%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV398^5 : 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 : n002.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 08:39:27 AM UTC 2026
% Result : Theorem 2.10s 0.60s
% Output : Refutation 2.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV398^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 15:46:52 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 2.10/0.60 % (1451883)Will run a generic schedule for satisfiability detection.
% 2.10/0.60 % (1451890)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2585017416:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.10/0.60 % (1451889)% WARNING: option uhcvi not known.
% 2.10/0.60 % (1451888)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1871757078_2999 on theBenchmark for (2999ds/0Mi)
% 2.10/0.60 % (1451889)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=630463638:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.10/0.60 % (1451892)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=838513329:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.10/0.60 % (1451889)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.10/0.60 % (1451893)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3730949940:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.10/0.60 % (1451894)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1383448984:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.10/0.60 % Exception at run slice level
% 2.10/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.10/0.60 % (1451892)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.10/0.60 % (1451889)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.10/0.60 % (1451891)dis+10_1_sil=32000:sp=arity:random_seed=638614704:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.10/0.60 % (1451901)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2607033291:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.10/0.60 % Exception at run slice level
% 2.10/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.10/0.60 % (1451904)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1523874238:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.10/0.60 % (1451892)Instruction limit reached!
% 2.10/0.60 % (1451892)------------------------------
% 2.10/0.60 % (1451892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.60 % (1451892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.60 % (1451892)CaDiCaL version: 2.1.3
% 2.10/0.60 % (1451892)Termination reason: Instruction limit
% 2.10/0.60 % (1451892)Termination phase: Saturation
% 2.10/0.60 % (1451892)Time elapsed: 0.058 s
% 2.10/0.60 % (1451892)Peak memory usage: 12 MB
% 2.10/0.60 % (1451892)Instructions burned: 118 (million)
% 2.10/0.60 % (1451893)Instruction limit reached!
% 2.10/0.60 % (1451893)------------------------------
% 2.10/0.60 % (1451893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.60 % (1451893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.60 % (1451893)CaDiCaL version: 2.1.3
% 2.10/0.60 % (1451893)Termination reason: Instruction limit
% 2.10/0.60 % (1451893)Termination phase: Saturation
% 2.10/0.60 % (1451893)Time elapsed: 0.066 s
% 2.10/0.60 % (1451893)Peak memory usage: 12 MB
% 2.10/0.60 % (1451893)Instructions burned: 133 (million)
% 2.10/0.60 % (1451906)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=3320048208:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.10/0.60 % (1451906)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.10/0.60 % (1451906)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.10/0.60 % (1451894)Instruction limit reached!
% 2.10/0.60 % (1451894)------------------------------
% 2.10/0.60 % (1451894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.60 % (1451894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.60 % (1451894)CaDiCaL version: 2.1.3
% 2.10/0.60 % (1451894)Termination reason: Instruction limit
% 2.10/0.60 % (1451894)Termination phase: Saturation
% 2.10/0.60 % (1451894)Time elapsed: 0.080 s
% 2.10/0.60 % (1451894)Peak memory usage: 12 MB
% 2.10/0.60 % (1451894)Instructions burned: 159 (million)
% 2.10/0.60 % (1451907)ott-21_1_sil=16000:fs=off:random_seed=4003812451:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.10/0.60 % (1451891)Instruction limit reached!
% 2.10/0.60 % (1451891)------------------------------
% 2.10/0.60 % (1451891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.60 % (1451891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.60 % (1451891)CaDiCaL version: 2.1.3
% 2.10/0.60 % (1451891)Termination reason: Instruction limit
% 2.10/0.60 % (1451891)Termination phase: Saturation
% 2.10/0.60 % (1451891)Time elapsed: 0.070 s
% 2.10/0.60 % (1451891)Peak memory usage: 12 MB
% 2.10/0.60 % (1451891)Instructions burned: 103 (million)
% 2.10/0.60 % (1451909)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1727806514:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.10/0.60 % (1451911)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=821545270:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.10/0.60 % Exception at run slice level
% 2.10/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.10/0.60 % (1451904)Instruction limit reached!
