1044605)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=567666458:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.11/0.73 % (1044606)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2954992569:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.11/0.73 % (1044603)Instruction limit reached!
% 3.11/0.73 % (1044603)------------------------------
% 3.11/0.73 % (1044603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.11/0.73 % (1044603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/0.73 % (1044603)CaDiCaL version: 2.1.3
% 3.11/0.73 % (1044603)Termination reason: Instruction limit
% 3.11/0.73 % (1044603)Termination phase: Saturation
% 3.11/0.73 % (1044603)Time elapsed: 0.026 s
% 3.11/0.73 % (1044603)Peak memory usage: 13 MB
% 3.11/0.73 % (1044603)Instructions burned: 104 (million)
% 3.11/0.73 % (1044618)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=776917090:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.11/0.73 % Exception at run slice level
% 3.11/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.11/0.73 % (1044622)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3880946228:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.11/0.73 % (1044623)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=323646004:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.11/0.73 % (1044623)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.11/0.73 % (1044623)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.11/0.73 % (1044604)Instruction limit reached!
% 3.11/0.73 % (1044604)------------------------------
% 3.11/0.73 % (1044604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.11/0.73 % (1044604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/0.73 % (1044604)CaDiCaL version: 2.1.3
% 3.11/0.73 % (1044604)Termination reason: Instruction limit
% 3.11/0.73 % (1044604)Termination phase: Saturation
% 3.11/0.73 % (1044604)Time elapsed: 0.058 s
% 3.11/0.73 % (1044604)Peak memory usage: 12 MB
% 3.11/0.73 % (1044604)Instructions burned: 117 (million)
% 3.11/0.73 % (1044605)Instruction limit reached!
% 3.11/0.73 % (1044605)------------------------------
% 3.11/0.73 % (1044605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.11/0.73 % (1044605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/0.73 % (1044605)CaDiCaL version: 2.1.3
% 3.11/0.73 % (1044605)Termination reason: Instruction limit
% 3.11/0.73 % (1044605)Termination phase: Saturation
% 3.11/0.73 % (1044605)Time elapsed: 0.061 s
% 3.11/0.73 % (1044605)Peak memory usage: 14 MB
% 3.11/0.73 % (1044605)Instructions burned: 133 (million)
% 3.11/0.73 % (1044622)Instruction limit reached!
% 3.11/0.73 % (1044622)------------------------------
% 3.11/0.73 % (1044622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.11/0.73 % (1044622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/0.73 % (1044622)CaDiCaL version: 2.1.3
% 3.11/0.73 % (1044622)Termination reason: Instruction limit
% 3.11/0.73 % (1044622)Termination phase: Saturation
% 3.11/0.73 % (1044622)Time elapsed: 0.033 s
% 3.11/0.73 % (1044622)Peak memory usage: 14 MB
% 3.11/0.73 % (1044622)Instructions burned: 135 (million)
% 3.11/0.73 % (1044628)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=14531177:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 3.11/0.73 % Exception at run slice level
% 3.11/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.11/0.73 % (1044626)ott-21_1_sil=16000:fs=off:random_seed=269893750:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.11/0.73 % (1044627)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1476980494:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 3.11/0.73 % (1044606)Instruction limit reached!
% 3.11/0.73 % (1044606)------------------------------
% 3.11/0.73 % (1044606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.11/0.73 % (1044606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/0.73 % (1044606)CaDiCaL version: 2.1.3
% 3.11/0.73 % (1044606)Termination reason: Instruction limit
% 3.11/0.73 % (1044606)Termination phase: Saturation
% 3.11/0.73 % (1044606)Time elapsed: 0.081 s
% 3.11/0.73 % (1044606)Peak memory usage: 14 MB
% 3.11/0.73 % (1044606)Instructions burned: 161 (million)
% 3.11/0.73 % (1044630)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2120988469:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.11/0.73 % (1044633)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1897341827:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.11/0.73 % Exception at run slice level
% 3.11/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.11/0.73 % (1044636)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=4112934170: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)
% 3.11/0.73 % (1044636)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.11/0.73 % (1044626)Instruction limit reached!
