%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO386^5 : 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 : n009.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 08:49:50 AM UTC 2026
% Result : Theorem 2.23s 0.57s
% Output : Refutation 2.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO386^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:50:15 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 2.23/0.57 % (59354)Will run a generic schedule for satisfiability detection.
% 2.23/0.57 % (59360)% WARNING: option uhcvi not known.
% 2.23/0.57 % (59360)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1143218957:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.23/0.57 % (59360)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.23/0.57 % (59360)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.23/0.57 % (59359)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2029697403_2999 on theBenchmark for (2999ds/0Mi)
% 2.23/0.57 % (59362)dis+10_1_sil=32000:sp=arity:random_seed=3240492991:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.23/0.57 % (59361)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=408010740:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.23/0.57 % Exception at run slice level
% 2.23/0.57 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.23/0.57 % (59363)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3810442417:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.23/0.57 % (59363)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.23/0.57 % (59364)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1711889141:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.23/0.57 % (59365)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3426380276:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.23/0.57 % (59370)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=552961688:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.23/0.57 % Exception at run slice level
% 2.23/0.57 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.23/0.57 % (59375)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3059213640:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.23/0.57 % (59362)Instruction limit reached!
% 2.23/0.57 % (59362)------------------------------
% 2.23/0.57 % (59362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.57 % (59362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.57 % (59362)CaDiCaL version: 2.1.3
% 2.23/0.57 % (59362)Termination reason: Instruction limit
% 2.23/0.57 % (59362)Termination phase: Saturation
% 2.23/0.57 % (59362)Time elapsed: 0.051 s
% 2.23/0.57 % (59362)Peak memory usage: 12 MB
% 2.23/0.57 % (59362)Instructions burned: 104 (million)
% 2.23/0.57 % (59363)Instruction limit reached!
% 2.23/0.57 % (59363)------------------------------
% 2.23/0.57 % (59363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.57 % (59363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.57 % (59363)CaDiCaL version: 2.1.3
% 2.23/0.57 % (59363)Termination reason: Instruction limit
% 2.23/0.57 % (59363)Termination phase: Saturation
% 2.23/0.57 % (59363)Time elapsed: 0.065 s
% 2.23/0.57 % (59363)Peak memory usage: 12 MB
% 2.23/0.57 % (59363)Instructions burned: 116 (million)
% 2.23/0.57 % (59377)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=3610018806:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.23/0.57 % (59364)Instruction limit reached!
% 2.23/0.57 % (59364)------------------------------
% 2.23/0.57 % (59364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.57 % (59364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.57 % (59364)CaDiCaL version: 2.1.3
% 2.23/0.57 % (59364)Termination reason: Instruction limit
% 2.23/0.57 % (59364)Termination phase: Saturation
% 2.23/0.57 % (59364)Time elapsed: 0.063 s
% 2.23/0.57 % (59364)Peak memory usage: 12 MB
% 2.23/0.57 % (59364)Instructions burned: 132 (million)
% 2.23/0.57 % (59377)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.23/0.57 % (59377)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.23/0.57 % (59379)ott-21_1_sil=16000:fs=off:random_seed=3854076078:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.23/0.57 % (59380)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2440132071:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.23/0.57 % (59375)Instruction limit reached!
% 2.23/0.57 % (59375)------------------------------
% 2.23/0.57 % (59375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.57 % (59375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.57 % (59375)CaDiCaL version: 2.1.3
% 2.23/0.57 % (59375)Termination reason: Instruction limit
% 2.23/0.57 % (59375)Termination phase: Saturation
% 2.23/0.57 % (59375)Time elapsed: 0.069 s
% 2.23/0.57 % (59375)Peak memory usage: 12 MB
% 2.23/0.57 % (59375)Instructions burned: 131 (million)
% 2.23/0.57 % (59383)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3143090594:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.23/0.57 % Exception at run slice level
% 2.23/0.57 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.23/0.57 % (59385)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3892348342:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.23/0.57 % (59365)Instruction limit reached!