% 2.10/0.60 % (1451904)------------------------------
% 2.10/0.60 % (1451904)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.60 % (1451904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.60 % (1451904)CaDiCaL version: 2.1.3
% 2.10/0.60 % (1451904)Termination reason: Instruction limit
% 2.10/0.60 % (1451904)Termination phase: Saturation
% 2.10/0.60 % (1451904)Time elapsed: 0.069 s
% 2.10/0.60 % (1451904)Peak memory usage: 12 MB
% 2.10/0.60 % (1451904)Instructions burned: 133 (million)
% 2.10/0.60 % (1451915)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=325971228:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.10/0.60 % Exception at run slice level
% 2.10/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.10/0.60 % (1451914)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4262046380:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.10/0.60 % (1451917)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=2307056208: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)
% 2.10/0.60 % (1451917)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.10/0.60 % (1451907)Instruction limit reached!
% 2.10/0.60 % (1451907)------------------------------
% 2.10/0.60 % (1451907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.60 % (1451907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.60 % (1451907)CaDiCaL version: 2.1.3
% 2.10/0.60 % (1451907)Termination reason: Instruction limit
% 2.10/0.60 % (1451907)Termination phase: Saturation
% 2.10/0.60 % (1451907)Time elapsed: 0.085 s
% 2.10/0.60 % (1451907)Peak memory usage: 12 MB
% 2.10/0.60 % (1451907)Instructions burned: 181 (million)
% 2.10/0.60 % (1451920)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1098513327:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.10/0.60 % (1451920)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.10/0.60 % (1451909)Instruction limit reached!
% 2.10/0.60 % (1451909)------------------------------
% 2.10/0.60 % (1451909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.60 % (1451909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.60 % (1451909)CaDiCaL version: 2.1.3
% 2.10/0.60 % (1451909)Termination reason: Instruction limit
% 2.10/0.60 % (1451909)Termination phase: Saturation
% 2.10/0.60 % (1451909)Time elapsed: 0.239 s
% 2.10/0.60 % (1451909)Peak memory usage: 13 MB
% 2.10/0.60 % (1451909)Instructions burned: 477 (million)
% 2.10/0.60 % (1451889) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1451883-1451889"...
% 2.10/0.60 % (1451889)...printing done.
% 2.10/0.60 % (1451889)Refutation found. Thanks to Tanya!
% 2.10/0.60 % SZS status Theorem for theBenchmark
% 2.10/0.60 % SZS output start Proof for theBenchmark
% 2.10/0.60 thf(type_def_5, type, a: $tType).
% 2.10/0.60 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 2.10/0.60 thf(func_def_0, type, cF: ((a > $o) > a > $o)).
% 2.10/0.60 thf(func_def_1, type, cG: ((a > $o) > a > $o)).
% 2.10/0.60 thf(func_def_5, type, sK0: (a > $o)).
% 2.10/0.60 thf(func_def_6, type, sK1: a).
% 2.10/0.60 thf(func_def_7, type, sK2: ((a > $o) > (a > $o) > a)).
% 2.10/0.60 thf(func_def_8, type, vNOT: ($o > $o)).
% 2.10/0.60 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 2.10/0.60 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.10/0.60 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 2.10/0.60 thf(func_def_13, type, sK4: (a > (a > a > $o) > a)).
% 2.10/0.60 thf(func_def_14, type, db2: !>[X0: $tType]:(X0)).
% 2.10/0.60 thf(func_def_15, type, sK5: (a > (a > a > $o) > a)).
% 2.10/0.60 thf(func_def_16, type, sK6: (a > (a > a > $o) > a)).
% 2.10/0.60 thf(func_def_17, type, sK7: (a > (a > a > $o) > a)).
% 2.10/0.60 thf(func_def_18, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.10/0.60 thf(func_def_19, type, sK8: ((a > $o) > a)).
% 2.10/0.60 thf(f1,conjecture,(
% 2.10/0.60 (! [X0 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (cG @ (cF @ X0) @ X2)) & ! [X2 : a] : ((X0 @ X2) => (cF @ (cG @ X0) @ X2))) & ! [X0 : (a > $o),X1 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cF @ X1 @ X2) => (cF @ X0 @ X2)))) => ! [X0 : (a > $o),X2 : a] : ((cF @ (cG @ (cF @ X0)) @ X2) <=> (cF @ X0 @ X2))),
% 2.10/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM67A_pme)).