% 3.11/0.73 % (1044626)------------------------------
% 3.11/0.73 % (1044626)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.11/0.73 % (1044626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/0.73 % (1044626)CaDiCaL version: 2.1.3
% 3.11/0.73 % (1044626)Termination reason: Instruction limit
% 3.11/0.73 % (1044626)Termination phase: Saturation
% 3.11/0.73 % (1044626)Time elapsed: 0.083 s
% 3.11/0.73 % (1044626)Peak memory usage: 13 MB
% 3.11/0.73 % (1044626)Instructions burned: 181 (million)
% 3.11/0.73 % (1044638)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=187951296:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 3.11/0.73 % (1044638)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.11/0.73 % (1044627)Instruction limit reached!
% 3.11/0.73 % (1044627)------------------------------
% 3.11/0.73 % (1044627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.11/0.73 % (1044627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/0.73 % (1044627)CaDiCaL version: 2.1.3
% 3.11/0.73 % (1044627)Termination reason: Instruction limit
% 3.11/0.73 % (1044627)Termination phase: Saturation
% 3.11/0.73 % (1044627)Time elapsed: 0.215 s
% 3.11/0.73 % (1044627)Peak memory usage: 17 MB
% 3.11/0.73 % (1044627)Instructions burned: 478 (million)
% 3.11/0.73 % (1044640)fmb+10_1_sil=64000:random_seed=2510843458:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 3.11/0.73 % (1044640)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.11/0.73 % Exception at run slice level
% 3.11/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.11/0.73 % (1044642)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=553585487:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 3.11/0.73 % Exception at run slice level
% 3.11/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.11/0.73 % (1044623)Instruction limit reached!
% 3.11/0.73 % (1044623)------------------------------
% 3.11/0.73 % (1044623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.11/0.73 % (1044623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/0.73 % (1044623)CaDiCaL version: 2.1.3
% 3.11/0.73 % (1044623)Termination reason: Instruction limit
% 3.11/0.73 % (1044623)Termination phase: Saturation
% 3.11/0.73 % (1044623)Time elapsed: 0.312 s
% 3.11/0.73 % (1044623)Peak memory usage: 23 MB
% 3.11/0.73 % (1044623)Instructions burned: 685 (million)
% 3.11/0.73 % (1044644)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1859375741:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 3.11/0.73 % Exception at run slice level
% 3.11/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.11/0.73 % (1044630)Instruction limit reached!
% 3.11/0.73 % (1044630)------------------------------
% 3.11/0.73 % (1044630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.11/0.73 % (1044630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/0.73 % (1044630)CaDiCaL version: 2.1.3
% 3.11/0.73 % (1044630)Termination reason: Instruction limit
% 3.11/0.73 % (1044630)Termination phase: Saturation
% 3.11/0.73 % (1044630)Time elapsed: 0.284 s
% 3.11/0.73 % (1044630)Peak memory usage: 15 MB
% 3.11/0.73 % (1044630)Instructions burned: 1181 (million)
% 3.11/0.73 % (1044645)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3403524343:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 3.11/0.73 % (1044645)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.11/0.73 % (1044647)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=4194725148:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 3.11/0.73 % (1044647)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.11/0.73 % (1044647)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.11/0.73 % (1044648)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=698618878:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 3.11/0.73 % Exception at run slice level
% 3.11/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.11/0.73 % (1044652)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3535368425:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 3.11/0.73 % Exception at run slice level
% 3.11/0.73 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.11/0.73 % (1044654)ott-2_1_sil=16000:newcnf=on:random_seed=822021639:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 3.11/0.73 % (1044654)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.11/0.73 % (1044647) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1044580-1044647"...
% 3.11/0.73 % (1044647)...printing done.
% 3.11/0.73 % (1044647)Refutation found. Thanks to Tanya!
% 3.11/0.73 % SZS status Theorem for theBenchmark
% 3.11/0.73 % SZS output start Proof for theBenchmark
% 3.11/0.73 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 3.11/0.73 thf(func_def_0, type, n: ($i > $i)).
% 3.11/0.73 thf(func_def_1, type, m: ($i > $i)).
% 3.11/0.73 thf(func_def_5, type, sK0: (($i > $i) > $o)).
% 3.11/0.73 thf(func_def_6, type, sP1: ($o > $o)).
% 3.11/0.73 thf(func_def_7, type, vNOT: ($o > $o)).
% 3.11/0.73 thf(func_def_8, type, sF2: !>[X0: $tType]:(($i > ($i > X0) > X0))).
