%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT143+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:37:00 PM UTC 2026
% Result : ContradictoryAxioms 10.17s 2.44s
% Output : Refutation 10.17s
% 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(f43,axiom,
! [X0,X1,X2] : X2 != hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).
fof(f511,axiom,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(f1339,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2,
inference(cnf_transformation,[],[f43]) ).
fof(f2074,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f511]) ).
fof(f2078,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(f2340,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,[],[f1339,f2078]) ).
fof(f2343,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,[],[f2340,f2078]) ).
fof(f2344,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,[],[f2343,f2074]) ).
fof(f2355,plain,
$false,
inference(equality_resolution,[],[f2344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT143+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 23:46:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.52/2.24 % (1899282)Detected formulas, will run a generic FOF schedule.
% 9.52/2.24 % (1899291)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1271738265:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.52/2.24 % (1899291)Instruction limit reached!
% 9.52/2.24 % (1899291)------------------------------
% 9.52/2.24 % (1899291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.52/2.24 % (1899291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.52/2.24 % (1899291)CaDiCaL version: 2.1.3
% 9.52/2.24 % (1899291)Termination reason: Instruction limit
% 9.52/2.24 % (1899291)Termination phase: Saturation
% 9.52/2.24 % (1899291)Time elapsed: 0.039 s
% 9.52/2.24 % (1899291)Peak memory usage: 89 MB
% 9.52/2.24 % (1899291)Instructions burned: 122 (million)
% 9.52/2.24 % (1899289)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=3562117683:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.52/2.24 % (1899292)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2127482282:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.52/2.24 % (1899287)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=1259326181:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.52/2.24 % (1899288)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=2737413316:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.52/2.24 % (1899293)dis-21_1_sil=8000:lcm=predicate:random_seed=656011947: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)
% 9.52/2.24 % (1899290)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2503179094:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.52/2.24 % (1899290)Instruction limit reached!
% 9.52/2.24 % (1899290)------------------------------
% 9.52/2.24 % (1899290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.52/2.24 % (1899290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.52/2.24 % (1899290)CaDiCaL version: 2.1.3
% 9.52/2.24 % (1899290)Termination reason: Instruction limit
% 9.52/2.24 % (1899290)Termination phase: Saturation
% 9.52/2.24 % (1899290)Time elapsed: 0.064 s
% 9.52/2.24 % (1899290)Peak memory usage: 90 MB
% 9.52/2.24 % (1899290)Instructions burned: 110 (million)
% 9.52/2.24 % (1899293)Instruction limit reached!
% 9.52/2.24 % (1899293)------------------------------
% 9.52/2.24 % (1899293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.52/2.24 % (1899293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.52/2.24 % (1899293)CaDiCaL version: 2.1.3
% 9.52/2.24 % (1899293)Termination reason: Instruction limit
% 9.52/2.24 % (1899293)Termination phase: Saturation
% 9.52/2.24 % (1899293)Time elapsed: 0.068 s
% 9.52/2.24 % (1899293)Peak memory usage: 89 MB
% 9.52/2.24 % (1899293)Instructions burned: 132 (million)
% 9.52/2.24 % (1899292)Instruction limit reached!
% 9.52/2.24 % (1899292)------------------------------
% 9.52/2.24 % (1899292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.52/2.24 % (1899292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.52/2.24 % (1899292)CaDiCaL version: 2.1.3
% 9.52/2.24 % (1899292)Termination reason: Instruction limit
% 9.52/2.24 % (1899292)Termination phase: Saturation
% 9.52/2.24 % (1899292)Time elapsed: 0.075 s
% 9.52/2.24 % (1899292)Peak memory usage: 90 MB
% 9.52/2.24 % (1899292)Instructions burned: 140 (million)
% 9.52/2.24 % (1899295)lrs+10_1_sil=8000:sp=occurrence:random_seed=1065483104:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 9.52/2.24 % (1899295)Instruction limit reached!
% 9.52/2.24 % (1899295)------------------------------
% 9.52/2.24 % (1899295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.52/2.24 % (1899295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.52/2.24 % (1899295)CaDiCaL version: 2.1.3
% 9.52/2.24 % (1899295)Termination reason: Instruction limit
% 9.52/2.24 % (1899295)Termination phase: Saturation
% 9.52/2.24 % (1899295)Time elapsed: 0.088 s
% 9.52/2.24 % (1899295)Peak memory usage: 91 MB
% 9.52/2.24 % (1899295)Instructions burned: 286 (million)
% 10.17/2.44 % (1899302)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3437584901:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.17/2.44 % (1899303)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2410685916:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.17/2.44 % (1899304)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=1268337237:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 10.17/2.44 % (1899302)Instruction limit reached!
% 10.17/2.44 % (1899302)------------------------------
% 10.17/2.44 % (1899302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.17/2.44 % (1899302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.17/2.44 % (1899302)CaDiCaL version: 2.1.3
% 10.17/2.44 % (1899302)Termination reason: Instruction limit
% 10.17/2.44 % (1899302)Termination phase: Saturation
% 10.17/2.44 % (1899302)Time elapsed: 0.087 s
% 10.17/2.44 % (1899302)Peak memory usage: 89 MB
% 10.17/2.44 % (1899302)Instructions burned: 157 (million)
% 10.17/2.44 % (1899306)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1628333217:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 10.17/2.44 % (1899304)Instruction limit reached!
% 10.17/2.44 % (1899304)------------------------------
% 10.17/2.44 % (1899304)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.17/2.44 % (1899304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.17/2.44 % (1899304)CaDiCaL version: 2.1.3
% 10.17/2.44 % (1899304)Termination reason: Instruction limit
% 10.17/2.44 % (1899304)Termination phase: Saturation
% 10.17/2.44 % (1899304)Time elapsed: 0.140 s
% 10.17/2.44 % (1899304)Peak memory usage: 91 MB
% 10.17/2.44 % (1899304)Instructions burned: 250 (million)
% 10.17/2.44 % (1899306)Instruction limit reached!
