%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO387^5 : 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 : 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 08:49:50 AM UTC 2026
% Result : Theorem 3.30s 0.78s
% Output : Refutation 3.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO387^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n003.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:51:59 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 3.30/0.78 % (2747918)Will run a generic schedule for satisfiability detection.
% 3.30/0.78 % (2747931)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3927231724:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 3.30/0.78 % (2747926)% WARNING: option uhcvi not known.
% 3.30/0.78 % (2747928)dis+10_1_sil=32000:sp=arity:random_seed=2703896141:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 3.30/0.78 % (2747926)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4154341580:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 3.30/0.78 % (2747925)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=993157769_3000 on theBenchmark for (3000ds/0Mi)
% 3.30/0.78 % (2747927)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1414697246:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 3.30/0.78 % (2747930)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3968530891:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 3.30/0.78 % (2747929)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3987873532:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 3.30/0.78 % (2747926)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.30/0.78 % (2747929)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.30/0.78 % (2747926)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.30/0.78 % Exception at run slice level
% 3.30/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.30/0.78 % (2747940)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2968990338:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.30/0.78 % Exception at run slice level
% 3.30/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.30/0.78 % (2747931)Instruction limit reached!
% 3.30/0.78 % (2747931)------------------------------
% 3.30/0.78 % (2747931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.78 % (2747931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.78 % (2747931)CaDiCaL version: 2.1.3
% 3.30/0.78 % (2747931)Termination reason: Instruction limit
% 3.30/0.78 % (2747931)Termination phase: Saturation
% 3.30/0.78 % (2747931)Time elapsed: 0.041 s
% 3.30/0.78 % (2747931)Peak memory usage: 12 MB
% 3.30/0.78 % (2747931)Instructions burned: 159 (million)
% 3.30/0.78 % (2747943)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=1582065275:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.30/0.78 % (2747942)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=936364465:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.30/0.78 % (2747943)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.30/0.78 % (2747943)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.30/0.78 % (2747928)Instruction limit reached!
% 3.30/0.78 % (2747928)------------------------------
% 3.30/0.78 % (2747928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.78 % (2747928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.78 % (2747928)CaDiCaL version: 2.1.3
% 3.30/0.78 % (2747928)Termination reason: Instruction limit
% 3.30/0.78 % (2747928)Termination phase: Saturation
% 3.30/0.78 % (2747928)Time elapsed: 0.050 s
% 3.30/0.78 % (2747928)Peak memory usage: 12 MB
% 3.30/0.78 % (2747928)Instructions burned: 104 (million)
% 3.30/0.78 % (2747929)Instruction limit reached!
% 3.30/0.78 % (2747929)------------------------------
% 3.30/0.78 % (2747929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.78 % (2747929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.78 % (2747929)CaDiCaL version: 2.1.3
% 3.30/0.78 % (2747929)Termination reason: Instruction limit
% 3.30/0.78 % (2747929)Termination phase: Saturation
% 3.30/0.78 % (2747929)Time elapsed: 0.054 s
% 3.30/0.78 % (2747929)Peak memory usage: 12 MB
% 3.30/0.78 % (2747929)Instructions burned: 116 (million)
% 3.30/0.78 % (2747930)Instruction limit reached!
% 3.30/0.78 % (2747930)------------------------------
% 3.30/0.78 % (2747930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.78 % (2747930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.78 % (2747930)CaDiCaL version: 2.1.3
% 3.30/0.78 % (2747930)Termination reason: Instruction limit
% 3.30/0.78 % (2747930)Termination phase: Saturation
% 3.30/0.78 % (2747930)Time elapsed: 0.064 s
% 3.30/0.78 % (2747930)Peak memory usage: 12 MB
% 3.30/0.78 % (2747930)Instructions burned: 133 (million)
% 3.30/0.78 % (2747946)ott-21_1_sil=16000:fs=off:random_seed=528694839:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.30/0.78 % (2747947)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1955654981:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 3.30/0.78 % (2747948)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=523303330:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 3.30/0.78 % Exception at run slice level
% 3.30/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.30/0.78 % (2747952)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1305381:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.30/0.78 % (2747942)Instruction limit reached!
% 3.30/0.78 % (2747942)------------------------------
% 3.30/0.78 % (2747942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.78 % (2747942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.78 % (2747942)CaDiCaL version: 2.1.3
% 3.30/0.78 % (2747942)Termination reason: Instruction limit
% 3.30/0.78 % (2747942)Termination phase: Saturation
% 3.30/0.78 % (2747942)Time elapsed: 0.069 s
% 3.30/0.78 % (2747942)Peak memory usage: 12 MB
% 3.30/0.78 % (2747942)Instructions burned: 131 (million)
% 3.30/0.78 % (2747954)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3826846998:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.30/0.78 % Exception at run slice level
% 3.30/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.30/0.78 % (2747946)Instruction limit reached!
% 3.30/0.78 % (2747946)------------------------------
% 3.30/0.78 % (2747946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.78 % (2747946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.78 % (2747946)CaDiCaL version: 2.1.3
% 3.30/0.78 % (2747946)Termination reason: Instruction limit
% 3.30/0.78 % (2747946)Termination phase: Saturation
% 3.30/0.78 % (2747946)Time elapsed: 0.076 s
% 3.30/0.78 % (2747946)Peak memory usage: 12 MB
% 3.30/0.78 % (2747946)Instructions burned: 182 (million)
% 3.30/0.78 % (2747956)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=966504888: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)
% 3.30/0.78 % (2747956)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.30/0.78 % (2747957)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1909949313:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 3.30/0.78 % (2747957)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.30/0.78 % (2747943)Instruction limit reached!
