%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU464^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 08:32:08 AM UTC 2026
% Result : Theorem 0.20s 0.70s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU464^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.17 % Computer : n004.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 13:41:52 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.21 Running first-order model finding
% 0.12/0.21 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
% 2.90/0.70 % (1303236)Will run a generic schedule for satisfiability detection.
% 2.90/0.70 % (1303249)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=774301151:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.90/0.70 % (1303248)% WARNING: option uhcvi not known.
% 2.90/0.70 % (1303247)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3446547411_2999 on theBenchmark for (2999ds/0Mi)
% 2.90/0.70 % (1303250)dis+10_1_sil=32000:sp=arity:random_seed=3433276919:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.90/0.70 % (1303251)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4031852235:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.90/0.70 % (1303248)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3604988148:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.90/0.70 % (1303251)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.90/0.70 % (1303248)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.90/0.70 % (1303248)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.90/0.70 % Exception at run slice level
% 2.90/0.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.90/0.70 % (1303253)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=240462519:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.90/0.70 % (1303252)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1917326764:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.90/0.70 % (1303261)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3471484712:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.90/0.70 % Exception at run slice level
% 2.90/0.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.90/0.70 % (1303250)Instruction limit reached!
% 2.90/0.70 % (1303250)------------------------------
% 2.90/0.70 % (1303250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.70 % (1303250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.70 % (1303250)CaDiCaL version: 2.1.3
% 2.90/0.70 % (1303250)Termination reason: Instruction limit
% 2.90/0.70 % (1303250)Termination phase: Saturation
% 2.90/0.70 % (1303250)Time elapsed: 0.052 s
% 2.90/0.70 % (1303250)Peak memory usage: 12 MB
% 2.90/0.70 % (1303250)Instructions burned: 105 (million)
% 2.90/0.70 % (1303251)Instruction limit reached!
% 2.90/0.70 % (1303251)------------------------------
% 2.90/0.70 % (1303251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.70 % (1303251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.70 % (1303251)CaDiCaL version: 2.1.3
% 2.90/0.70 % (1303251)Termination reason: Instruction limit
% 2.90/0.70 % (1303251)Termination phase: Saturation
% 2.90/0.70 % (1303251)Time elapsed: 0.052 s
% 2.90/0.70 % (1303251)Peak memory usage: 12 MB
% 2.90/0.70 % (1303251)Instructions burned: 119 (million)
% 2.90/0.70 % (1303274)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=897283580:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.90/0.70 % (1303275)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=939251115:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.90/0.70 % (1303276)ott-21_1_sil=16000:fs=off:random_seed=3143487325:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.90/0.70 % (1303275)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.90/0.70 % (1303275)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.90/0.70 % (1303252)Instruction limit reached!
% 2.90/0.70 % (1303252)------------------------------
% 2.90/0.70 % (1303252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.70 % (1303252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.70 % (1303252)CaDiCaL version: 2.1.3
% 2.90/0.70 % (1303252)Termination reason: Instruction limit
% 2.90/0.70 % (1303252)Termination phase: Saturation
% 2.90/0.70 % (1303252)Time elapsed: 0.101 s
% 2.90/0.70 % (1303252)Peak memory usage: 12 MB
% 2.90/0.70 % (1303252)Instructions burned: 131 (million)
% 2.90/0.70 % (1303253)Instruction limit reached!
% 2.90/0.70 % (1303253)------------------------------
% 2.90/0.70 % (1303253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.70 % (1303253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.70 % (1303253)CaDiCaL version: 2.1.3
% 2.90/0.70 % (1303253)Termination reason: Instruction limit
% 2.90/0.70 % (1303253)Termination phase: Saturation
% 2.90/0.70 % (1303253)Time elapsed: 0.110 s
% 2.90/0.70 % (1303253)Peak memory usage: 12 MB
% 2.90/0.70 % (1303253)Instructions burned: 159 (million)
% 2.90/0.70 % (1303281)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1264664564:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.90/0.70 % (1303282)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=176157349:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.90/0.70 % Exception at run slice level
% 2.90/0.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.90/0.70 % (1303274)Instruction limit reached!
% 2.90/0.70 % (1303274)------------------------------
% 2.90/0.70 % (1303274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.70 % (1303274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.70 % (1303274)CaDiCaL version: 2.1.3
% 2.90/0.70 % (1303274)Termination reason: Instruction limit
% 2.90/0.70 % (1303274)Termination phase: Saturation
% 2.90/0.70 % (1303274)Time elapsed: 0.097 s
% 2.90/0.70 % (1303274)Peak memory usage: 12 MB
% 2.90/0.70 % (1303274)Instructions burned: 132 (million)
% 2.90/0.70 % (1303276)Instruction limit reached!