% 2.23/0.57 % (59365)------------------------------
% 2.23/0.57 % (59365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.57 % (59365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.57 % (59365)CaDiCaL version: 2.1.3
% 2.23/0.57 % (59365)Termination reason: Instruction limit
% 2.23/0.57 % (59365)Termination phase: Saturation
% 2.23/0.57 % (59365)Time elapsed: 0.139 s
% 2.23/0.57 % (59365)Peak memory usage: 12 MB
% 2.23/0.57 % (59365)Instructions burned: 160 (million)
% 2.23/0.57 % (59387)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=369308199:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.23/0.57 % Exception at run slice level
% 2.23/0.57 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.23/0.57 % (59389)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=4120892087: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)
% 2.23/0.57 % (59389)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.23/0.57 % (59379)Instruction limit reached!
% 2.23/0.57 % (59379)------------------------------
% 2.23/0.57 % (59379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.57 % (59379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.57 % (59379)CaDiCaL version: 2.1.3
% 2.23/0.57 % (59379)Termination reason: Instruction limit
% 2.23/0.57 % (59379)Termination phase: Saturation
% 2.23/0.57 % (59379)Time elapsed: 0.129 s
% 2.23/0.57 % (59379)Peak memory usage: 12 MB
% 2.23/0.57 % (59379)Instructions burned: 181 (million)
% 2.23/0.57 % (59391)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2876722459:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.23/0.57 % (59391)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.23/0.57 % (59360) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-59354-59360"...
% 2.23/0.57 % (59360)...printing done.
% 2.23/0.57 % (59360)Refutation found. Thanks to Tanya!
% 2.23/0.57 % SZS status Theorem for theBenchmark
% 2.23/0.57 % SZS output start Proof for theBenchmark
% 2.23/0.57 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 2.23/0.58 thf(func_def_0, type, cQ_4: ($i > $i > $i > $o)).
% 2.23/0.58 thf(func_def_1, type, f: ($i > $i)).
% 2.23/0.58 thf(func_def_2, type, cP_3: ($i > $i > $o)).
% 2.23/0.58 thf(func_def_3, type, cQ_3: ($i > $i > $i > $o)).
% 2.23/0.58 thf(func_def_8, type, cP_2: ($i > $i > $o)).
% 2.23/0.58 thf(func_def_9, type, cQ_2: ($i > $i > $i > $o)).
% 2.23/0.58 thf(func_def_10, type, cP_1: ($i > $i > $o)).
% 2.23/0.58 thf(func_def_11, type, cQ_1: ($i > $i > $i > $o)).
% 2.23/0.58 thf(f1,conjecture,(
% 2.23/0.58 ~(! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_4 @ X0 @ X1 @ X2) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_4 @ X3 @ X4 @ X5) | ~(cP_3 @ (f @ X2) @ X5) | ~(cP_3 @ (f @ X1) @ X4) | ~(cP_3 @ (f @ X0) @ X3) | ~(cQ_3 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_3 @ (f @ X0) @ X1) | ~(cP_3 @ X0 @ X1)) & ! [X0 : $i] : (cP_3 @ d @ X0) & (cP_3 @ c @ c) & (cP_3 @ b @ b) & (cP_3 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X2) @ X5) | ~(cP_2 @ (f @ X1) @ X4) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_2 @ (f @ X0) @ X1) | ~(cP_2 @ X0 @ X1)) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_2 @ c @ c) & (cP_2 @ b @ b) & (cP_2 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_2 @ X3 @ X4 @ X5) | ~(cP_1 @ (f @ X2) @ X5) | ~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X0) @ X3) | ~(cQ_1 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_1 @ (f @ X0) @ X1) | ~(cP_1 @ X0 @ X1)) & ! [X0 : $i] : (cP_1 @ d @ X0) & (cP_1 @ c @ c) & (cP_1 @ b @ b) & (cP_1 @ a @ a) & (cQ_1 @ a @ b @ c))),
% 2.23/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM409_3)).