% 3.30/0.78 % (2747943)------------------------------
% 3.30/0.78 % (2747943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.78 % (2747943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.78 % (2747943)CaDiCaL version: 2.1.3
% 3.30/0.78 % (2747943)Termination reason: Instruction limit
% 3.30/0.78 % (2747943)Termination phase: Saturation
% 3.30/0.78 % (2747943)Time elapsed: 0.161 s
% 3.30/0.78 % (2747943)Peak memory usage: 13 MB
% 3.30/0.78 % (2747943)Instructions burned: 684 (million)
% 3.30/0.78 % (2747960)fmb+10_1_sil=64000:random_seed=3350923045:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 3.30/0.78 % (2747960)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.30/0.78 % Exception at run slice level
% 3.30/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.30/0.78 % (2747962)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=163260139:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 3.30/0.78 % Exception at run slice level
% 3.30/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.30/0.78 % (2747964)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3679851855:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 3.30/0.78 % Exception at run slice level
% 3.30/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.30/0.78 % (2747966)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4081785624:i=5131_2997 on theBenchmark for (2997ds/5131Mi)
% 3.30/0.78 % (2747966)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.30/0.78 % (2747947)Instruction limit reached!
% 3.30/0.78 % (2747947)------------------------------
% 3.30/0.78 % (2747947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.78 % (2747947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.78 % (2747947)CaDiCaL version: 2.1.3
% 3.30/0.78 % (2747947)Termination reason: Instruction limit
% 3.30/0.78 % (2747947)Termination phase: Saturation
% 3.30/0.78 % (2747947)Time elapsed: 0.250 s
% 3.30/0.78 % (2747947)Peak memory usage: 12 MB
% 3.30/0.78 % (2747947)Instructions burned: 477 (million)
% 3.30/0.78 % (2747968)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3051157075:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 3.30/0.78 % (2747968)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.30/0.78 % (2747968)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.30/0.78 % (2747956)Instruction limit reached!
% 3.30/0.78 % (2747956)------------------------------
% 3.30/0.78 % (2747956)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.78 % (2747956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.78 % (2747956)CaDiCaL version: 2.1.3
% 3.30/0.78 % (2747956)Termination reason: Instruction limit
% 3.30/0.78 % (2747956)Termination phase: Saturation
% 3.30/0.78 % (2747956)Time elapsed: 0.306 s
% 3.30/0.78 % (2747956)Peak memory usage: 15 MB
% 3.30/0.78 % (2747956)Instructions burned: 693 (million)
% 3.30/0.78 % (2747970)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=4194731405:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 3.30/0.78 % Exception at run slice level
% 3.30/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.30/0.78 % (2747972)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2806672332:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 3.30/0.78 % Exception at run slice level
% 3.30/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.30/0.78 % (2747974)ott-2_1_sil=16000:newcnf=on:random_seed=2205471036:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 3.30/0.78 % (2747974)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.30/0.78 % (2747957) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2747918-2747957"...
% 3.30/0.78 % (2747957)...printing done.
% 3.30/0.78 % (2747957)Refutation found. Thanks to Tanya!
% 3.30/0.78 % SZS status Theorem for theBenchmark
% 3.30/0.78 % SZS output start Proof for theBenchmark
% 3.30/0.78 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 3.30/0.78 thf(func_def_0, type, cQ_5: ($i > $i > $i > $o)).
% 3.30/0.78 thf(func_def_1, type, f: ($i > $i)).
% 3.30/0.78 thf(func_def_2, type, cP_4: ($i > $i > $o)).
% 3.30/0.78 thf(func_def_3, type, cQ_4: ($i > $i > $i > $o)).
% 3.30/0.78 thf(func_def_8, type, cP_3: ($i > $i > $o)).
% 3.30/0.78 thf(func_def_9, type, cQ_3: ($i > $i > $i > $o)).
% 3.30/0.78 thf(func_def_10, type, cP_2: ($i > $i > $o)).
% 3.30/0.78 thf(func_def_11, type, cQ_2: ($i > $i > $i > $o)).
% 3.30/0.78 thf(func_def_12, type, cP_1: ($i > $i > $o)).
% 3.30/0.78 thf(func_def_13, type, cQ_1: ($i > $i > $i > $o)).
% 3.30/0.78 thf(f1,conjecture,(
% 3.30/0.78 ~(! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_5 @ X0 @ X1 @ X2) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_5 @ X3 @ X4 @ X5) | ~(cP_4 @ (f @ X2) @ X5) | ~(cP_4 @ (f @ X1) @ X4) | ~(cP_4 @ (f @ X0) @ X3) | ~(cQ_4 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_4 @ (f @ X0) @ X1) | ~(cP_4 @ X0 @ X1)) & ! [X0 : $i] : (cP_4 @ d @ X0) & (cP_4 @ c @ c) & (cP_4 @ b @ b) & (cP_4 @ a @ a) & ! [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))),
% 3.30/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM409_4)).