% 2.10/0.60 thf(f2,negated_conjecture,(
% 2.10/0.60 ~((! [X0 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (cG @ (cF @ X0) @ X2)) & ! [X2 : a] : ((X0 @ X2) => (cF @ (cG @ X0) @ X2))) & ! [X0 : (a > $o),X1 : (a > $o)] : (! [X2 : a] : ((X0 @ X2) => (X1 @ X2)) => ! [X2 : a] : ((cF @ X1 @ X2) => (cF @ X0 @ X2)))) => ! [X0 : (a > $o),X2 : a] : ((cF @ (cG @ (cF @ X0)) @ X2) <=> (cF @ X0 @ X2)))),
% 2.10/0.60 inference(negated_conjecture,[status(cth)],[f1])).
% 2.10/0.60 thf(f3,plain,(
% 2.10/0.60 ~((! [X0 : (a > $o)] : (! [X1 : a] : ((X0 @ X1) => (cG @ (cF @ X0) @ X1)) & ! [X2 : a] : ((X0 @ X2) => (cF @ (cG @ X0) @ X2))) & ! [X3 : (a > $o),X4 : (a > $o)] : (! [X5 : a] : ((X3 @ X5) => (X4 @ X5)) => ! [X6 : a] : ((cF @ X4 @ X6) => (cF @ X3 @ X6)))) => ! [X7 : (a > $o),X8 : a] : ((cF @ (cG @ (cF @ X7)) @ X8) <=> (cF @ X7 @ X8)))),
% 2.10/0.60 inference(rectify,[],[f2])).
% 2.10/0.60 thf(f4,plain,(
% 2.10/0.60 ~((! [X0 : (a > $o)] : (! [X1 : a] : ((((X0 @ X1)) = $true) => (((cG @ (cF @ X0) @ X1)) = $true)) & ! [X2 : a] : ((((X0 @ X2)) = $true) => (((cF @ (cG @ X0) @ X2)) = $true))) & ! [X3 : (a > $o),X4 : (a > $o)] : (! [X5 : a] : ((((X3 @ X5)) = $true) => (((X4 @ X5)) = $true)) => ! [X6 : a] : ((((cF @ X4 @ X6)) = $true) => (((cF @ X3 @ X6)) = $true)))) => ! [X7 : (a > $o),X8 : a] : (((cF @ (cG @ (cF @ X7)) @ X8)) = ((cF @ X7 @ X8))))),
% 2.10/0.60 inference(fool_elimination,[],[f3])).
% 2.10/0.60 thf(f5,plain,(
% 2.10/0.60 ? [X7 : (a > $o),X8 : a] : (((cF @ (cG @ (cF @ X7)) @ X8)) != ((cF @ X7 @ X8))) & (! [X0 : (a > $o)] : (! [X1 : a] : ((((cG @ (cF @ X0) @ X1)) = $true) | (((X0 @ X1)) != $true)) & ! [X2 : a] : ((((cF @ (cG @ X0) @ X2)) = $true) | (((X0 @ X2)) != $true))) & ! [X3 : (a > $o),X4 : (a > $o)] : (! [X6 : a] : ((((cF @ X3 @ X6)) = $true) | (((cF @ X4 @ X6)) != $true)) | ? [X5 : a] : ((((X4 @ X5)) != $true) & (((X3 @ X5)) = $true))))),
% 2.10/0.60 inference(ennf_transformation,[],[f4])).
% 2.10/0.60 thf(f6,plain,(
% 2.10/0.60 ? [X7 : (a > $o),X8 : a] : (((cF @ (cG @ (cF @ X7)) @ X8)) != ((cF @ X7 @ X8))) & ! [X0 : (a > $o)] : (! [X1 : a] : ((((cG @ (cF @ X0) @ X1)) = $true) | (((X0 @ X1)) != $true)) & ! [X2 : a] : ((((cF @ (cG @ X0) @ X2)) = $true) | (((X0 @ X2)) != $true))) & ! [X3 : (a > $o),X4 : (a > $o)] : (! [X6 : a] : ((((cF @ X3 @ X6)) = $true) | (((cF @ X4 @ X6)) != $true)) | ? [X5 : a] : ((((X4 @ X5)) != $true) & (((X3 @ X5)) = $true)))),
% 2.10/0.60 inference(flattening,[],[f5])).