% 2.23/0.58 thf(f2,negated_conjecture,(
% 2.23/0.58 ~ ~(! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_4 @ X0 @ X1 @ X2) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_4 @ X3 @ X4 @ X5) | ~(cP_3 @ (f @ X2) @ X5) | ~(cP_3 @ (f @ X1) @ X4) | ~(cP_3 @ (f @ X0) @ X3) | ~(cQ_3 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_3 @ (f @ X0) @ X1) | ~(cP_3 @ X0 @ X1)) & ! [X0 : $i] : (cP_3 @ d @ X0) & (cP_3 @ c @ c) & (cP_3 @ b @ b) & (cP_3 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_3 @ X3 @ X4 @ X5) | ~(cP_2 @ (f @ X2) @ X5) | ~(cP_2 @ (f @ X1) @ X4) | ~(cP_2 @ (f @ X0) @ X3) | ~(cQ_2 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_2 @ (f @ X0) @ X1) | ~(cP_2 @ X0 @ X1)) & ! [X0 : $i] : (cP_2 @ d @ X0) & (cP_2 @ c @ c) & (cP_2 @ b @ b) & (cP_2 @ a @ a) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_2 @ X3 @ X4 @ X5) | ~(cP_1 @ (f @ X2) @ X5) | ~(cP_1 @ (f @ X1) @ X4) | ~(cP_1 @ (f @ X0) @ X3) | ~(cQ_1 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_1 @ (f @ X0) @ X1) | ~(cP_1 @ X0 @ X1)) & ! [X0 : $i] : (cP_1 @ d @ X0) & (cP_1 @ c @ c) & (cP_1 @ b @ b) & (cP_1 @ a @ a) & (cQ_1 @ a @ b @ c))),
% 2.23/0.58 inference(negated_conjecture,[status(cth)],[f1])).
% 2.23/0.58 thf(f3,plain,(
% 2.23/0.58 ~ ~(! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_4 @ X0 @ X1 @ X2) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : ((cQ_4 @ X6 @ X7 @ X8) | ~(cP_3 @ (f @ X5) @ X8) | ~(cP_3 @ (f @ X4) @ X7) | ~(cP_3 @ (f @ X3) @ X6) | ~(cQ_3 @ X3 @ X4 @ X5)) & ! [X9 : $i,X10 : $i] : ((cP_3 @ (f @ X9) @ X10) | ~(cP_3 @ X9 @ X10)) & ! [X11 : $i] : (cP_3 @ d @ X11) & (cP_3 @ c @ c) & (cP_3 @ b @ b) & (cP_3 @ a @ a) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : ((cQ_3 @ X15 @ X16 @ X17) | ~(cP_2 @ (f @ X14) @ X17) | ~(cP_2 @ (f @ X13) @ X16) | ~(cP_2 @ (f @ X12) @ X15) | ~(cQ_2 @ X12 @ X13 @ X14)) & ! [X18 : $i,X19 : $i] : ((cP_2 @ (f @ X18) @ X19) | ~(cP_2 @ X18 @ X19)) & ! [X20 : $i] : (cP_2 @ d @ X20) & (cP_2 @ c @ c) & (cP_2 @ b @ b) & (cP_2 @ a @ a) & ! [X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i] : ((cQ_2 @ X24 @ X25 @ X26) | ~(cP_1 @ (f @ X23) @ X26) | ~(cP_1 @ (f @ X22) @ X25) | ~(cP_1 @ (f @ X21) @ X24) | ~(cQ_1 @ X21 @ X22 @ X23)) & ! [X27 : $i,X28 : $i] : ((cP_1 @ (f @ X27) @ X28) | ~(cP_1 @ X27 @ X28)) & ! [X29 : $i] : (cP_1 @ d @ X29) & (cP_1 @ c @ c) & (cP_1 @ b @ b) & (cP_1 @ a @ a) & (cQ_1 @ a @ b @ c))),
% 2.23/0.58 inference(rectify,[],[f2])).