% 3.30/0.78 thf(f2,negated_conjecture,(
% 3.30/0.78 ~ ~(! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_5 @ X0 @ X1 @ X2) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i,X4 : $i,X5 : $i] : ((cQ_5 @ X3 @ X4 @ X5) | ~(cP_4 @ (f @ X2) @ X5) | ~(cP_4 @ (f @ X1) @ X4) | ~(cP_4 @ (f @ X0) @ X3) | ~(cQ_4 @ X0 @ X1 @ X2)) & ! [X0 : $i,X1 : $i] : ((cP_4 @ (f @ X0) @ X1) | ~(cP_4 @ X0 @ X1)) & ! [X0 : $i] : (cP_4 @ d @ X0) & (cP_4 @ c @ c) & (cP_4 @ b @ b) & (cP_4 @ a @ a) & ! [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))),
% 3.30/0.78 inference(negated_conjecture,[status(cth)],[f1])).
% 3.30/0.78 thf(f3,plain,(
% 3.30/0.78 ~ ~(! [X0 : $i,X1 : $i,X2 : $i] : ~(cQ_5 @ X0 @ X1 @ X2) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : ((cQ_5 @ X6 @ X7 @ X8) | ~(cP_4 @ (f @ X5) @ X8) | ~(cP_4 @ (f @ X4) @ X7) | ~(cP_4 @ (f @ X3) @ X6) | ~(cQ_4 @ X3 @ X4 @ X5)) & ! [X9 : $i,X10 : $i] : ((cP_4 @ (f @ X9) @ X10) | ~(cP_4 @ X9 @ X10)) & ! [X11 : $i] : (cP_4 @ d @ X11) & (cP_4 @ c @ c) & (cP_4 @ b @ b) & (cP_4 @ a @ a) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : ((cQ_4 @ X15 @ X16 @ X17) | ~(cP_3 @ (f @ X14) @ X17) | ~(cP_3 @ (f @ X13) @ X16) | ~(cP_3 @ (f @ X12) @ X15) | ~(cQ_3 @ X12 @ X13 @ X14)) & ! [X18 : $i,X19 : $i] : ((cP_3 @ (f @ X18) @ X19) | ~(cP_3 @ X18 @ X19)) & ! [X20 : $i] : (cP_3 @ d @ X20) & (cP_3 @ c @ c) & (cP_3 @ b @ b) & (cP_3 @ a @ a) & ! [X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i] : ((cQ_3 @ X24 @ X25 @ X26) | ~(cP_2 @ (f @ X23) @ X26) | ~(cP_2 @ (f @ X22) @ X25) | ~(cP_2 @ (f @ X21) @ X24) | ~(cQ_2 @ X21 @ X22 @ X23)) & ! [X27 : $i,X28 : $i] : ((cP_2 @ (f @ X27) @ X28) | ~(cP_2 @ X27 @ X28)) & ! [X29 : $i] : (cP_2 @ d @ X29) & (cP_2 @ c @ c) & (cP_2 @ b @ b) & (cP_2 @ a @ a) & ! [X30 : $i,X31 : $i,X32 : $i,X33 : $i,X34 : $i,X35 : $i] : ((cQ_2 @ X33 @ X34 @ X35) | ~(cP_1 @ (f @ X32) @ X35) | ~(cP_1 @ (f @ X31) @ X34) | ~(cP_1 @ (f @ X30) @ X33) | ~(cQ_1 @ X30 @ X31 @ X32)) & ! [X36 : $i,X37 : $i] : ((cP_1 @ (f @ X36) @ X37) | ~(cP_1 @ X36 @ X37)) & ! [X38 : $i] : (cP_1 @ d @ X38) & (cP_1 @ c @ c) & (cP_1 @ b @ b) & (cP_1 @ a @ a) & (cQ_1 @ a @ b @ c))),
% 3.30/0.78 inference(rectify,[],[f2])).