% 2.10/0.60 thf(f7,plain,(
% 2.10/0.60 ? [X0 : (a > $o),X1 : a] : (((cF @ (cG @ (cF @ X0)) @ X1)) != ((cF @ X0 @ X1))) & ! [X2 : (a > $o)] : (! [X3 : a] : (($true = ((cG @ (cF @ X2) @ X3))) | ($true != ((X2 @ X3)))) & ! [X4 : a] : (($true = ((cF @ (cG @ X2) @ X4))) | ($true != ((X2 @ X4))))) & ! [X5 : (a > $o),X6 : (a > $o)] : (! [X7 : a] : (($true = ((cF @ X5 @ X7))) | ($true != ((cF @ X6 @ X7)))) | ? [X8 : a] : (($true != ((X6 @ X8))) & ($true = ((X5 @ X8)))))),
% 2.10/0.60 inference(rectify,[],[f6])).
% 2.10/0.60 thf(f8,plain,(
% 2.10/0.60 (((cF @ (cG @ (cF @ sK0)) @ sK1)) != ((cF @ sK0 @ sK1))) & ! [X2 : (a > $o)] : (! [X3 : a] : (($true = ((cG @ (cF @ X2) @ X3))) | ($true != ((X2 @ X3)))) & ! [X4 : a] : (($true = ((cF @ (cG @ X2) @ X4))) | ($true != ((X2 @ X4))))) & ! [X5 : (a > $o),X6 : (a > $o)] : (! [X7 : a] : (($true = ((cF @ X5 @ X7))) | ($true != ((cF @ X6 @ X7)))) | (($true != ((X6 @ (sK2 @ X6 @ X5)))) & ($true = ((X5 @ (sK2 @ X6 @ X5))))))),
% 2.10/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X8,sK2 @ X6 @ X5)],[f7])).
% 2.10/0.60 thf(f9,plain,(
% 2.10/0.60 ( ! [X6 : (a > $o),X7 : a,X5 : (a > $o)] : (($true != ((cF @ X6 @ X7))) | ($true = ((cF @ X5 @ X7))) | ($true = ((X5 @ (sK2 @ X6 @ X5))))) )),
% 2.10/0.60 inference(cnf_transformation,[],[f8])).
% 2.10/0.60 thf(f10,plain,(
% 2.10/0.60 ( ! [X6 : (a > $o),X7 : a,X5 : (a > $o)] : (($true != ((X6 @ (sK2 @ X6 @ X5)))) | ($true != ((cF @ X6 @ X7))) | ($true = ((cF @ X5 @ X7)))) )),
% 2.10/0.60 inference(cnf_transformation,[],[f8])).
% 2.10/0.60 thf(f11,plain,(
% 2.10/0.60 ( ! [X2 : (a > $o),X4 : a] : (($true != ((X2 @ X4))) | ($true = ((cF @ (cG @ X2) @ X4)))) )),
% 2.10/0.60 inference(cnf_transformation,[],[f8])).
% 2.10/0.60 thf(f12,plain,(
% 2.10/0.60 ( ! [X2 : (a > $o),X3 : a] : (($true != ((X2 @ X3))) | ($true = ((cG @ (cF @ X2) @ X3)))) )),
% 2.10/0.60 inference(cnf_transformation,[],[f8])).
% 2.10/0.60 thf(f13,plain,(
% 2.10/0.60 (((cF @ (cG @ (cF @ sK0)) @ sK1)) != ((cF @ sK0 @ sK1)))),
% 2.10/0.60 inference(cnf_transformation,[],[f8])).
% 2.10/0.60 thf(f15,definition,(
% 2.10/0.60 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 2.10/0.60 introduced(theory,[fool_exhaustiveness_axiom])).
% 2.10/0.60 thf(f16,plain,(
% 2.10/0.60 ($true = ((cF @ (cG @ (cF @ sK0)) @ sK1))) | ($true = ((cF @ sK0 @ sK1)))),
% 2.10/0.60 inference(xor_proxy_clausification,[],[f13])).
% 2.10/0.60 thf(f17,plain,(
% 2.10/0.60 (((cF @ (cG @ (cF @ sK0)) @ sK1)) = $false) | (((cF @ sK0 @ sK1)) = $false)),
% 2.10/0.60 inference(xor_proxy_clausification,[],[f13])).