% 3.11/0.73 thf(func_def_9, type, sF3: !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 3.11/0.73 thf(func_def_10, type, sF4: !>[X0: $tType, X1: $tType]:(((($i > X0) > X1) > ($i > X0) > X1))).
% 3.11/0.73 thf(func_def_11, type, sF5: ($o > $o)).
% 3.11/0.73 thf(func_def_12, type, sF6: (($o > $o) > $o > $o)).
% 3.11/0.73 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.11/0.73 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 3.11/0.73 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.11/0.73 thf(func_def_16, type, db1: !>[X0: $tType]:(X0)).
% 3.11/0.73 thf(func_def_17, type, sF7: ($i > $i > $i)).
% 3.11/0.73 thf(func_def_18, type, sF8: (($i > $i) > $i > $o)).
% 3.11/0.73 thf(func_def_20, type, sF10: ($i > $i)).
% 3.11/0.73 thf(func_def_21, type, sF11: (($i > $i) > $i > $i)).
% 3.11/0.73 thf(func_def_22, type, sF12: (($i > $i) > $i > $i > $i)).
% 3.11/0.73 thf(func_def_23, type, sF13: !>[X0: $tType]:(($i > ($i > $i) > (($i > $i) > $i > X0) > X0))).
% 3.11/0.73 thf(func_def_24, type, sF14: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > ((X0 > X2) > X1) > X1))).
% 3.11/0.73 thf(func_def_25, type, sF15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > ($i > X1) > $i > (X0 > $o) > $o))).
% 3.11/0.73 thf(func_def_26, type, sK16: ($i > $i)).
% 3.11/0.73 thf(func_def_27, type, sF17: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > (X1 > X0) > X1 > X2))).
% 3.11/0.73 thf(func_def_28, type, sF18: !>[X0: $tType]:((($i > X0) > $i > X0))).
% 3.11/0.73 thf(func_def_29, type, sF19: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > (X1 > X2) > X2) > X0 > (X1 > X2) > X2))).
% 3.11/0.73 thf(func_def_30, type, sF20: ($i > $i > $i)).
% 3.11/0.73 thf(func_def_31, type, sK21: ($i > ($i > $i > $i) > $i)).
% 3.11/0.73 thf(func_def_32, type, sF22: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > X0 > X1 > X2))).
% 3.11/0.73 thf(func_def_33, type, sF23: !>[X0: $tType]:((X0 > (X0 > $i) > $i))).
% 3.11/0.73 thf(func_def_34, type, sF24: !>[X0: $tType, X1: $tType]:((X1 > (X1 > X0) > (X0 > $o) > $o))).
% 3.11/0.73 thf(func_def_35, type, sF25: (($i > $i > $i) > $i > $i > $i)).
% 3.11/0.73 thf(func_def_36, type, sF26: ($i > $i > $i)).
% 3.11/0.73 thf(func_def_37, type, sK27: ($i > $i)).
% 3.11/0.73 thf(func_def_38, type, sF28: !>[X0: $tType]:(($i > ($i > X0) > (X0 > $o) > $o))).
% 3.11/0.73 thf(func_def_39, type, sF29: !>[X0: $tType]:((X0 > (X0 > X0) > X0))).
% 3.11/0.73 thf(func_def_40, type, sK30: ($i > $i)).
% 3.11/0.73 thf(func_def_41, type, sF31: !>[X0: $tType, X1: $tType]:(((X0 > X0) > ((X0 > X0) > X1) > X1))).
% 3.11/0.73 thf(func_def_42, type, sK32: ($i > $i)).
% 3.11/0.73 thf(func_def_43, type, sF33: !>[X0: $tType, X1: $tType]:(($i > ($i > X0) > (X0 > X1) > X1))).
% 3.11/0.73 thf(func_def_44, type, sK34: ($i > $i)).
% 3.11/0.73 thf(func_def_45, type, sK35: (($i > $i > $i) > $i > $i)).
% 3.11/0.73 thf(func_def_46, type, sF36: (($i > $i) > $i > $o)).
% 3.11/0.73 thf(func_def_47, type, sF37: ($i > ($i > $i > $i) > ($i > $i > $i) > $o)).
% 3.11/0.73 thf(func_def_48, type, sF38: ($i > ($i > $i > $i) > $i)).