% 2.23/0.58 thf(f4,plain,(
% 2.23/0.58 ~ ~(! [X0 : $i,X1 : $i,X2 : $i] : ~ (((cQ_4 @ X0 @ X1 @ X2)) = $true) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : ((((cQ_4 @ X6 @ X7 @ X8)) = $true) | ~ (((cP_3 @ (f @ X5) @ X8)) = $true) | ~ (((cP_3 @ (f @ X4) @ X7)) = $true) | ~ (((cP_3 @ (f @ X3) @ X6)) = $true) | ~ (((cQ_3 @ X3 @ X4 @ X5)) = $true)) & ! [X9 : $i,X10 : $i] : ((((cP_3 @ (f @ X9) @ X10)) = $true) | ~ (((cP_3 @ X9 @ X10)) = $true)) & ! [X11 : $i] : (((cP_3 @ d @ X11)) = $true) & (((cP_3 @ c @ c)) = $true) & (((cP_3 @ b @ b)) = $true) & (((cP_3 @ a @ a)) = $true) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : ((((cQ_3 @ X15 @ X16 @ X17)) = $true) | ~ (((cP_2 @ (f @ X14) @ X17)) = $true) | ~ (((cP_2 @ (f @ X13) @ X16)) = $true) | ~ (((cP_2 @ (f @ X12) @ X15)) = $true) | ~ (((cQ_2 @ X12 @ X13 @ X14)) = $true)) & ! [X18 : $i,X19 : $i] : ((((cP_2 @ (f @ X18) @ X19)) = $true) | ~ (((cP_2 @ X18 @ X19)) = $true)) & ! [X20 : $i] : (((cP_2 @ d @ X20)) = $true) & (((cP_2 @ c @ c)) = $true) & (((cP_2 @ b @ b)) = $true) & (((cP_2 @ a @ a)) = $true) & ! [X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i] : ((((cQ_2 @ X24 @ X25 @ X26)) = $true) | ~ (((cP_1 @ (f @ X23) @ X26)) = $true) | ~ (((cP_1 @ (f @ X22) @ X25)) = $true) | ~ (((cP_1 @ (f @ X21) @ X24)) = $true) | ~ (((cQ_1 @ X21 @ X22 @ X23)) = $true)) & ! [X27 : $i,X28 : $i] : ((((cP_1 @ (f @ X27) @ X28)) = $true) | ~ (((cP_1 @ X27 @ X28)) = $true)) & ! [X29 : $i] : (((cP_1 @ d @ X29)) = $true) & (((cP_1 @ c @ c)) = $true) & (((cP_1 @ b @ b)) = $true) & (((cP_1 @ a @ a)) = $true) & (((cQ_1 @ a @ b @ c)) = $true))),
% 2.23/0.58 inference(fool_elimination,[],[f3])).
% 2.23/0.58 thf(f5,plain,(
% 2.23/0.58 ! [X0 : $i,X1 : $i,X2 : $i] : (((cQ_4 @ X0 @ X1 @ X2)) != $true) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : ((((cQ_4 @ X6 @ X7 @ X8)) = $true) | (((cP_3 @ (f @ X5) @ X8)) != $true) | (((cP_3 @ (f @ X4) @ X7)) != $true) | (((cP_3 @ (f @ X3) @ X6)) != $true) | (((cQ_3 @ X3 @ X4 @ X5)) != $true)) & ! [X9 : $i,X10 : $i] : ((((cP_3 @ (f @ X9) @ X10)) = $true) | (((cP_3 @ X9 @ X10)) != $true)) & ! [X11 : $i] : (((cP_3 @ d @ X11)) = $true) & (((cP_3 @ c @ c)) = $true) & (((cP_3 @ b @ b)) = $true) & (((cP_3 @ a @ a)) = $true) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : ((((cQ_3 @ X15 @ X16 @ X17)) = $true) | (((cP_2 @ (f @ X14) @ X17)) != $true) | (((cP_2 @ (f @ X13) @ X16)) != $true) | (((cP_2 @ (f @ X12) @ X15)) != $true) | (((cQ_2 @ X12 @ X13 @ X14)) != $true)) & ! [X18 : $i,X19 : $i] : ((((cP_2 @ (f @ X18) @ X19)) = $true) | (((cP_2 @ X18 @ X19)) != $true)) & ! [X20 : $i] : (((cP_2 @ d @ X20)) = $true) & (((cP_2 @ c @ c)) = $true) & (((cP_2 @ b @ b)) = $true) & (((cP_2 @ a @ a)) = $true) & ! [X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i] : ((((cQ_2 @ X24 @ X25 @ X26)) = $true) | (((cP_1 @ (f @ X23) @ X26)) != $true) | (((cP_1 @ (f @ X22) @ X25)) != $true) | (((cP_1 @ (f @ X21) @ X24)) != $true) | (((cQ_1 @ X21 @ X22 @ X23)) != $true)) & ! [X27 : $i,X28 : $i] : ((((cP_1 @ (f @ X27) @ X28)) = $true) | (((cP_1 @ X27 @ X28)) != $true)) & ! [X29 : $i] : (((cP_1 @ d @ X29)) = $true) & (((cP_1 @ c @ c)) = $true) & (((cP_1 @ b @ b)) = $true) & (((cP_1 @ a @ a)) = $true) & (((cQ_1 @ a @ b @ c)) = $true)),
% 2.23/0.58 inference(flattening,[],[f4])).
