%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT136+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Tue Sep 29 12:36:59 PM UTC 2026
% Result : ContradictoryAxioms 9.62s 2.34s
% Output : Refutation 9.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-3 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
fof(f511,axiom,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f515,axiom,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X5,X4,X3),X2),X1),X0) = hAPP(hAPP(X2,X0),hAPP(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(f1274,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != X0,
inference(cnf_transformation,[],[f27]) ).
fof(f2026,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f511]) ).
fof(f2030,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X5,X4,X3),X2),X1),X0) = hAPP(hAPP(X2,X0),hAPP(X1,X0)),
inference(cnf_transformation,[],[f515]) ).
fof(f2286,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(X4,X5) != hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_List_Olist_OCons(X3)),X4),X5),
inference(superposition,[],[f1274,f2030]) ).
fof(f2289,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(X8,hAPP(X7,X8)) != hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),hAPP(c_COMBS(X3,X4,X5),c_List_Olist_OCons(X6))),X7),X8),
inference(superposition,[],[f2286,f2030]) ).
fof(f2295,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),hAPP(c_COMBS(X5,X6,X7),c_List_Olist_OCons(X8))),c_COMBI(X1)),X0) != hAPP(X0,X0),
inference(superposition,[],[f2289,f2026]) ).
fof(f2303,plain,
$false,
inference(equality_resolution,[],[f2295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT136+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 23:47:47 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.24/2.15 % (1432117)Detected formulas, will run a generic FOF schedule.
% 5.24/2.15 % (1432124)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2433029944:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.24/2.15 % (1432128)dis-21_1_sil=8000:lcm=predicate:random_seed=3140566646:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.24/2.15 % (1432126)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2216458150:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.24/2.15 % (1432125)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=159431255:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.24/2.15 % (1432122)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1424354873:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.24/2.15 % (1432123)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3240043223:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.24/2.15 % (1432127)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1134198313:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.24/2.15 % (1432125)Refutation not found, incomplete strategy
% 5.24/2.15 % (1432125)------------------------------
% 5.24/2.15 % (1432125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/2.15 % (1432125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/2.15 % (1432125)CaDiCaL version: 2.1.3
% 5.24/2.15 % (1432125)Termination reason: Refutation not found, incomplete strategy
% 5.24/2.15 % (1432125)Time elapsed: 0.010 s
% 5.24/2.15 % (1432125)Peak memory usage: 89 MB
% 5.24/2.15 % (1432125)Instructions burned: 17 (million)
% 5.24/2.15 % (1432128)Instruction limit reached!
% 5.24/2.15 % (1432128)------------------------------
% 5.24/2.15 % (1432128)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/2.15 % (1432128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/2.15 % (1432128)CaDiCaL version: 2.1.3
% 5.24/2.15 % (1432128)Termination reason: Instruction limit
% 5.24/2.15 % (1432128)Termination phase: Saturation
% 5.24/2.15 % (1432128)Time elapsed: 0.067 s
% 5.24/2.15 % (1432128)Peak memory usage: 90 MB
% 5.24/2.15 % (1432128)Instructions burned: 130 (million)
% 5.24/2.15 % (1432126)Instruction limit reached!
% 5.24/2.15 % (1432126)------------------------------
% 5.24/2.15 % (1432126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/2.15 % (1432126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/2.15 % (1432126)CaDiCaL version: 2.1.3
% 5.24/2.15 % (1432126)Termination reason: Instruction limit
% 5.24/2.15 % (1432126)Termination phase: Saturation
% 5.24/2.15 % (1432126)Time elapsed: 0.072 s
% 5.24/2.15 % (1432126)Peak memory usage: 89 MB
% 5.24/2.15 % (1432126)Instructions burned: 121 (million)
% 5.24/2.15 % (1432127)Instruction limit reached!