% 3.11/0.73 thf(func_def_49, type, sF39: ($i > ($i > $i > $i) > ($i > $i) > $i > $i)).
% 3.11/0.73 thf(func_def_50, type, sK40: ($i > ($i > $i > $i) > $i)).
% 3.11/0.73 thf(func_def_51, type, sF41: !>[X0: $tType]:((($i > $i) > (($i > $i) > X0) > X0))).
% 3.11/0.73 thf(func_def_52, type, sF42: !>[X0: $tType, X1: $tType]:((X0 > X1 > (X1 > X0 > $i) > $i))).
% 3.11/0.73 thf(func_def_53, type, sF43: !>[X0: $tType]:((($i > X0) > (($i > X0) > $o) > $o))).
% 3.11/0.73 thf(func_def_54, type, sF44: (($i > $i) > $i > $i > $i)).
% 3.11/0.73 thf(func_def_55, type, sF45: ($i > $o)).
% 3.11/0.73 thf(func_def_56, type, sF46: (($i > $i > $i) > $i > $i)).
% 3.11/0.73 thf(func_def_57, type, sF47: (($i > $i) > $o)).
% 3.11/0.73 thf(func_def_58, type, sK48: ($i > $i)).
% 3.11/0.73 thf(func_def_59, type, sF49: ((($i > $i) > $o) > ($i > $i) > $o)).
% 3.11/0.73 thf(func_def_60, type, sF50: ($i > ($i > $i) > ($i > $i) > $i > $i)).
% 3.11/0.73 thf(func_def_61, type, sF51: !>[X0: $tType, X1: $tType]:((((X0 > X1) > $o) > (X0 > X1) > $o))).
% 3.11/0.73 thf(func_def_62, type, sK52: (($i > $i > $i) > $i > $i)).
% 3.11/0.73 thf(func_def_63, type, sF53: ($i > $o)).
% 3.11/0.73 thf(func_def_64, type, sF54: ($i > ($i > $i > $i) > $i)).
% 3.11/0.73 thf(func_def_65, type, sK55: ($i > $i)).
% 3.11/0.73 thf(func_def_66, type, sF56: ($i > $i > $i)).
% 3.11/0.73 thf(func_def_67, type, sK57: ($i > $i)).
% 3.11/0.73 thf(func_def_68, type, sK58: ($i > $i)).
% 3.11/0.73 thf(func_def_69, type, sF59: (($i > $i) > $i > $o)).
% 3.11/0.73 thf(func_def_70, type, sF60: ($i > $i > $i)).
% 3.11/0.73 thf(func_def_71, type, sF61: (($i > $i) > $i > $o)).
% 3.11/0.73 thf(func_def_72, type, sK62: ($i > $i)).
% 3.11/0.73 thf(func_def_73, type, sK63: ($i > $i)).
% 3.11/0.73 thf(func_def_74, type, sF64: (($i > $i > $i) > $i > $o)).
% 3.11/0.73 thf(func_def_75, type, sK65: ($i > $i)).
% 3.11/0.73 thf(func_def_76, type, sK66: ($i > ($i > $i) > $i)).
% 3.11/0.73 thf(func_def_77, type, sF67: (($i > $i) > $o)).
% 3.11/0.73 thf(func_def_78, type, sK68: ($i > ($i > $i) > $i)).
% 3.11/0.73 thf(func_def_79, type, sK69: (($i > $i) > $i > $i)).
% 3.11/0.73 thf(func_def_80, type, sF70: ($i > $i)).
% 3.11/0.73 thf(func_def_81, type, sF71: ($i > $i > $i)).
% 3.11/0.73 thf(func_def_82, type, sK72: (($i > $i) > $i)).
% 3.11/0.73 thf(func_def_83, type, sF73: (($i > $i > $i) > $i > $i)).
% 3.11/0.73 thf(f1,conjecture,(
% 3.11/0.73 ! [X0 : $i,X1 : ($i > $o)] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : (($i > $i) > $o)] : ((X2 @ m) => (X2 @ n))),
% 3.11/0.73 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE5EXT)).
% 3.11/0.73 thf(f2,negated_conjecture,(
% 3.11/0.73 ~(! [X0 : $i,X1 : ($i > $o)] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : (($i > $i) > $o)] : ((X2 @ m) => (X2 @ n)))),
% 3.11/0.73 inference(negated_conjecture,[status(cth)],[f1])).