% 2.23/0.58 thf(f6,plain,(
% 2.23/0.58 (((cQ_1 @ a @ b @ c)) = $true)),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f7,plain,(
% 2.23/0.58 (((cP_1 @ a @ a)) = $true)),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f8,plain,(
% 2.23/0.58 (((cP_1 @ b @ b)) = $true)),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f9,plain,(
% 2.23/0.58 (((cP_1 @ c @ c)) = $true)),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f11,plain,(
% 2.23/0.58 ( ! [X28 : $i,X27 : $i] : ((((cP_1 @ X27 @ X28)) != $true) | (((cP_1 @ (f @ X27) @ X28)) = $true)) )),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f12,plain,(
% 2.23/0.58 ( ! [X21 : $i,X26 : $i,X24 : $i,X22 : $i,X25 : $i,X23 : $i] : ((((cQ_1 @ X21 @ X22 @ X23)) != $true) | (((cP_1 @ (f @ X23) @ X26)) != $true) | (((cP_1 @ (f @ X22) @ X25)) != $true) | (((cP_1 @ (f @ X21) @ X24)) != $true) | (((cQ_2 @ X24 @ X25 @ X26)) = $true)) )),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f13,plain,(
% 2.23/0.58 (((cP_2 @ a @ a)) = $true)),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f14,plain,(
% 2.23/0.58 (((cP_2 @ b @ b)) = $true)),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f15,plain,(
% 2.23/0.58 (((cP_2 @ c @ c)) = $true)),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f17,plain,(
% 2.23/0.58 ( ! [X18 : $i,X19 : $i] : ((((cP_2 @ X18 @ X19)) != $true) | (((cP_2 @ (f @ X18) @ X19)) = $true)) )),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f18,plain,(
% 2.23/0.58 ( ! [X16 : $i,X14 : $i,X17 : $i,X15 : $i,X12 : $i,X13 : $i] : ((((cQ_2 @ X12 @ X13 @ X14)) != $true) | (((cP_2 @ (f @ X14) @ X17)) != $true) | (((cP_2 @ (f @ X13) @ X16)) != $true) | (((cP_2 @ (f @ X12) @ X15)) != $true) | (((cQ_3 @ X15 @ X16 @ X17)) = $true)) )),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f19,plain,(
% 2.23/0.58 (((cP_3 @ a @ a)) = $true)),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f20,plain,(
% 2.23/0.58 (((cP_3 @ b @ b)) = $true)),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f21,plain,(
% 2.23/0.58 (((cP_3 @ c @ c)) = $true)),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f23,plain,(
% 2.23/0.58 ( ! [X10 : $i,X9 : $i] : ((((cP_3 @ X9 @ X10)) != $true) | (((cP_3 @ (f @ X9) @ X10)) = $true)) )),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f24,plain,(
% 2.23/0.58 ( ! [X3 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((cQ_4 @ X6 @ X7 @ X8)) = $true) | (((cP_3 @ (f @ X5) @ X8)) != $true) | (((cP_3 @ (f @ X4) @ X7)) != $true) | (((cP_3 @ (f @ X3) @ X6)) != $true) | (((cQ_3 @ X3 @ X4 @ X5)) != $true)) )),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f25,plain,(
% 2.23/0.58 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((cQ_4 @ X0 @ X1 @ X2)) != $true)) )),
% 2.23/0.58 inference(cnf_transformation,[],[f5])).
% 2.23/0.58 thf(f27,definition,(
% 2.23/0.58 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 2.23/0.58 introduced(theory,[fool_exhaustiveness_axiom])).
% 2.23/0.58 thf(f29,plain,(
% 2.23/0.58 ($true != $true) | ($true = ((cP_1 @ (f @ c) @ c)))),
% 2.23/0.58 inference(constrained_superposition,[],[f11,f9])).
% 2.23/0.58 thf(f30,plain,(
% 2.23/0.58 ($true != $true) | ($true = ((cP_1 @ (f @ b) @ b)))),
% 2.23/0.58 inference(constrained_superposition,[],[f11,f8])).