% 10.17/2.44 % (1899306)------------------------------
% 10.17/2.44 % (1899306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.17/2.44 % (1899306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.17/2.44 % (1899306)CaDiCaL version: 2.1.3
% 10.17/2.44 % (1899306)Termination reason: Instruction limit
% 10.17/2.44 % (1899306)Termination phase: Saturation
% 10.17/2.44 % (1899306)Time elapsed: 0.083 s
% 10.17/2.44 % (1899306)Peak memory usage: 91 MB
% 10.17/2.44 % (1899306)Instructions burned: 297 (million)
% 10.17/2.44 % (1899303)Instruction limit reached!
% 10.17/2.44 % (1899303)------------------------------
% 10.17/2.44 % (1899303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.17/2.44 % (1899303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.17/2.44 % (1899303)CaDiCaL version: 2.1.3
% 10.17/2.44 % (1899303)Termination reason: Instruction limit
% 10.17/2.44 % (1899303)Termination phase: Saturation
% 10.17/2.44 % (1899303)Time elapsed: 0.191 s
% 10.17/2.44 % (1899303)Peak memory usage: 93 MB
% 10.17/2.44 % (1899303)Instructions burned: 328 (million)
% 10.17/2.44 % (1899310)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1447307777:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 10.17/2.44 % (1899314)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2493703582:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 10.17/2.44 % (1899312)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3999185575:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 10.17/2.44 % (1899314)Instruction limit reached!
% 10.17/2.44 % (1899314)------------------------------
% 10.17/2.44 % (1899314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.17/2.44 % (1899314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.17/2.44 % (1899314)CaDiCaL version: 2.1.3
% 10.17/2.44 % (1899314)Termination reason: Instruction limit
% 10.17/2.44 % (1899314)Termination phase: Saturation
% 10.17/2.44 % (1899314)Time elapsed: 0.031 s
% 10.17/2.44 % (1899314)Peak memory usage: 90 MB
% 10.17/2.44 % (1899314)Instructions burned: 114 (million)
% 10.17/2.44 % (1899313)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3116845901:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 10.17/2.44 % (1899312)Instruction limit reached!
% 10.17/2.44 % (1899312)------------------------------
% 10.17/2.44 % (1899312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.17/2.44 % (1899312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.17/2.44 % (1899312)CaDiCaL version: 2.1.3
% 10.17/2.44 % (1899312)Termination reason: Instruction limit
% 10.17/2.44 % (1899312)Termination phase: Saturation
% 10.17/2.44 % (1899312)Time elapsed: 0.055 s
% 10.17/2.44 % (1899312)Peak memory usage: 90 MB
% 10.17/2.44 % (1899312)Instructions burned: 114 (million)
% 10.17/2.44 % (1899313)Instruction limit reached!
% 10.17/2.44 % (1899313)------------------------------
% 10.17/2.44 % (1899313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.17/2.44 % (1899313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.17/2.44 % (1899313)CaDiCaL version: 2.1.3
% 10.17/2.44 % (1899313)Termination reason: Instruction limit
% 10.17/2.44 % (1899313)Termination phase: Saturation
% 10.17/2.44 % (1899313)Time elapsed: 0.059 s
% 10.17/2.44 % (1899313)Peak memory usage: 89 MB
% 10.17/2.44 % (1899313)Instructions burned: 130 (million)
% 10.17/2.44 % (1899318)lrs+10_1_sil=8000:sp=occurrence:random_seed=3265702745:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 10.17/2.44 % (1899320)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3013005642:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 10.17/2.44 % (1899321)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2992404615:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 10.17/2.44 % (1899288)First to succeed.
% 10.17/2.44 % (1899288)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1899282"
% 10.17/2.44 % (1899287)Also succeeded, but the first one will report.
% 10.17/2.44 % (1899320)Instruction limit reached!
% 10.17/2.44 % (1899320)------------------------------
% 10.17/2.44 % (1899320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.17/2.44 % (1899320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.17/2.44 % (1899320)CaDiCaL version: 2.1.3
% 10.17/2.44 % (1899320)Termination reason: Instruction limit
% 10.17/2.44 % (1899320)Termination phase: Saturation
% 10.17/2.44 % (1899320)Time elapsed: 0.238 s
% 10.17/2.44 % (1899320)Peak memory usage: 93 MB
% 10.17/2.44 % (1899320)Instructions burned: 438 (million)
% 10.17/2.44 % (1899325)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3934957095:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 10.17/2.44 % (1899288)Refutation found. Thanks to Tanya!
% 10.17/2.44 % SZS status ContradictoryAxioms for theBenchmark
% 10.17/2.44 % SZS output start Proof for theBenchmark
% See solution above
% 10.17/2.44 % (1899288)------------------------------
% 10.17/2.44 % (1899288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.17/2.44 % (1899288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.17/2.44 % (1899288)CaDiCaL version: 2.1.3
% 10.17/2.44 % (1899288)Termination reason: Refutation
% 10.17/2.44 % (1899288)Time elapsed: 0.912 s
% 10.17/2.44 % (1899288)Peak memory usage: 145 MB
% 10.17/2.44 % (1899288)Instructions burned: 1484 (million)
% 10.17/2.44 % (1899288)------------------------------
% 10.17/2.44 % (1899288)------------------------------
% 10.17/2.44 % (1899282)Success in time 1.387 s
% 10.17/2.44 % Vampire exiting
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