% 3.30/0.78 thf(f4,plain,(
% 3.30/0.78 ~ ~(! [X0 : $i,X1 : $i,X2 : $i] : ~ (((cQ_5 @ X0 @ X1 @ X2)) = $true) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : ((((cQ_5 @ X6 @ X7 @ X8)) = $true) | ~ (((cP_4 @ (f @ X5) @ X8)) = $true) | ~ (((cP_4 @ (f @ X4) @ X7)) = $true) | ~ (((cP_4 @ (f @ X3) @ X6)) = $true) | ~ (((cQ_4 @ X3 @ X4 @ X5)) = $true)) & ! [X9 : $i,X10 : $i] : ((((cP_4 @ (f @ X9) @ X10)) = $true) | ~ (((cP_4 @ X9 @ X10)) = $true)) & ! [X11 : $i] : (((cP_4 @ d @ X11)) = $true) & (((cP_4 @ c @ c)) = $true) & (((cP_4 @ b @ b)) = $true) & (((cP_4 @ a @ a)) = $true) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : ((((cQ_4 @ X15 @ X16 @ X17)) = $true) | ~ (((cP_3 @ (f @ X14) @ X17)) = $true) | ~ (((cP_3 @ (f @ X13) @ X16)) = $true) | ~ (((cP_3 @ (f @ X12) @ X15)) = $true) | ~ (((cQ_3 @ X12 @ X13 @ X14)) = $true)) & ! [X18 : $i,X19 : $i] : ((((cP_3 @ (f @ X18) @ X19)) = $true) | ~ (((cP_3 @ X18 @ X19)) = $true)) & ! [X20 : $i] : (((cP_3 @ d @ X20)) = $true) & (((cP_3 @ c @ c)) = $true) & (((cP_3 @ b @ b)) = $true) & (((cP_3 @ a @ a)) = $true) & ! [X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i] : ((((cQ_3 @ X24 @ X25 @ X26)) = $true) | ~ (((cP_2 @ (f @ X23) @ X26)) = $true) | ~ (((cP_2 @ (f @ X22) @ X25)) = $true) | ~ (((cP_2 @ (f @ X21) @ X24)) = $true) | ~ (((cQ_2 @ X21 @ X22 @ X23)) = $true)) & ! [X27 : $i,X28 : $i] : ((((cP_2 @ (f @ X27) @ X28)) = $true) | ~ (((cP_2 @ X27 @ X28)) = $true)) & ! [X29 : $i] : (((cP_2 @ d @ X29)) = $true) & (((cP_2 @ c @ c)) = $true) & (((cP_2 @ b @ b)) = $true) & (((cP_2 @ a @ a)) = $true) & ! [X30 : $i,X31 : $i,X32 : $i,X33 : $i,X34 : $i,X35 : $i] : ((((cQ_2 @ X33 @ X34 @ X35)) = $true) | ~ (((cP_1 @ (f @ X32) @ X35)) = $true) | ~ (((cP_1 @ (f @ X31) @ X34)) = $true) | ~ (((cP_1 @ (f @ X30) @ X33)) = $true) | ~ (((cQ_1 @ X30 @ X31 @ X32)) = $true)) & ! [X36 : $i,X37 : $i] : ((((cP_1 @ (f @ X36) @ X37)) = $true) | ~ (((cP_1 @ X36 @ X37)) = $true)) & ! [X38 : $i] : (((cP_1 @ d @ X38)) = $true) & (((cP_1 @ c @ c)) = $true) & (((cP_1 @ b @ b)) = $true) & (((cP_1 @ a @ a)) = $true) & (((cQ_1 @ a @ b @ c)) = $true))),
% 3.30/0.78 inference(fool_elimination,[],[f3])).
% 3.30/0.78 thf(f5,plain,(
% 3.30/0.78 ! [X0 : $i,X1 : $i,X2 : $i] : (((cQ_5 @ X0 @ X1 @ X2)) != $true) & ! [X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i,X8 : $i] : ((((cQ_5 @ X6 @ X7 @ X8)) = $true) | (((cP_4 @ (f @ X5) @ X8)) != $true) | (((cP_4 @ (f @ X4) @ X7)) != $true) | (((cP_4 @ (f @ X3) @ X6)) != $true) | (((cQ_4 @ X3 @ X4 @ X5)) != $true)) & ! [X9 : $i,X10 : $i] : ((((cP_4 @ (f @ X9) @ X10)) = $true) | (((cP_4 @ X9 @ X10)) != $true)) & ! [X11 : $i] : (((cP_4 @ d @ X11)) = $true) & (((cP_4 @ c @ c)) = $true) & (((cP_4 @ b @ b)) = $true) & (((cP_4 @ a @ a)) = $true) & ! [X12 : $i,X13 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : ((((cQ_4 @ X15 @ X16 @ X17)) = $true) | (((cP_3 @ (f @ X14) @ X17)) != $true) | (((cP_3 @ (f @ X13) @ X16)) != $true) | (((cP_3 @ (f @ X12) @ X15)) != $true) | (((cQ_3 @ X12 @ X13 @ X14)) != $true)) & ! [X18 : $i,X19 : $i] : ((((cP_3 @ (f @ X18) @ X19)) = $true) | (((cP_3 @ X18 @ X19)) != $true)) & ! [X20 : $i] : (((cP_3 @ d @ X20)) = $true) & (((cP_3 @ c @ c)) = $true) & (((cP_3 @ b @ b)) = $true) & (((cP_3 @ a @ a)) = $true) & ! [X21 : $i,X22 : $i,X23 : $i,X24 : $i,X25 : $i,X26 : $i] : ((((cQ_3 @ X24 @ X25 @ X26)) = $true) | (((cP_2 @ (f @ X23) @ X26)) != $true) | (((cP_2 @ (f @ X22) @ X25)) != $true) | (((cP_2 @ (f @ X21) @ X24)) != $true) | (((cQ_2 @ X21 @ X22 @ X23)) != $true)) & ! [X27 : $i,X28 : $i] : ((((cP_2 @ (f @ X27) @ X28)) = $true) | (((cP_2 @ X27 @ X28)) != $true)) & ! [X29 : $i] : (((cP_2 @ d @ X29)) = $true) & (((cP_2 @ c @ c)) = $true) & (((cP_2 @ b @ b)) = $true) & (((cP_2 @ a @ a)) = $true) & ! [X30 : $i,X31 : $i,X32 : $i,X33 : $i,X34 : $i,X35 : $i] : ((((cQ_2 @ X33 @ X34 @ X35)) = $true) | (((cP_1 @ (f @ X32) @ X35)) != $true) | (((cP_1 @ (f @ X31) @ X34)) != $true) | (((cP_1 @ (f @ X30) @ X33)) != $true) | (((cQ_1 @ X30 @ X31 @ X32)) != $true)) & ! [X36 : $i,X37 : $i] : ((((cP_1 @ (f @ X36) @ X37)) = $true) | (((cP_1 @ X36 @ X37)) != $true)) & ! [X38 : $i] : (((cP_1 @ d @ X38)) = $true) & (((cP_1 @ c @ c)) = $true) & (((cP_1 @ b @ b)) = $true) & (((cP_1 @ a @ a)) = $true) & (((cQ_1 @ a @ b @ c)) = $true)),
% 3.30/0.78 inference(flattening,[],[f4])).