% 2.23/0.58 thf(f31,plain,(
% 2.23/0.58 ($true != $true) | ($true = ((cP_1 @ (f @ a) @ a)))),
% 2.23/0.58 inference(constrained_superposition,[],[f11,f7])).
% 2.23/0.58 thf(f32,plain,(
% 2.23/0.58 ($true = ((cP_1 @ (f @ a) @ a)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f31])).
% 2.23/0.58 thf(f33,plain,(
% 2.23/0.58 ($true = ((cP_1 @ (f @ b) @ b)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f30])).
% 2.23/0.58 thf(f34,plain,(
% 2.23/0.58 ($true = ((cP_1 @ (f @ c) @ c)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f29])).
% 2.23/0.58 thf(f37,plain,(
% 2.23/0.58 ($true != $true) | ($true = ((cP_2 @ (f @ c) @ c)))),
% 2.23/0.58 inference(constrained_superposition,[],[f17,f15])).
% 2.23/0.58 thf(f38,plain,(
% 2.23/0.58 ($true != $true) | ($true = ((cP_2 @ (f @ b) @ b)))),
% 2.23/0.58 inference(constrained_superposition,[],[f17,f14])).
% 2.23/0.58 thf(f39,plain,(
% 2.23/0.58 ($true != $true) | ($true = ((cP_2 @ (f @ a) @ a)))),
% 2.23/0.58 inference(constrained_superposition,[],[f17,f13])).
% 2.23/0.58 thf(f40,plain,(
% 2.23/0.58 ($true = ((cP_2 @ (f @ a) @ a)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f39])).
% 2.23/0.58 thf(f41,plain,(
% 2.23/0.58 ($true = ((cP_2 @ (f @ b) @ b)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f38])).
% 2.23/0.58 thf(f42,plain,(
% 2.23/0.58 ($true = ((cP_2 @ (f @ c) @ c)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f37])).
% 2.23/0.58 thf(f45,plain,(
% 2.23/0.58 ($true != $true) | ($true = ((cP_3 @ (f @ c) @ c)))),
% 2.23/0.58 inference(constrained_superposition,[],[f23,f21])).
% 2.23/0.58 thf(f46,plain,(
% 2.23/0.58 ($true != $true) | ($true = ((cP_3 @ (f @ b) @ b)))),
% 2.23/0.58 inference(constrained_superposition,[],[f23,f20])).
% 2.23/0.58 thf(f47,plain,(
% 2.23/0.58 ($true != $true) | ($true = ((cP_3 @ (f @ a) @ a)))),
% 2.23/0.58 inference(constrained_superposition,[],[f23,f19])).
% 2.23/0.58 thf(f48,plain,(
% 2.23/0.58 ($true = ((cP_3 @ (f @ a) @ a)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f47])).
% 2.23/0.58 thf(f49,plain,(
% 2.23/0.58 ($true = ((cP_3 @ (f @ b) @ b)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f46])).
% 2.23/0.58 thf(f50,plain,(
% 2.23/0.58 ($true = ((cP_3 @ (f @ c) @ c)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f45])).
% 2.23/0.58 thf(f69,plain,(
% 2.23/0.58 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != ((cP_1 @ (f @ c) @ X0))) | ($true != ((cP_1 @ (f @ b) @ X1))) | ($true != ((cP_1 @ (f @ a) @ X2))) | ($true = ((cQ_2 @ X2 @ X1 @ X0)))) )),
% 2.23/0.58 inference(constrained_superposition,[],[f12,f6])).
% 2.23/0.58 thf(f72,plain,(
% 2.23/0.58 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((cP_1 @ (f @ a) @ X2))) | ($true != ((cP_1 @ (f @ b) @ X1))) | ($true != ((cP_1 @ (f @ c) @ X0))) | ($true = ((cQ_2 @ X2 @ X1 @ X0)))) )),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f69])).
% 2.23/0.58 thf(f77,plain,(
% 2.23/0.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != ((cP_2 @ (f @ X2) @ X3))) | (((cP_2 @ (f @ X1) @ X4)) != $true) | ($true != ((cP_2 @ (f @ X0) @ X5))) | ($true = ((cQ_3 @ X5 @ X4 @ X3))) | (((cQ_2 @ X0 @ X1 @ X2)) = $false)) )),
% 2.23/0.58 inference(constrained_superposition,[],[f18,f27])).