% 5.24/2.15 % (1432127)------------------------------
% 5.24/2.15 % (1432127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.24/2.15 % (1432127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.24/2.15 % (1432127)CaDiCaL version: 2.1.3
% 5.24/2.15 % (1432127)Termination reason: Instruction limit
% 5.24/2.15 % (1432127)Termination phase: Saturation
% 5.24/2.15 % (1432127)Time elapsed: 0.077 s
% 5.24/2.15 % (1432127)Peak memory usage: 90 MB
% 5.24/2.15 % (1432127)Instructions burned: 140 (million)
% 5.24/2.15 % (1432136)lrs+10_1_sil=8000:sp=occurrence:random_seed=535816607:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.24/2.15 % (1432138)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3572917618:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.24/2.15 % (1432137)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3010871045:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.24/2.15 % (1432125)------------------------------
% 5.24/2.15 % (1432125)------------------------------
% 5.24/2.15 % (1432137)Instruction limit reached!
% 5.24/2.15 % (1432137)------------------------------
% 5.24/2.15 % (1432137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.62/2.34 % (1432137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.62/2.34 % (1432137)CaDiCaL version: 2.1.3
% 9.62/2.34 % (1432137)Termination reason: Instruction limit
% 9.62/2.34 % (1432137)Termination phase: Saturation
% 9.62/2.34 % (1432137)Time elapsed: 0.087 s
% 9.62/2.34 % (1432137)Peak memory usage: 89 MB
% 9.62/2.34 % (1432137)Instructions burned: 161 (million)
% 9.62/2.34 % (1432136)Instruction limit reached!
% 9.62/2.34 % (1432136)------------------------------
% 9.62/2.34 % (1432136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.62/2.34 % (1432136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.62/2.34 % (1432136)CaDiCaL version: 2.1.3
% 9.62/2.34 % (1432136)Termination reason: Instruction limit
% 9.62/2.34 % (1432136)Termination phase: Saturation
% 9.62/2.34 % (1432136)Time elapsed: 0.177 s
% 9.62/2.34 % (1432136)Peak memory usage: 92 MB
% 9.62/2.34 % (1432136)Instructions burned: 285 (million)
% 9.62/2.34 % (1432142)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3707565532:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 9.62/2.34 % (1432138)Instruction limit reached!
% 9.62/2.34 % (1432138)------------------------------
% 9.62/2.34 % (1432138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.62/2.34 % (1432138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.62/2.34 % (1432138)CaDiCaL version: 2.1.3
% 9.62/2.34 % (1432138)Termination reason: Instruction limit
% 9.62/2.34 % (1432138)Termination phase: Saturation
% 9.62/2.34 % (1432138)Time elapsed: 0.195 s
% 9.62/2.34 % (1432138)Peak memory usage: 92 MB
% 9.62/2.34 % (1432138)Instructions burned: 326 (million)
% 9.62/2.34 % (1432143)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3941081314:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.62/2.34 % (1432144)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=837479956:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.62/2.34 % (1432146)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=131243215:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.62/2.34 % (1432142)Instruction limit reached!
% 9.62/2.34 % (1432142)------------------------------
% 9.62/2.34 % (1432142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.62/2.34 % (1432142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.62/2.34 % (1432142)CaDiCaL version: 2.1.3
% 9.62/2.34 % (1432142)Termination reason: Instruction limit
% 9.62/2.34 % (1432142)Termination phase: Saturation
% 9.62/2.34 % (1432142)Time elapsed: 0.139 s
% 9.62/2.34 % (1432142)Peak memory usage: 91 MB
% 9.62/2.34 % (1432142)Instructions burned: 248 (million)
% 9.62/2.34 % (1432146)Instruction limit reached!
% 9.62/2.34 % (1432146)------------------------------
% 9.62/2.34 % (1432146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.62/2.34 % (1432146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.62/2.34 % (1432146)CaDiCaL version: 2.1.3
% 9.62/2.34 % (1432146)Termination reason: Instruction limit
% 9.62/2.34 % (1432146)Termination phase: Saturation
% 9.62/2.34 % (1432146)Time elapsed: 0.054 s
% 9.62/2.34 % (1432146)Peak memory usage: 90 MB
% 9.62/2.34 % (1432146)Instructions burned: 114 (million)
% 9.62/2.34 % (1432143)Instruction limit reached!