% 2.10/0.60 thf(f19,definition,(
% 2.10/0.60 spl3_1 <=> (((cF @ sK0 @ sK1)) = $false)),
% 2.10/0.60 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 2.10/0.60 thf(f21,plain,(
% 2.10/0.60 (((cF @ sK0 @ sK1)) = $false) | ~spl3_1),
% 2.10/0.60 inference(avatar_component_clause,[],[f19])).
% 2.10/0.60 thf(f23,definition,(
% 2.10/0.60 spl3_2 <=> (((cF @ (cG @ (cF @ sK0)) @ sK1)) = $false)),
% 2.10/0.60 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 2.10/0.60 thf(f25,plain,(
% 2.10/0.60 (((cF @ (cG @ (cF @ sK0)) @ sK1)) = $false) | ~spl3_2),
% 2.10/0.60 inference(avatar_component_clause,[],[f23])).
% 2.10/0.60 thf(f26,plain,(
% 2.10/0.60 spl3_1 | spl3_2),
% 2.10/0.60 inference(avatar_split_clause,[],[f17,f23,f19])).
% 2.10/0.60 thf(f28,definition,(
% 2.10/0.60 spl3_3 <=> ($true = ((cF @ sK0 @ sK1)))),
% 2.10/0.60 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 2.10/0.60 thf(f30,plain,(
% 2.10/0.60 ($true = ((cF @ sK0 @ sK1))) | ~spl3_3),
% 2.10/0.60 inference(avatar_component_clause,[],[f28])).
% 2.10/0.60 thf(f32,definition,(
% 2.10/0.60 spl3_4 <=> ($true = ((cF @ (cG @ (cF @ sK0)) @ sK1)))),
% 2.10/0.60 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 2.10/0.60 thf(f34,plain,(
% 2.10/0.60 ($true = ((cF @ (cG @ (cF @ sK0)) @ sK1))) | ~spl3_4),
% 2.10/0.60 inference(avatar_component_clause,[],[f32])).
% 2.10/0.60 thf(f35,plain,(
% 2.10/0.60 spl3_3 | spl3_4),
% 2.10/0.60 inference(avatar_split_clause,[],[f16,f32,f28])).
% 2.10/0.60 thf(f84,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o),X1 : a] : (($true != $true) | (((cG @ (cF @ X0) @ X1)) = $true) | (((X0 @ X1)) = $false)) )),
% 2.10/0.60 inference(constrained_superposition,[],[f12,f15])).
% 2.10/0.60 thf(f85,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o),X1 : a] : (($true != $true) | ($true = ((cF @ (cG @ X0) @ X1))) | (((X0 @ X1)) = $false)) )),
% 2.10/0.60 inference(constrained_superposition,[],[f11,f15])).
% 2.10/0.60 thf(f87,plain,(
% 2.10/0.60 ( ! [X2 : a,X0 : (a > $o),X1 : (a > $o)] : (($true != $true) | (((cF @ X0 @ X2)) != $true) | (((cF @ X1 @ X2)) = $true) | ($false = ((X0 @ (sK2 @ X0 @ X1))))) )),
% 2.10/0.60 inference(constrained_superposition,[],[f10,f15])).
% 2.10/0.60 thf(f89,plain,(
% 2.10/0.60 ( ! [X2 : a,X0 : (a > $o),X1 : (a > $o)] : ((((cF @ X0 @ X2)) != $true) | (((cF @ X1 @ X2)) = $true) | ($false = ((X0 @ (sK2 @ X0 @ X1))))) )),
% 2.10/0.60 inference(trivial_inequality_removal,[],[f87])).
% 2.10/0.60 thf(f91,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o),X1 : a] : (($true = ((cF @ (cG @ X0) @ X1))) | (((X0 @ X1)) = $false)) )),
% 2.10/0.60 inference(trivial_inequality_removal,[],[f85])).
% 2.10/0.60 thf(f92,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o),X1 : a] : ((((cG @ (cF @ X0) @ X1)) = $true) | (((X0 @ X1)) = $false)) )),
% 2.10/0.60 inference(trivial_inequality_removal,[],[f84])).
% 2.10/0.60 thf(f250,plain,(
% 2.10/0.60 ($true = $false) | (((cF @ sK0 @ sK1)) = $false) | ~spl3_2),
% 2.10/0.60 inference(constrained_superposition,[],[f91,f25])).