% 3.30/0.78 thf(f6,plain,(
% 3.30/0.78 (((cQ_1 @ a @ b @ c)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f7,plain,(
% 3.30/0.78 (((cP_1 @ a @ a)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f8,plain,(
% 3.30/0.78 (((cP_1 @ b @ b)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f9,plain,(
% 3.30/0.78 (((cP_1 @ c @ c)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f11,plain,(
% 3.30/0.78 ( ! [X36 : $i,X37 : $i] : ((((cP_1 @ X36 @ X37)) != $true) | (((cP_1 @ (f @ X36) @ X37)) = $true)) )),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f12,plain,(
% 3.30/0.78 ( ! [X31 : $i,X34 : $i,X35 : $i,X32 : $i,X30 : $i,X33 : $i] : ((((cQ_1 @ X30 @ X31 @ X32)) != $true) | (((cP_1 @ (f @ X32) @ X35)) != $true) | (((cP_1 @ (f @ X31) @ X34)) != $true) | (((cP_1 @ (f @ X30) @ X33)) != $true) | (((cQ_2 @ X33 @ X34 @ X35)) = $true)) )),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f13,plain,(
% 3.30/0.78 (((cP_2 @ a @ a)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f14,plain,(
% 3.30/0.78 (((cP_2 @ b @ b)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f15,plain,(
% 3.30/0.78 (((cP_2 @ c @ c)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f17,plain,(
% 3.30/0.78 ( ! [X28 : $i,X27 : $i] : ((((cP_2 @ X27 @ X28)) != $true) | (((cP_2 @ (f @ X27) @ X28)) = $true)) )),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f18,plain,(
% 3.30/0.78 ( ! [X21 : $i,X26 : $i,X24 : $i,X22 : $i,X25 : $i,X23 : $i] : ((((cQ_2 @ X21 @ X22 @ X23)) != $true) | (((cP_2 @ (f @ X23) @ X26)) != $true) | (((cP_2 @ (f @ X22) @ X25)) != $true) | (((cP_2 @ (f @ X21) @ X24)) != $true) | (((cQ_3 @ X24 @ X25 @ X26)) = $true)) )),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f19,plain,(
% 3.30/0.78 (((cP_3 @ a @ a)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f20,plain,(
% 3.30/0.78 (((cP_3 @ b @ b)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f21,plain,(
% 3.30/0.78 (((cP_3 @ c @ c)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f23,plain,(
% 3.30/0.78 ( ! [X18 : $i,X19 : $i] : ((((cP_3 @ X18 @ X19)) != $true) | (((cP_3 @ (f @ X18) @ X19)) = $true)) )),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f24,plain,(
% 3.30/0.78 ( ! [X16 : $i,X14 : $i,X17 : $i,X15 : $i,X12 : $i,X13 : $i] : ((((cQ_3 @ X12 @ X13 @ X14)) != $true) | (((cP_3 @ (f @ X14) @ X17)) != $true) | (((cP_3 @ (f @ X13) @ X16)) != $true) | (((cP_3 @ (f @ X12) @ X15)) != $true) | (((cQ_4 @ X15 @ X16 @ X17)) = $true)) )),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f25,plain,(
% 3.30/0.78 (((cP_4 @ a @ a)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f26,plain,(
% 3.30/0.78 (((cP_4 @ b @ b)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f27,plain,(
% 3.30/0.78 (((cP_4 @ c @ c)) = $true)),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f29,plain,(
% 3.30/0.78 ( ! [X10 : $i,X9 : $i] : ((((cP_4 @ X9 @ X10)) != $true) | (((cP_4 @ (f @ X9) @ X10)) = $true)) )),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f30,plain,(
% 3.30/0.78 ( ! [X3 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((cQ_5 @ X6 @ X7 @ X8)) = $true) | (((cP_4 @ (f @ X5) @ X8)) != $true) | (((cP_4 @ (f @ X4) @ X7)) != $true) | (((cP_4 @ (f @ X3) @ X6)) != $true) | (((cQ_4 @ X3 @ X4 @ X5)) != $true)) )),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f31,plain,(
% 3.30/0.78 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((cQ_5 @ X0 @ X1 @ X2)) != $true)) )),
% 3.30/0.78 inference(cnf_transformation,[],[f5])).
% 3.30/0.78 thf(f33,definition,(
% 3.30/0.78 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.30/0.78 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.30/0.78 thf(f176,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_2 @ (f @ c) @ c)))),
% 3.30/0.78 inference(constrained_superposition,[],[f17,f15])).
% 3.30/0.78 thf(f177,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_2 @ (f @ b) @ b)))),
% 3.30/0.78 inference(constrained_superposition,[],[f17,f14])).