% 9.62/2.34 % (1432143)------------------------------
% 9.62/2.34 % (1432143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.62/2.34 % (1432143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.62/2.34 % (1432143)CaDiCaL version: 2.1.3
% 9.62/2.34 % (1432143)Termination reason: Instruction limit
% 9.62/2.34 % (1432143)Termination phase: Saturation
% 9.62/2.34 % (1432143)Time elapsed: 0.168 s
% 9.62/2.34 % (1432143)Peak memory usage: 91 MB
% 9.62/2.34 % (1432143)Instructions burned: 295 (million)
% 9.62/2.34 % (1432150)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3283672716:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 9.62/2.34 % (1432151)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2701723132:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 9.62/2.34 % (1432152)lrs+10_1_sil=8000:sp=occurrence:random_seed=4136477744:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 9.62/2.34 % (1432150)Instruction limit reached!
% 9.62/2.34 % (1432150)------------------------------
% 9.62/2.34 % (1432150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.62/2.34 % (1432150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.62/2.34 % (1432150)CaDiCaL version: 2.1.3
% 9.62/2.34 % (1432150)Termination reason: Instruction limit
% 9.62/2.34 % (1432150)Termination phase: Saturation
% 9.62/2.34 % (1432150)Time elapsed: 0.059 s
% 9.62/2.34 % (1432150)Peak memory usage: 89 MB
% 9.62/2.34 % (1432150)Instructions burned: 128 (million)
% 9.62/2.34 % (1432151)Instruction limit reached!
% 9.62/2.34 % (1432151)------------------------------
% 9.62/2.34 % (1432151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.62/2.34 % (1432151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.62/2.34 % (1432151)CaDiCaL version: 2.1.3
% 9.62/2.34 % (1432151)Termination reason: Instruction limit
% 9.62/2.34 % (1432151)Termination phase: Saturation
% 9.62/2.34 % (1432151)Time elapsed: 0.057 s
% 9.62/2.34 % (1432151)Peak memory usage: 90 MB
% 9.62/2.34 % (1432151)Instructions burned: 115 (million)
% 9.62/2.34 % (1432157)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=807326022:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 9.62/2.34 % (1432122)First to succeed.
% 9.62/2.34 % (1432122)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1432117"
% 9.62/2.34 % (1432123)Also succeeded, but the first one will report.
% 9.62/2.34 % (1432158)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3102552484:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 9.62/2.34 % (1432157)Instruction limit reached!
% 9.62/2.34 % (1432157)------------------------------
% 9.62/2.34 % (1432157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.62/2.34 % (1432157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.62/2.34 % (1432157)CaDiCaL version: 2.1.3
% 9.62/2.34 % (1432157)Termination reason: Instruction limit
% 9.62/2.34 % (1432157)Termination phase: Saturation
% 9.62/2.34 % (1432157)Time elapsed: 0.223 s
% 9.62/2.34 % (1432157)Peak memory usage: 92 MB
% 9.62/2.34 % (1432157)Instructions burned: 438 (million)
% 9.62/2.34 % (1432122)Refutation found. Thanks to Tanya!
% 9.62/2.34 % SZS status ContradictoryAxioms for theBenchmark
% 9.62/2.34 % SZS output start Proof for theBenchmark
% See solution above
% 9.62/2.34 % (1432122)------------------------------
% 9.62/2.34 % (1432122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.62/2.34 % (1432122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.62/2.34 % (1432122)CaDiCaL version: 2.1.3
% 9.62/2.34 % (1432122)Termination reason: Refutation
% 9.62/2.34 % (1432122)Time elapsed: 0.872 s
% 9.62/2.34 % (1432122)Peak memory usage: 137 MB
% 9.62/2.34 % (1432122)Instructions burned: 1425 (million)
% 9.62/2.34 % (1432122)------------------------------
% 9.62/2.34 % (1432122)------------------------------
% 9.62/2.34 % (1432117)Success in time 1.311 s
% 9.62/2.34 % Vampire exiting
%------------------------------------------------------------------------------