% 2.10/0.60 thf(f253,plain,(
% 2.10/0.60 (((cF @ sK0 @ sK1)) = $false) | ~spl3_2),
% 2.10/0.60 inference(trivial_inequality_removal,[],[f250])).
% 2.10/0.60 thf(f260,plain,(
% 2.10/0.60 spl3_1 | ~spl3_2),
% 2.10/0.60 inference(avatar_split_clause,[],[f253,f23,f19])).
% 2.10/0.60 thf(f262,plain,(
% 2.10/0.60 ($true = $false) | (~spl3_1 | ~spl3_3)),
% 2.10/0.60 inference(constrained_superposition,[],[f21,f30])).
% 2.10/0.60 thf(f277,plain,(
% 2.10/0.60 $false | (~spl3_1 | ~spl3_3)),
% 2.10/0.60 inference(trivial_inequality_removal,[],[f262])).
% 2.10/0.60 thf(f278,plain,(
% 2.10/0.60 ~spl3_1 | ~spl3_3),
% 2.10/0.60 inference(avatar_contradiction_clause,[],[f277])).
% 2.10/0.60 thf(f290,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((cF @ X0 @ sK1))) | ($true = ((X0 @ (sK2 @ (cG @ (cF @ sK0)) @ X0))))) ) | ~spl3_4),
% 2.10/0.60 inference(constrained_superposition,[],[f9,f34])).
% 2.10/0.60 thf(f295,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o)] : (($true = ((X0 @ (sK2 @ (cG @ (cF @ sK0)) @ X0)))) | ($true = ((cF @ X0 @ sK1)))) ) | ~spl3_4),
% 2.10/0.60 inference(trivial_inequality_removal,[],[f290])).
% 2.10/0.60 thf(f368,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o)] : (($true != $true) | ($true = ((cF @ X0 @ sK1))) | ($false = ((cG @ (cF @ sK0) @ (sK2 @ (cG @ (cF @ sK0)) @ X0))))) ) | ~spl3_4),
% 2.10/0.60 inference(constrained_superposition,[],[f89,f34])).
% 2.10/0.60 thf(f372,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o)] : (($false = ((cG @ (cF @ sK0) @ (sK2 @ (cG @ (cF @ sK0)) @ X0)))) | ($true = ((cF @ X0 @ sK1)))) ) | ~spl3_4),
% 2.10/0.60 inference(trivial_inequality_removal,[],[f368])).
% 2.10/0.60 thf(f2163,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o)] : (($true = $false) | ($false = ((sK0 @ (sK2 @ (cG @ (cF @ sK0)) @ X0)))) | ($true = ((cF @ X0 @ sK1)))) ) | ~spl3_4),
% 2.10/0.60 inference(constrained_superposition,[],[f92,f372])).
% 2.10/0.60 thf(f2201,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o)] : (($false = ((sK0 @ (sK2 @ (cG @ (cF @ sK0)) @ X0)))) | ($true = ((cF @ X0 @ sK1)))) ) | ~spl3_4),
% 2.10/0.60 inference(trivial_inequality_removal,[],[f2163])).
% 2.10/0.60 thf(f3998,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o)] : (($true = $false) | ($true = ((cF @ (^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK1))) | ($true = ((cF @ X0 @ sK1))) | (sK0 != X0)) ) | ~spl3_4),
% 2.10/0.60 inference(constrained_superposition,[],[f295,f2201])).
% 2.10/0.60 thf(f4035,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o)] : (($true = ((cF @ (^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK1))) | ($true = ((cF @ X0 @ sK1))) | (sK0 != X0)) ) | ~spl3_4),
% 2.10/0.60 inference(trivial_inequality_removal,[],[f3998])).
% 2.10/0.60 thf(f4036,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o)] : (($true = ((cF @ sK0 @ sK1))) | ($true = ((cF @ X0 @ sK1))) | (sK0 != X0)) ) | ~spl3_4),
% 2.10/0.60 inference(beta-eta_normalization,[],[f4035])).
% 2.10/0.60 thf(f4097,definition,(
% 2.10/0.60 spl3_15 <=> ! [X1 : (a > $o)] : (($true = ((cF @ X1 @ sK1))) | (sK0 != X1))),
% 2.10/0.60 introduced(definition,[new_symbols(definition,[spl3_15])],[avatar_definition])).