% 3.11/0.73 thf(f3,plain,(
% 3.11/0.73 ~(! [X0 : $i,X1 : ($i > $o)] : ((X1 @ (m @ X0)) => (X1 @ (n @ X0))) => ! [X2 : (($i > $i) > $o)] : ((X2 @ m) => (X2 @ n)))),
% 3.11/0.73 inference(rectify,[],[f2])).
% 3.11/0.73 thf(f4,plain,(
% 3.11/0.73 ~(! [X0 : $i,X1 : ($i > $o)] : ((((X1 @ (m @ X0))) = $true) => (((X1 @ (n @ X0))) = $true)) => ! [X2 : (($i > $i) > $o)] : ((((X2 @ m)) = $true) => (((X2 @ n)) = $true)))),
% 3.11/0.73 inference(fool_elimination,[],[f3])).
% 3.11/0.73 thf(f5,plain,(
% 3.11/0.73 ? [X2 : (($i > $i) > $o)] : ((((X2 @ n)) != $true) & (((X2 @ m)) = $true)) & ! [X0 : $i,X1 : ($i > $o)] : ((((X1 @ (n @ X0))) = $true) | (((X1 @ (m @ X0))) != $true))),
% 3.11/0.73 inference(ennf_transformation,[],[f4])).
% 3.11/0.73 thf(f6,plain,(
% 3.11/0.73 ? [X0 : (($i > $i) > $o)] : (($true != ((X0 @ n))) & ($true = ((X0 @ m)))) & ! [X1 : $i,X2 : ($i > $o)] : (($true = ((X2 @ (n @ X1)))) | ($true != ((X2 @ (m @ X1)))))),
% 3.11/0.73 inference(rectify,[],[f5])).
% 3.11/0.73 thf(f7,plain,(
% 3.11/0.73 (($true != ((sK0 @ n))) & ($true = ((sK0 @ m)))) & ! [X1 : $i,X2 : ($i > $o)] : (($true = ((X2 @ (n @ X1)))) | ($true != ((X2 @ (m @ X1)))))),
% 3.11/0.73 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6])).
% 3.11/0.73 thf(f8,plain,(
% 3.11/0.73 ( ! [X2 : ($i > $o),X1 : $i] : (($true != ((X2 @ (m @ X1)))) | ($true = ((X2 @ (n @ X1))))) )),
% 3.11/0.73 inference(cnf_transformation,[],[f7])).
% 3.11/0.73 thf(f9,plain,(
% 3.11/0.73 ($true = ((sK0 @ m)))),
% 3.11/0.73 inference(cnf_transformation,[],[f7])).
% 3.11/0.73 thf(f10,plain,(
% 3.11/0.73 ($true != ((sK0 @ n)))),
% 3.11/0.73 inference(cnf_transformation,[],[f7])).
% 3.11/0.73 thf(f12,definition,(
% 3.11/0.73 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.11/0.73 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.11/0.73 thf(f13,definition,(
% 3.11/0.73 ($false = ((sP1 @ (sK0 @ n))))),
% 3.11/0.73 introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction])).
% 3.11/0.73 thf(f14,plain,(
% 3.11/0.73 ($true = ((sP1 @ $true)))),
% 3.11/0.73 inference(inequality_splitting,[],[f10,f13])).
% 3.11/0.73 thf(f25,plain,(
% 3.11/0.73 ($false = ((sP1 @ $true))) | (((sK0 @ n)) = $false)),
% 3.11/0.73 inference(constrained_superposition,[],[f13,f12])).
% 3.11/0.73 thf(f35,plain,(
% 3.11/0.73 ($true = $false) | (((sK0 @ n)) = $false)),
% 3.11/0.73 inference(forward_demodulation,[],[f25,f14])).
% 3.11/0.73 thf(f36,plain,(
% 3.11/0.73 (((sK0 @ n)) = $false)),
% 3.11/0.73 inference(trivial_inequality_removal,[],[f35])).
% 3.11/0.73 thf(f57,plain,(
% 3.11/0.73 ( ! [X0 : $i] : ((((m @ X0)) = ((n @ X0)))) )),
% 3.11/0.73 inference(leibniz_equality_elimination,[],[f8])).