% 2.90/0.70 % (1303276)------------------------------
% 2.90/0.70 % (1303276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.70 % (1303276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.70 % (1303276)CaDiCaL version: 2.1.3
% 2.90/0.70 % (1303276)Termination reason: Instruction limit
% 2.90/0.70 % (1303276)Termination phase: Saturation
% 2.90/0.70 % (1303276)Time elapsed: 0.094 s
% 2.90/0.70 % (1303276)Peak memory usage: 12 MB
% 2.90/0.70 % (1303276)Instructions burned: 181 (million)
% 2.90/0.70 % (1303285)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3727295651:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.90/0.70 % (1303286)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=521612017:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.90/0.70 % Exception at run slice level
% 2.90/0.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.90/0.70 % (1303287)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=855433437: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)
% 2.90/0.70 % (1303287)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.90/0.70 % (1303290)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3350423966:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.90/0.70 % (1303290)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.90/0.70 % (1303281)Instruction limit reached!
% 2.90/0.70 % (1303281)------------------------------
% 2.90/0.70 % (1303281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.70 % (1303281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.70 % (1303281)CaDiCaL version: 2.1.3
% 2.90/0.70 % (1303281)Termination reason: Instruction limit
% 2.90/0.70 % (1303281)Termination phase: Saturation
% 2.90/0.70 % (1303281)Time elapsed: 0.212 s
% 2.90/0.70 % (1303281)Peak memory usage: 13 MB
% 2.90/0.70 % (1303281)Instructions burned: 478 (million)
% 2.90/0.70 % (1303275)Instruction limit reached!
% 2.90/0.70 % (1303275)------------------------------
% 2.90/0.70 % (1303275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.90/0.70 % (1303275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/0.70 % (1303275)CaDiCaL version: 2.1.3
% 2.90/0.70 % (1303275)Termination reason: Instruction limit
% 2.90/0.70 % (1303275)Termination phase: Saturation
% 2.90/0.70 % (1303275)Time elapsed: 0.287 s
% 2.90/0.70 % (1303275)Peak memory usage: 14 MB
% 2.90/0.70 % (1303275)Instructions burned: 686 (million)
% 2.90/0.70 % (1303293)fmb+10_1_sil=64000:random_seed=885389373:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 0.20/0.70 % (1303293)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.70 % Exception at run slice level
% 0.20/0.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.70 % (1303294)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=619781204:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 0.20/0.70 % Exception at run slice level
% 0.20/0.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.70 % (1303296)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1060443100:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 0.20/0.70 % Exception at run slice level
% 0.20/0.70 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.70 % (1303298)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2032777655:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 0.20/0.70 % (1303298)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.70 % (1303300)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3752621930:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 0.20/0.70 % (1303300)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.70 % (1303300)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.70 % (1303300) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1303236-1303300"...
% 0.20/0.70 % (1303300)...printing done.
% 0.20/0.70 % (1303300)Refutation found. Thanks to Tanya!
% 0.20/0.70 % SZS status Theorem for theBenchmark
% 0.20/0.70 % SZS output start Proof for theBenchmark
% 0.20/0.70 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.70 thf(func_def_0, type, subrel: (($i > $i > $o) > ($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_2, type, inv: (($i > $i > $o) > $i > $i > $o)).
% 0.20/0.70 thf(func_def_3, type, idem: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_4, type, infl: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_5, type, mono: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_6, type, refl: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_7, type, irrefl: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_8, type, rc: (($i > $i > $o) > $i > $i > $o)).
% 0.20/0.70 thf(func_def_9, type, symm: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_10, type, antisymm: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_11, type, asymm: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_12, type, sc: (($i > $i > $o) > $i > $i > $o)).
% 0.20/0.70 thf(func_def_13, type, trans: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_14, type, tc: (($i > $i > $o) > $i > $i > $o)).
% 0.20/0.70 thf(func_def_15, type, trc: (($i > $i > $o) > $i > $i > $o)).
% 0.20/0.70 thf(func_def_16, type, trsc: (($i > $i > $o) > $i > $i > $o)).
% 0.20/0.70 thf(func_def_17, type, po: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_18, type, so: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_19, type, total: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_20, type, term: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_21, type, ind: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_22, type, innf: (($i > $i > $o) > $i > $o)).
% 0.20/0.70 thf(func_def_23, type, nfof: (($i > $i > $o) > $i > $i > $o)).
% 0.20/0.70 thf(func_def_24, type, norm: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_25, type, join: (($i > $i > $o) > $i > $i > $o)).