% 2.23/0.58 thf(f78,plain,(
% 2.23/0.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != ((cP_2 @ (f @ X2) @ X3))) | (((cP_2 @ (f @ X1) @ X4)) != $true) | ($true != ((cP_2 @ (f @ X0) @ X5))) | ($true = ((cQ_3 @ X5 @ X4 @ X3))) | (((cQ_2 @ X0 @ X1 @ X2)) = $false)) )),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f77])).
% 2.23/0.58 thf(f79,plain,(
% 2.23/0.58 ( ! [X3 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((cQ_3 @ X3 @ X4 @ X5)) != $true) | (((cP_3 @ (f @ X4) @ X7)) != $true) | (((cP_3 @ (f @ X3) @ X6)) != $true) | (((cP_3 @ (f @ X5) @ X8)) != $true)) )),
% 2.23/0.58 inference(forward_subsumption_resolution,[],[f24,f25])).
% 2.23/0.58 thf(f80,plain,(
% 2.23/0.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != ((cP_3 @ (f @ X1) @ X3))) | ($true != ((cP_3 @ (f @ X0) @ X4))) | (((cP_3 @ (f @ X2) @ X5)) != $true) | (((cQ_3 @ X0 @ X1 @ X2)) = $false)) )),
% 2.23/0.58 inference(constrained_superposition,[],[f79,f27])).
% 2.23/0.58 thf(f81,plain,(
% 2.23/0.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != ((cP_3 @ (f @ X1) @ X3))) | ($true != ((cP_3 @ (f @ X0) @ X4))) | (((cP_3 @ (f @ X2) @ X5)) != $true) | (((cQ_3 @ X0 @ X1 @ X2)) = $false)) )),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f80])).
% 2.23/0.58 thf(f122,plain,(
% 2.23/0.58 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != ((cP_1 @ (f @ b) @ X0))) | ($true != ((cP_1 @ (f @ c) @ X1))) | ($true = ((cQ_2 @ a @ X0 @ X1)))) )),
% 2.23/0.58 inference(constrained_superposition,[],[f72,f32])).
% 2.23/0.58 thf(f125,plain,(
% 2.23/0.58 ( ! [X0 : $i,X1 : $i] : (($true != ((cP_1 @ (f @ b) @ X0))) | ($true != ((cP_1 @ (f @ c) @ X1))) | ($true = ((cQ_2 @ a @ X0 @ X1)))) )),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f122])).
% 2.23/0.58 thf(f130,plain,(
% 2.23/0.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((cP_3 @ (f @ X0) @ X1)) != $true) | ($true != ((cP_3 @ (f @ X2) @ X3))) | ($false = ((cQ_3 @ X0 @ b @ X2)))) )),
% 2.23/0.58 inference(constrained_superposition,[],[f81,f49])).
% 2.23/0.58 thf(f135,plain,(
% 2.23/0.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((cP_3 @ (f @ X2) @ X3))) | (((cP_3 @ (f @ X0) @ X1)) != $true) | ($false = ((cQ_3 @ X0 @ b @ X2)))) )),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f130])).
% 2.23/0.58 thf(f166,plain,(
% 2.23/0.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((cP_2 @ (f @ X0) @ X1)) != $true) | ($true != ((cP_2 @ (f @ X2) @ X3))) | ($true = ((cQ_3 @ X3 @ X1 @ c))) | ($false = ((cQ_2 @ X2 @ X0 @ c)))) )),
% 2.23/0.58 inference(constrained_superposition,[],[f78,f42])).
% 2.23/0.58 thf(f179,plain,(
% 2.23/0.58 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((cP_2 @ (f @ X2) @ X3))) | (((cP_2 @ (f @ X0) @ X1)) != $true) | ($true = ((cQ_3 @ X3 @ X1 @ c))) | ($false = ((cQ_2 @ X2 @ X0 @ c)))) )),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f166])).
% 2.23/0.58 thf(f220,plain,(
% 2.23/0.58 ( ! [X0 : $i] : (($true != $true) | ($true != ((cP_1 @ (f @ c) @ X0))) | ($true = ((cQ_2 @ a @ b @ X0)))) )),
% 2.23/0.58 inference(constrained_superposition,[],[f125,f33])).