% 3.11/0.73 thf(f60,plain,(
% 3.11/0.73 ( ! [X3 : ($i > $o),X1 : $i] : (($true != (((^[Y0 : $i]: (~ (X3 @ Y0))) @ (m @ X1)))) | ($true = (((^[Y0 : $i]: (~ (X3 @ Y0))) @ (n @ X1))))) )),
% 3.11/0.73 inference(primitive_instantiation,[],[f8])).
% 3.11/0.73 thf(f90,plain,(
% 3.11/0.73 ( ! [X3 : ($i > $o),X1 : $i] : (($true != ((~ (X3 @ (m @ X1))))) | ($true = ((~ (X3 @ (n @ X1)))))) )),
% 3.11/0.73 inference(beta-eta_normalization,[],[f60])).
% 3.11/0.73 thf(f91,plain,(
% 3.11/0.73 ( ! [X3 : ($i > $o),X1 : $i] : (($true = ((X3 @ (m @ X1)))) | ($true = ((~ (X3 @ (n @ X1)))))) )),
% 3.11/0.73 inference(not_proxy_clausification,[],[f90])).
% 3.11/0.73 thf(f92,plain,(
% 3.11/0.73 ( ! [X3 : ($i > $o),X1 : $i] : (($true = ((X3 @ (m @ X1)))) | ($false = ((X3 @ (n @ X1))))) )),
% 3.11/0.73 inference(not_proxy_clausification,[],[f91])).
% 3.11/0.73 thf(f877,definition,(
% 3.11/0.73 ( ! [X0 : ($i > $i)] : ((((sF47 @ X0)) = ((sK0 @ X0)))) )),
% 3.11/0.73 introduced(definition,[new_symbols(definition,[sF47])],[function_definition])).
% 3.11/0.73 thf(f878,plain,(
% 3.11/0.73 ( ! [X0 : ($i > $i)] : ((((sK0 @ X0)) = ((sF47 @ X0)))) )),
% 3.11/0.73 inference(reorient_equations,[],[f877])).
% 3.11/0.73 thf(f881,plain,(
% 3.11/0.73 ( ! [X0 : ($i > $i)] : (($false = ((sF47 @ X0))) | ($true = ((sK0 @ X0)))) )),
% 3.11/0.73 inference(iff_proxy_clausification,[],[f878])).
% 3.11/0.73 thf(f882,plain,(
% 3.11/0.73 ( ! [X0 : ($i > $i)] : (($true = ((sF47 @ X0))) | ($false = ((sK0 @ X0)))) )),
% 3.11/0.73 inference(iff_proxy_clausification,[],[f878])).
% 3.11/0.73 thf(f978,plain,(
% 3.11/0.73 ( ! [X2 : ($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)) )),
% 3.11/0.73 inference(constrained_superposition,[],[f92,f881])).
% 3.11/0.73 thf(f981,plain,(
% 3.11/0.73 ( ! [X2 : ($i > $i),X0 : ($i > $i > $i),X1 : $i] : (($false = (((^[Y0 : $i]: (sF47 @ (X0 @ Y0))) @ (n @ X1)))) | ($true = ((sK0 @ X2))) | (((X0 @ (m @ X1))) != X2)) )),
% 3.11/0.73 inference(trivial_inequality_removal,[],[f978])).
% 3.11/0.73 thf(f982,plain,(
% 3.11/0.73 ( ! [X2 : ($i > $i),X0 : ($i > $i > $i),X1 : $i] : (($false = ((sF47 @ (X0 @ (n @ X1))))) | ($true = ((sK0 @ X2))) | (((X0 @ (m @ X1))) != X2)) )),
% 3.11/0.73 inference(beta-eta_normalization,[],[f981])).
% 3.11/0.73 thf(f986,plain,(
% 3.11/0.73 ( ! [X2 : ($i > $i),X0 : ($i > $i > $i),X1 : $i] : (($false = ((sF47 @ (X0 @ (n @ X1))))) | ($true = ((sK0 @ X2))) | (((X0 @ (n @ X1))) != X2)) )),
% 3.11/0.73 inference(forward_demodulation,[],[f982,f57])).