% 0.20/0.70 thf(func_def_26, type, lconfl: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_27, type, sconfl: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_28, type, confl: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_29, type, cr: (($i > $i > $o) > $o)).
% 0.20/0.70 thf(func_def_30, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.70 thf(func_def_31, type, vIMP: ($o > $o > $o)).
% 0.20/0.70 thf(func_def_32, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.70 thf(func_def_33, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.70 thf(func_def_34, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.70 thf(func_def_35, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.70 thf(func_def_36, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.70 thf(func_def_37, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.70 thf(func_def_38, type, vNOT: ($o > $o)).
% 0.20/0.70 thf(func_def_39, type, vOR: ($o > $o > $o)).
% 0.20/0.70 thf(func_def_40, type, vAND: ($o > $o > $o)).
% 0.20/0.70 thf(func_def_41, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.70 thf(func_def_44, type, sK0: ($i > $i > $o)).
% 0.20/0.70 thf(func_def_47, type, sK3: ($i > $i > $o)).
% 0.20/0.70 thf(func_def_48, type, sP4: ($o > $o)).
% 0.20/0.70 thf(func_def_49, type, sF5: !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.20/0.70 thf(func_def_50, type, sF6: !>[X0: $tType]:((X0 > X0 > (X0 > X0 > $o) > $o))).
% 0.20/0.70 thf(func_def_51, type, sF7: !>[X0: $tType]:((X0 > ($i > $i > $o) > X0))).
% 0.20/0.70 thf(func_def_52, type, sF8: !>[X0: $tType, X1: $tType]:((X0 > X1 > (X1 > X0 > $o) > $o))).
% 0.20/0.70 thf(func_def_53, type, sF9: ((($i > $i > $o) > $o) > ($i > $i > $o) > $o)).
% 0.20/0.70 thf(f30,conjecture,(
% 0.20/0.70 ! [X0 : ($i > $i > $o),X1 : $i,X2 : $i,X3 : ($i > $i > $o)] : ((! [X3 : ($i > $i > $o)] : (((subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2)) & (subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2))),
% 0.20/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_is_transitive4)).
% 0.20/0.70 thf(f31,negated_conjecture,(
% 0.20/0.70 ~ ! [X0 : ($i > $i > $o),X1 : $i,X2 : $i,X3 : ($i > $i > $o)] : ((! [X3 : ($i > $i > $o)] : (((subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2)) & (subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2))),
% 0.20/0.70 inference(negated_conjecture,[status(cth)],[f30])).
% 0.20/0.70 thf(f86,plain,(
% 0.20/0.70 ~ ! [X0 : ($i > $i > $o),X1 : $i,X2 : $i,X3 : ($i > $i > $o)] : ((! [X4 : ($i > $i > $o)] : (((subrel @ X0 @ X4) & (trans @ X4)) => (X4 @ X1 @ X2)) & (subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2))),
% 0.20/0.70 inference(rectify,[],[f31])).
% 0.20/0.70 thf(f87,plain,(
% 0.20/0.70 ~ ! [X0 : ($i > $i > $o),X1 : $i,X2 : $i,X3 : ($i > $i > $o)] : ((! [X4 : ($i > $i > $o)] : (((((subrel @ X0 @ X4)) = $true) & (((trans @ X4)) = $true)) => (((X4 @ X1 @ X2)) = $true)) & (((subrel @ X0 @ X3)) = $true) & (((trans @ X3)) = $true)) => (((X3 @ X1 @ X2)) = $true))),
% 0.20/0.70 inference(fool_elimination,[],[f86])).
% 0.20/0.70 thf(f88,plain,(
% 0.20/0.70 ? [X0 : ($i > $i > $o),X1 : $i,X2 : $i,X3 : ($i > $i > $o)] : ((((X3 @ X1 @ X2)) != $true) & (! [X4 : ($i > $i > $o)] : ((((X4 @ X1 @ X2)) = $true) | ((((subrel @ X0 @ X4)) != $true) | (((trans @ X4)) != $true))) & (((subrel @ X0 @ X3)) = $true) & (((trans @ X3)) = $true)))),
% 0.20/0.70 inference(ennf_transformation,[],[f87])).
% 0.20/0.70 thf(f89,plain,(
% 0.20/0.70 ? [X0 : ($i > $i > $o),X1 : $i,X2 : $i,X3 : ($i > $i > $o)] : ((((X3 @ X1 @ X2)) != $true) & ! [X4 : ($i > $i > $o)] : ((((X4 @ X1 @ X2)) = $true) | (((subrel @ X0 @ X4)) != $true) | (((trans @ X4)) != $true)) & (((subrel @ X0 @ X3)) = $true) & (((trans @ X3)) = $true))),
% 0.20/0.70 inference(flattening,[],[f88])).