% 3.30/0.78 thf(f178,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_2 @ (f @ a) @ a)))),
% 3.30/0.78 inference(constrained_superposition,[],[f17,f13])).
% 3.30/0.78 thf(f179,plain,(
% 3.30/0.78 ($true = ((cP_2 @ (f @ a) @ a)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f178])).
% 3.30/0.78 thf(f180,plain,(
% 3.30/0.78 ($true = ((cP_2 @ (f @ b) @ b)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f177])).
% 3.30/0.78 thf(f181,plain,(
% 3.30/0.78 ($true = ((cP_2 @ (f @ c) @ c)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f176])).
% 3.30/0.78 thf(f191,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_3 @ (f @ c) @ c)))),
% 3.30/0.78 inference(constrained_superposition,[],[f23,f21])).
% 3.30/0.78 thf(f192,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_3 @ (f @ b) @ b)))),
% 3.30/0.78 inference(constrained_superposition,[],[f23,f20])).
% 3.30/0.78 thf(f193,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_3 @ (f @ a) @ a)))),
% 3.30/0.78 inference(constrained_superposition,[],[f23,f19])).
% 3.30/0.78 thf(f194,plain,(
% 3.30/0.78 ($true = ((cP_3 @ (f @ a) @ a)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f193])).
% 3.30/0.78 thf(f195,plain,(
% 3.30/0.78 ($true = ((cP_3 @ (f @ b) @ b)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f192])).
% 3.30/0.78 thf(f196,plain,(
% 3.30/0.78 ($true = ((cP_3 @ (f @ c) @ c)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f191])).
% 3.30/0.78 thf(f199,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_4 @ (f @ c) @ c)))),
% 3.30/0.78 inference(constrained_superposition,[],[f29,f27])).
% 3.30/0.78 thf(f200,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_4 @ (f @ b) @ b)))),
% 3.30/0.78 inference(constrained_superposition,[],[f29,f26])).
% 3.30/0.78 thf(f201,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_4 @ (f @ a) @ a)))),
% 3.30/0.78 inference(constrained_superposition,[],[f29,f25])).
% 3.30/0.78 thf(f202,plain,(
% 3.30/0.78 ($true = ((cP_4 @ (f @ a) @ a)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f201])).
% 3.30/0.78 thf(f203,plain,(
% 3.30/0.78 ($true = ((cP_4 @ (f @ b) @ b)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f200])).
% 3.30/0.78 thf(f204,plain,(
% 3.30/0.78 ($true = ((cP_4 @ (f @ c) @ c)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f199])).
% 3.30/0.78 thf(f322,plain,(
% 3.30/0.78 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((cQ_5 @ X0 @ X1 @ X2)) = $false)) )),
% 3.30/0.78 inference(constrained_superposition,[],[f31,f33])).
% 3.30/0.78 thf(f326,plain,(
% 3.30/0.78 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((cQ_5 @ X0 @ X1 @ X2)) = $false)) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f322])).
% 3.30/0.78 thf(f568,plain,(
% 3.30/0.78 ( ! [X3 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = $false) | (((cP_4 @ (f @ X5) @ X8)) != $true) | (((cP_4 @ (f @ X4) @ X7)) != $true) | (((cP_4 @ (f @ X3) @ X6)) != $true) | (((cQ_4 @ X3 @ X4 @ X5)) != $true)) )),
% 3.30/0.78 inference(forward_demodulation,[],[f30,f326])).
% 3.30/0.78 thf(f569,plain,(
% 3.30/0.78 ( ! [X3 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((cQ_4 @ X3 @ X4 @ X5)) != $true) | (((cP_4 @ (f @ X4) @ X7)) != $true) | (((cP_4 @ (f @ X3) @ X6)) != $true) | (((cP_4 @ (f @ X5) @ X8)) != $true)) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f568])).
% 3.30/0.78 thf(f574,plain,(
% 3.30/0.78 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != ((cP_4 @ (f @ X1) @ X3))) | ($true != ((cP_4 @ (f @ X0) @ X4))) | (((cP_4 @ (f @ X2) @ X5)) != $true) | (((cQ_4 @ X0 @ X1 @ X2)) = $false)) )),
% 3.30/0.78 inference(constrained_superposition,[],[f569,f33])).
% 3.30/0.78 thf(f575,plain,(
% 3.30/0.78 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != ((cP_4 @ (f @ X1) @ X3))) | ($true != ((cP_4 @ (f @ X0) @ X4))) | (((cP_4 @ (f @ X2) @ X5)) != $true) | (((cQ_4 @ X0 @ X1 @ X2)) = $false)) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f574])).
% 3.30/0.78 thf(f716,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_1 @ (f @ c) @ c)))),
% 3.30/0.78 inference(constrained_superposition,[],[f11,f9])).
% 3.30/0.78 thf(f717,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_1 @ (f @ b) @ b)))),
% 3.30/0.78 inference(constrained_superposition,[],[f11,f8])).
% 3.30/0.78 thf(f718,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cP_1 @ (f @ a) @ a)))),
% 3.30/0.78 inference(constrained_superposition,[],[f11,f7])).
% 3.30/0.78 thf(f721,plain,(
% 3.30/0.78 ($true = ((cP_1 @ (f @ a) @ a)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f718])).