% 2.10/0.60 thf(f4098,plain,(
% 2.10/0.60 ( ! [X1 : (a > $o)] : ((sK0 != X1) | ($true = ((cF @ X1 @ sK1)))) ) | ~spl3_15),
% 2.10/0.60 inference(avatar_component_clause,[],[f4097])).
% 2.10/0.60 thf(f4116,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o)] : (($true = $false) | ($true = ((cF @ X0 @ sK1))) | (sK0 != X0)) ) | (~spl3_1 | ~spl3_4)),
% 2.10/0.60 inference(forward_demodulation,[],[f4036,f21])).
% 2.10/0.60 thf(f4117,plain,(
% 2.10/0.60 ( ! [X0 : (a > $o)] : (($true = ((cF @ X0 @ sK1))) | (sK0 != X0)) ) | (~spl3_1 | ~spl3_4)),
% 2.10/0.60 inference(trivial_inequality_removal,[],[f4116])).
% 2.10/0.60 thf(f4130,plain,(
% 2.10/0.60 spl3_15 | ~spl3_1 | ~spl3_4),
% 2.10/0.60 inference(avatar_split_clause,[],[f4117,f32,f19,f4097])).
% 2.10/0.60 thf(f5082,plain,(
% 2.10/0.60 ($true = ((cF @ sK0 @ sK1))) | ~spl3_15),
% 2.10/0.60 inference(equality_resolution,[],[f4098])).
% 2.10/0.60 thf(f5085,plain,(
% 2.10/0.60 ($true = $false) | (~spl3_1 | ~spl3_15)),
% 2.10/0.60 inference(forward_demodulation,[],[f5082,f21])).
% 2.10/0.60 thf(f5086,plain,(
% 2.10/0.60 $false | (~spl3_1 | ~spl3_15)),
% 2.10/0.60 inference(trivial_inequality_removal,[],[f5085])).
% 2.10/0.60 thf(f5087,plain,(
% 2.10/0.60 ~spl3_1 | ~spl3_15),
% 2.10/0.60 inference(avatar_contradiction_clause,[],[f5086])).
% 2.10/0.60 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f26])).
% 2.10/0.60 cnf(s2, plain, spl3_3 | spl3_4, inference(sat_conversion,[],[f35])).
% 2.10/0.60 cnf(s23, plain, spl3_1 | ~spl3_2, inference(sat_conversion,[],[f260])).
% 2.10/0.60 cnf(s26, plain, ~spl3_1 | ~spl3_3, inference(sat_conversion,[],[f278])).
% 2.10/0.60 cnf(s45, plain, ~spl3_1 | ~spl3_4 | spl3_15, inference(sat_conversion,[],[f4130])).
% 2.10/0.60 cnf(s47, plain, ~spl3_1 | ~spl3_15, inference(sat_conversion,[],[f5087])).
% 2.10/0.60 cnf(s49, plain, spl3_1, inference(rat,[],[s1,s23])).
% 2.10/0.60 cnf(s50, plain, ~spl3_15, inference(rat,[],[s47,s49])).
% 2.10/0.60 cnf(s51, plain, ~spl3_4, inference(rat,[],[s45,s50,s49])).
% 2.10/0.60 cnf(s52, plain, ~spl3_3, inference(rat,[],[s26,s49])).
% 2.10/0.60 cnf(s53, plain, $false, inference(rat,[],[s2,s51,s52])).
% 2.10/0.60 thf(f5088,plain,(
% 2.10/0.60 $false),
% 2.10/0.60 inference(avatar_sat_refutation,[],[s53])).
% 2.10/0.60 % SZS output end Proof for theBenchmark
% 2.10/0.60 % (1451889)------------------------------
% 2.10/0.60 % (1451889)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.10/0.60 % (1451889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.10/0.60 % (1451889)CaDiCaL version: 2.1.3
% 2.10/0.60 % (1451889)Termination reason: Refutation
% 2.10/0.60 % (1451889)Time elapsed: 0.345 s
% 2.10/0.60 % (1451889)Peak memory usage: 15 MB
% 2.10/0.60 % (1451889)Instructions burned: 753 (million)
% 2.10/0.60 % (1451883)Success in time 0.386 s
% 2.10/0.60 % Vampire exiting
%------------------------------------------------------------------------------