% 0.20/0.70 thf(f90,plain,(
% 0.20/0.70 ($true != ((sK3 @ sK1 @ sK2))) & ! [X4 : ($i > $i > $o)] : (($true = ((X4 @ sK1 @ sK2))) | ($true != ((subrel @ sK0 @ X4))) | (((trans @ X4)) != $true)) & ($true = ((subrel @ sK0 @ sK3))) & ($true = ((trans @ sK3)))),
% 0.20/0.70 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f89])).
% 0.20/0.70 thf(f120,plain,(
% 0.20/0.70 ($true = ((trans @ sK3)))),
% 0.20/0.70 inference(cnf_transformation,[],[f90])).
% 0.20/0.70 thf(f121,plain,(
% 0.20/0.70 ($true = ((subrel @ sK0 @ sK3)))),
% 0.20/0.70 inference(cnf_transformation,[],[f90])).
% 0.20/0.70 thf(f122,plain,(
% 0.20/0.70 ( ! [X4 : ($i > $i > $o)] : (($true != ((subrel @ sK0 @ X4))) | ($true = ((X4 @ sK1 @ sK2))) | (((trans @ X4)) != $true)) )),
% 0.20/0.70 inference(cnf_transformation,[],[f90])).
% 0.20/0.70 thf(f123,plain,(
% 0.20/0.70 ($true != ((sK3 @ sK1 @ sK2)))),
% 0.20/0.70 inference(cnf_transformation,[],[f90])).
% 0.20/0.70 thf(f125,definition,(
% 0.20/0.70 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.70 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.70 thf(f126,definition,(
% 0.20/0.70 ($false = ((sP4 @ (sK3 @ sK1 @ sK2))))),
% 0.20/0.70 introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction])).
% 0.20/0.70 thf(f127,plain,(
% 0.20/0.70 ($true = ((sP4 @ $true)))),
% 0.20/0.70 inference(inequality_splitting,[],[f123,f126])).
% 0.20/0.70 thf(f146,plain,(
% 0.20/0.70 ($false = ((sP4 @ $true))) | (((sK3 @ sK1 @ sK2)) = $false)),
% 0.20/0.70 inference(constrained_superposition,[],[f126,f125])).
% 0.20/0.70 thf(f156,plain,(
% 0.20/0.70 ($true = $false) | (((sK3 @ sK1 @ sK2)) = $false)),
% 0.20/0.70 inference(forward_demodulation,[],[f146,f127])).
% 0.20/0.70 thf(f157,plain,(
% 0.20/0.70 (((sK3 @ sK1 @ sK2)) = $false)),
% 0.20/0.70 inference(trivial_inequality_removal,[],[f156])).
% 0.20/0.70 thf(f167,plain,(
% 0.20/0.70 ($true != $true) | ($true = ((sK3 @ sK1 @ sK2))) | ($true != ((trans @ sK3)))),
% 0.20/0.70 inference(constrained_superposition,[],[f122,f121])).
% 0.20/0.70 thf(f170,plain,(
% 0.20/0.70 ($true = ((sK3 @ sK1 @ sK2))) | ($true != ((trans @ sK3)))),
% 0.20/0.70 inference(trivial_inequality_removal,[],[f167])).
% 0.20/0.70 thf(f174,plain,(
% 0.20/0.70 ($true = ((sK3 @ sK1 @ sK2)))),
% 0.20/0.70 inference(forward_subsumption_resolution,[],[f170,f120])).
% 0.20/0.70 thf(f175,plain,(
% 0.20/0.70 ($true = $false)),
% 0.20/0.70 inference(forward_demodulation,[],[f174,f157])).
% 0.20/0.70 thf(f176,plain,(
% 0.20/0.70 $false),
% 0.20/0.70 inference(trivial_inequality_removal,[],[f175])).
% 0.20/0.70 % SZS output end Proof for theBenchmark
% 0.20/0.70 % (1303300)------------------------------
% 0.20/0.70 % (1303300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.70 % (1303300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.70 % (1303300)CaDiCaL version: 2.1.3
% 0.20/0.70 % (1303300)Termination reason: Refutation
% 0.20/0.70 % (1303300)Time elapsed: 0.008 s
% 0.20/0.70 % (1303300)Peak memory usage: 13 MB
% 0.20/0.70 % (1303300)Instructions burned: 13 (million)
% 0.20/0.70 % (1303236)Success in time 0.478 s
% 0.20/0.70 % Vampire exiting
%------------------------------------------------------------------------------