% 3.30/0.78 thf(f722,plain,(
% 3.30/0.78 ($true = ((cP_1 @ (f @ b) @ b)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f717])).
% 3.30/0.78 thf(f723,plain,(
% 3.30/0.78 ($true = ((cP_1 @ (f @ c) @ c)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f716])).
% 3.30/0.78 thf(f762,plain,(
% 3.30/0.78 ( ! [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)))) )),
% 3.30/0.78 inference(constrained_superposition,[],[f12,f6])).
% 3.30/0.78 thf(f765,plain,(
% 3.30/0.78 ( ! [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)))) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f762])).
% 3.30/0.78 thf(f854,plain,(
% 3.30/0.78 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((cP_4 @ (f @ X0) @ X1)) != $true) | ($true != ((cP_4 @ (f @ X2) @ X3))) | ($false = ((cQ_4 @ X0 @ b @ X2)))) )),
% 3.30/0.78 inference(constrained_superposition,[],[f575,f203])).
% 3.30/0.78 thf(f863,plain,(
% 3.30/0.78 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((cP_4 @ (f @ X2) @ X3))) | (((cP_4 @ (f @ X0) @ X1)) != $true) | ($false = ((cQ_4 @ X0 @ b @ X2)))) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f854])).
% 3.30/0.78 thf(f1337,plain,(
% 3.30/0.78 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cP_4 @ (f @ X0) @ X1)) != $true) | ($false = ((cQ_4 @ X0 @ b @ c)))) )),
% 3.30/0.78 inference(constrained_superposition,[],[f863,f204])).
% 3.30/0.78 thf(f1350,plain,(
% 3.30/0.78 ( ! [X0 : $i,X1 : $i] : ((((cP_4 @ (f @ X0) @ X1)) != $true) | ($false = ((cQ_4 @ X0 @ b @ c)))) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f1337])).
% 3.30/0.78 thf(f1992,plain,(
% 3.30/0.78 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != ((cP_3 @ (f @ X2) @ X3))) | (((cP_3 @ (f @ X1) @ X4)) != $true) | ($true != ((cP_3 @ (f @ X0) @ X5))) | ($true = ((cQ_4 @ X5 @ X4 @ X3))) | (((cQ_3 @ X0 @ X1 @ X2)) = $false)) )),
% 3.30/0.78 inference(constrained_superposition,[],[f24,f33])).
% 3.30/0.78 thf(f1993,plain,(
% 3.30/0.78 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true != ((cP_3 @ (f @ X2) @ X3))) | (((cP_3 @ (f @ X1) @ X4)) != $true) | ($true != ((cP_3 @ (f @ X0) @ X5))) | ($true = ((cQ_4 @ X5 @ X4 @ X3))) | (((cQ_3 @ X0 @ X1 @ X2)) = $false)) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f1992])).
% 3.30/0.78 thf(f2007,plain,(
% 3.30/0.78 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((cP_3 @ (f @ X0) @ X1)) != $true) | ($true != ((cP_3 @ (f @ X2) @ X3))) | ($true = ((cQ_4 @ X3 @ X1 @ c))) | ($false = ((cQ_3 @ X2 @ X0 @ c)))) )),
% 3.30/0.78 inference(constrained_superposition,[],[f1993,f196])).
% 3.30/0.78 thf(f2020,plain,(
% 3.30/0.78 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((cP_3 @ (f @ X2) @ X3))) | (((cP_3 @ (f @ X0) @ X1)) != $true) | ($true = ((cQ_4 @ X3 @ X1 @ c))) | ($false = ((cQ_3 @ X2 @ X0 @ c)))) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f2007])).
% 3.30/0.78 thf(f2121,plain,(
% 3.30/0.78 ( ! [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)) )),
% 3.30/0.78 inference(constrained_superposition,[],[f18,f33])).
% 3.30/0.78 thf(f2122,plain,(
% 3.30/0.78 ( ! [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)) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f2121])).
% 3.30/0.78 thf(f2135,plain,(
% 3.30/0.78 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != ((cP_1 @ (f @ b) @ X0))) | ($true != ((cP_1 @ (f @ c) @ X1))) | ($true = ((cQ_2 @ a @ X0 @ X1)))) )),
% 3.30/0.78 inference(constrained_superposition,[],[f765,f721])).
% 3.30/0.78 thf(f2138,plain,(
% 3.30/0.78 ( ! [X0 : $i,X1 : $i] : (($true != ((cP_1 @ (f @ b) @ X0))) | ($true != ((cP_1 @ (f @ c) @ X1))) | ($true = ((cQ_2 @ a @ X0 @ X1)))) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f2135])).
% 3.30/0.78 thf(f2228,plain,(
% 3.30/0.78 ( ! [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)))) )),
% 3.30/0.78 inference(constrained_superposition,[],[f2122,f181])).
% 3.30/0.78 thf(f2241,plain,(
% 3.30/0.78 ( ! [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)))) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f2228])).
% 3.30/0.78 thf(f2402,plain,(
% 3.30/0.78 ( ! [X0 : $i] : (($true != $true) | ($true != ((cP_1 @ (f @ c) @ X0))) | ($true = ((cQ_2 @ a @ b @ X0)))) )),
% 3.30/0.78 inference(constrained_superposition,[],[f2138,f722])).