% 2.23/0.58 thf(f223,plain,(
% 2.23/0.58 ( ! [X0 : $i] : (($true != ((cP_1 @ (f @ c) @ X0))) | ($true = ((cQ_2 @ a @ b @ X0)))) )),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f220])).
% 2.23/0.58 thf(f251,plain,(
% 2.23/0.58 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cP_3 @ (f @ X0) @ X1)) != $true) | ($false = ((cQ_3 @ X0 @ b @ c)))) )),
% 2.23/0.58 inference(constrained_superposition,[],[f135,f50])).
% 2.23/0.58 thf(f264,plain,(
% 2.23/0.58 ( ! [X0 : $i,X1 : $i] : ((((cP_3 @ (f @ X0) @ X1)) != $true) | ($false = ((cQ_3 @ X0 @ b @ c)))) )),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f251])).
% 2.23/0.58 thf(f648,plain,(
% 2.23/0.58 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cP_2 @ (f @ X0) @ X1)) != $true) | ($true = ((cQ_3 @ a @ X1 @ c))) | ($false = ((cQ_2 @ a @ X0 @ c)))) )),
% 2.23/0.58 inference(constrained_superposition,[],[f179,f40])).
% 2.23/0.58 thf(f655,plain,(
% 2.23/0.58 ( ! [X0 : $i,X1 : $i] : ((((cP_2 @ (f @ X0) @ X1)) != $true) | ($true = ((cQ_3 @ a @ X1 @ c))) | ($false = ((cQ_2 @ a @ X0 @ c)))) )),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f648])).
% 2.23/0.58 thf(f866,plain,(
% 2.23/0.58 ($true != $true) | ($true = ((cQ_2 @ a @ b @ c)))),
% 2.23/0.58 inference(constrained_superposition,[],[f223,f34])).
% 2.23/0.58 thf(f869,plain,(
% 2.23/0.58 ($true = ((cQ_2 @ a @ b @ c)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f866])).
% 2.23/0.58 thf(f1095,plain,(
% 2.23/0.58 ($true != $true) | ($false = ((cQ_3 @ a @ b @ c)))),
% 2.23/0.58 inference(constrained_superposition,[],[f264,f48])).
% 2.23/0.58 thf(f1102,plain,(
% 2.23/0.58 ($false = ((cQ_3 @ a @ b @ c)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f1095])).
% 2.23/0.58 thf(f5389,plain,(
% 2.23/0.58 ($true != $true) | ($true = ((cQ_3 @ a @ b @ c))) | ($false = ((cQ_2 @ a @ b @ c)))),
% 2.23/0.58 inference(constrained_superposition,[],[f655,f41])).
% 2.23/0.58 thf(f5402,plain,(
% 2.23/0.58 ($true = ((cQ_3 @ a @ b @ c))) | ($false = ((cQ_2 @ a @ b @ c)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f5389])).
% 2.23/0.58 thf(f5422,plain,(
% 2.23/0.58 ($true = $false) | ($false = ((cQ_2 @ a @ b @ c)))),
% 2.23/0.58 inference(forward_demodulation,[],[f5402,f1102])).
% 2.23/0.58 thf(f5423,plain,(
% 2.23/0.58 ($false = ((cQ_2 @ a @ b @ c)))),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f5422])).
% 2.23/0.58 thf(f13103,plain,(
% 2.23/0.58 ($true = $false)),
% 2.23/0.58 inference(constrained_superposition,[],[f869,f5423])).
% 2.23/0.58 thf(f13104,plain,(
% 2.23/0.58 $false),
% 2.23/0.58 inference(trivial_inequality_removal,[],[f13103])).
% 2.23/0.58 % SZS output end Proof for theBenchmark
% 2.23/0.58 % (59360)------------------------------
% 2.23/0.58 % (59360)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.23/0.58 % (59360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.58 % (59360)CaDiCaL version: 2.1.3
% 2.23/0.58 % (59360)Termination reason: Refutation
% 2.23/0.58 % (59360)Time elapsed: 0.303 s
% 2.23/0.58 % (59360)Peak memory usage: 17 MB
% 2.23/0.58 % (59360)Instructions burned: 1228 (million)
% 2.23/0.58 % (59354)Success in time 0.34 s
% 2.23/0.58 % Vampire exiting
%------------------------------------------------------------------------------