% 3.11/0.73 thf(f1054,plain,(
% 3.11/0.73 ( ! [X2 : ($i > $i),X0 : ($i > $i > $i),X1 : $i] : (($true = $false) | ($true = ((sK0 @ X2))) | (((X0 @ (n @ X1))) != X2) | ($false = ((sK0 @ (X0 @ (n @ X1)))))) )),
% 3.11/0.73 inference(constrained_superposition,[],[f986,f882])).
% 3.11/0.73 thf(f1060,plain,(
% 3.11/0.73 ( ! [X2 : ($i > $i),X0 : ($i > $i > $i),X1 : $i] : (($true = ((sK0 @ X2))) | ($false = ((sK0 @ (X0 @ (n @ X1))))) | (((X0 @ (n @ X1))) != X2)) )),
% 3.11/0.73 inference(trivial_inequality_removal,[],[f1054])).
% 3.11/0.73 thf(f1139,plain,(
% 3.11/0.73 ( ! [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)) )),
% 3.11/0.73 inference(constrained_superposition,[],[f9,f1060])).
% 3.11/0.73 thf(f1147,plain,(
% 3.11/0.73 ( ! [X0 : $i,X1 : ($i > $i)] : (($true = ((sK0 @ X1))) | ((((^[Y0 : $i]: ((^[Y1 : $i]: (m @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1))))) @ (n @ X0))) != X1)) )),
% 3.11/0.73 inference(trivial_inequality_removal,[],[f1139])).
% 3.11/0.73 thf(f1148,plain,(
% 3.11/0.73 ( ! [X1 : ($i > $i)] : ((m != X1) | ($true = ((sK0 @ X1)))) )),
% 3.11/0.73 inference(beta-eta_normalization,[],[f1147])).
% 3.11/0.73 thf(f1171,plain,(
% 3.11/0.73 ( ! [X1 : ($i > $i)] : ((((m @ (sK72 @ X1))) != ((X1 @ (sK72 @ X1)))) | ($true = ((sK0 @ X1)))) )),
% 3.11/0.73 inference(negative_extensionality,[],[f1148])).
% 3.11/0.73 thf(f1173,plain,(
% 3.11/0.73 ( ! [X1 : ($i > $i)] : ((((X1 @ (sK72 @ X1))) != ((n @ (sK72 @ X1)))) | ($true = ((sK0 @ X1)))) )),
% 3.11/0.73 inference(forward_demodulation,[],[f1171,f57])).
% 3.11/0.73 thf(f1182,plain,(
% 3.11/0.73 ($true = ((sK0 @ (^[Y0 : $i]: (n @ ((^[Y1 : $i]: (Y1)) @ Y0)))))) | (n != (^[Y0 : $i]: (n @ ((^[Y1 : $i]: (Y1)) @ Y0))))),
% 3.11/0.73 inference(equality_resolution,[],[f1173])).
% 3.11/0.73 thf(f1185,plain,(
% 3.11/0.73 ($true = ((sK0 @ n))) | (n != n)),
% 3.11/0.73 inference(beta-eta_normalization,[],[f1182])).
% 3.11/0.73 thf(f1186,plain,(
% 3.11/0.73 ($true = ((sK0 @ n)))),
% 3.11/0.73 inference(trivial_inequality_removal,[],[f1185])).
% 3.11/0.73 thf(f1189,plain,(
% 3.11/0.73 ($true = $false)),
% 3.11/0.73 inference(forward_demodulation,[],[f1186,f36])).
% 3.11/0.73 thf(f1190,plain,(
% 3.11/0.73 $false),
% 3.11/0.73 inference(trivial_inequality_removal,[],[f1189])).
% 3.11/0.73 % SZS output end Proof for theBenchmark
% 3.11/0.73 % (1044647)------------------------------
% 3.11/0.73 % (1044647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.11/0.73 % (1044647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.11/0.73 % (1044647)CaDiCaL version: 2.1.3
% 3.11/0.73 % (1044647)Termination reason: Refutation
% 3.11/0.73 % (1044647)Time elapsed: 0.066 s
% 3.11/0.73 % (1044647)Peak memory usage: 13 MB
% 3.11/0.73 % (1044647)Instructions burned: 115 (million)
% 3.11/0.73 % (1044580)Success in time 0.486 s
% 3.11/0.73 % Vampire exiting
%------------------------------------------------------------------------------