% 3.30/0.78 thf(f2405,plain,(
% 3.30/0.78 ( ! [X0 : $i] : (($true != ((cP_1 @ (f @ c) @ X0))) | ($true = ((cQ_2 @ a @ b @ X0)))) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f2402])).
% 3.30/0.78 thf(f3773,plain,(
% 3.30/0.78 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cP_2 @ (f @ X0) @ X1)) != $true) | ($true = ((cQ_3 @ a @ X1 @ c))) | ($false = ((cQ_2 @ a @ X0 @ c)))) )),
% 3.30/0.78 inference(constrained_superposition,[],[f2241,f179])).
% 3.30/0.78 thf(f3778,plain,(
% 3.30/0.78 ( ! [X0 : $i,X1 : $i] : ((((cP_2 @ (f @ X0) @ X1)) != $true) | ($true = ((cQ_3 @ a @ X1 @ c))) | ($false = ((cQ_2 @ a @ X0 @ c)))) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f3773])).
% 3.30/0.78 thf(f4027,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cQ_2 @ a @ b @ c)))),
% 3.30/0.78 inference(constrained_superposition,[],[f2405,f723])).
% 3.30/0.78 thf(f4030,plain,(
% 3.30/0.78 ($true = ((cQ_2 @ a @ b @ c)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f4027])).
% 3.30/0.78 thf(f4450,plain,(
% 3.30/0.78 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cP_3 @ (f @ X0) @ X1)) != $true) | ($true = ((cQ_4 @ a @ X1 @ c))) | ($false = ((cQ_3 @ a @ X0 @ c)))) )),
% 3.30/0.78 inference(constrained_superposition,[],[f2020,f194])).
% 3.30/0.78 thf(f4455,plain,(
% 3.30/0.78 ( ! [X0 : $i,X1 : $i] : ((((cP_3 @ (f @ X0) @ X1)) != $true) | ($true = ((cQ_4 @ a @ X1 @ c))) | ($false = ((cQ_3 @ a @ X0 @ c)))) )),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f4450])).
% 3.30/0.78 thf(f4554,plain,(
% 3.30/0.78 ($true != $true) | ($false = ((cQ_4 @ a @ b @ c)))),
% 3.30/0.78 inference(constrained_superposition,[],[f1350,f202])).
% 3.30/0.78 thf(f4559,plain,(
% 3.30/0.78 ($false = ((cQ_4 @ a @ b @ c)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f4554])).
% 3.30/0.78 thf(f5856,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cQ_3 @ a @ b @ c))) | ($false = ((cQ_2 @ a @ b @ c)))),
% 3.30/0.78 inference(constrained_superposition,[],[f3778,f180])).
% 3.30/0.78 thf(f5869,plain,(
% 3.30/0.78 ($true = ((cQ_3 @ a @ b @ c))) | ($false = ((cQ_2 @ a @ b @ c)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f5856])).
% 3.30/0.78 thf(f5912,plain,(
% 3.30/0.78 ($true = $false) | ($true = ((cQ_3 @ a @ b @ c)))),
% 3.30/0.78 inference(forward_demodulation,[],[f5869,f4030])).
% 3.30/0.78 thf(f5913,plain,(
% 3.30/0.78 ($true = ((cQ_3 @ a @ b @ c)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f5912])).
% 3.30/0.78 thf(f6016,plain,(
% 3.30/0.78 ($true != $true) | ($true = ((cQ_4 @ a @ b @ c))) | ($false = ((cQ_3 @ a @ b @ c)))),
% 3.30/0.78 inference(constrained_superposition,[],[f4455,f195])).
% 3.30/0.78 thf(f6025,plain,(
% 3.30/0.78 ($true = ((cQ_4 @ a @ b @ c))) | ($false = ((cQ_3 @ a @ b @ c)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f6016])).
% 3.30/0.78 thf(f6038,plain,(
% 3.30/0.78 ($true = $false) | ($false = ((cQ_3 @ a @ b @ c)))),
% 3.30/0.78 inference(forward_demodulation,[],[f6025,f4559])).
% 3.30/0.78 thf(f6039,plain,(
% 3.30/0.78 ($false = ((cQ_3 @ a @ b @ c)))),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f6038])).
% 3.30/0.78 thf(f6270,plain,(
% 3.30/0.78 ($true = $false)),
% 3.30/0.78 inference(forward_demodulation,[],[f5913,f6039])).
% 3.30/0.78 thf(f6271,plain,(
% 3.30/0.78 $false),
% 3.30/0.78 inference(trivial_inequality_removal,[],[f6270])).
% 3.30/0.78 % SZS output end Proof for theBenchmark
% 3.30/0.78 % (2747957)------------------------------
% 3.30/0.78 % (2747957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.30/0.78 % (2747957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/0.78 % (2747957)CaDiCaL version: 2.1.3
% 3.30/0.78 % (2747957)Termination reason: Refutation
% 3.30/0.78 % (2747957)Time elapsed: 0.361 s
% 3.30/0.78 % (2747957)Peak memory usage: 14 MB
% 3.30/0.78 % (2747957)Instructions burned: 759 (million)
% 3.30/0.78 % (2747918)Success in time 0.55 s
% 3.30/0.78 % Vampire exiting
%------------------------------------------------------------------------------