%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT137+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 : n008.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 9.35s 2.06s
% Output : Refutation 9.35s
% 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(f35,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(f1314,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2,
inference(cnf_transformation,[],[f35]) ).
fof(f2048,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f511]) ).
fof(f2052,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(f2318,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,[],[f1314,f2052]) ).
fof(f2321,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,[],[f2318,f2052]) ).
fof(f2327,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,[],[f2321,f2048]) ).
fof(f2335,plain,
$false,
inference(equality_resolution,[],[f2327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT137+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n008.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 23:48:10 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.44 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
% 5.82/1.92 % (1732333)Detected formulas, will run a generic FOF schedule.
% 5.82/1.92 % (1732343)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3283375188:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.82/1.92 % (1732344)dis-21_1_sil=8000:lcm=predicate:random_seed=1615252819: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)
% 5.82/1.92 % (1732340)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=3137814571:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.82/1.92 % (1732341)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1694115808:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.82/1.92 % (1732338)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=922263619:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.82/1.92 % (1732342)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4220076898:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.82/1.92 % (1732339)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=161902195:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.82/1.92 % (1732341)Refutation not found, incomplete strategy
% 5.82/1.92 % (1732341)------------------------------
% 5.82/1.92 % (1732341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.92 % (1732341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.92 % (1732341)CaDiCaL version: 2.1.3
% 5.82/1.92 % (1732341)Termination reason: Refutation not found, incomplete strategy
% 5.82/1.92 % (1732341)Time elapsed: 0.026 s
% 5.82/1.92 % (1732341)Peak memory usage: 89 MB
% 5.82/1.92 % (1732341)Instructions burned: 50 (million)
% 5.82/1.92 % (1732343)Instruction limit reached!
% 5.82/1.92 % (1732343)------------------------------
% 5.82/1.92 % (1732343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.92 % (1732343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.92 % (1732343)CaDiCaL version: 2.1.3
% 5.82/1.92 % (1732343)Termination reason: Instruction limit
% 5.82/1.92 % (1732343)Termination phase: Saturation
% 5.82/1.92 % (1732343)Time elapsed: 0.051 s
% 5.82/1.92 % (1732343)Peak memory usage: 90 MB
% 5.82/1.92 % (1732343)Instructions burned: 140 (million)
% 5.82/1.92 % (1732344)Instruction limit reached!
% 5.82/1.92 % (1732344)------------------------------
% 5.82/1.92 % (1732344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.92 % (1732344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.92 % (1732344)CaDiCaL version: 2.1.3
% 5.82/1.92 % (1732344)Termination reason: Instruction limit
% 5.82/1.92 % (1732344)Termination phase: Saturation
% 5.82/1.92 % (1732344)Time elapsed: 0.063 s
% 5.82/1.92 % (1732344)Peak memory usage: 89 MB
% 5.82/1.92 % (1732344)Instructions burned: 129 (million)
% 5.82/1.92 % (1732342)Instruction limit reached!
% 5.82/1.92 % (1732342)------------------------------
% 5.82/1.92 % (1732342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.92 % (1732342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.92 % (1732342)CaDiCaL version: 2.1.3
% 5.82/1.92 % (1732342)Termination reason: Instruction limit
% 5.82/1.92 % (1732342)Termination phase: Saturation
% 5.82/1.92 % (1732342)Time elapsed: 0.069 s
% 5.82/1.92 % (1732342)Peak memory usage: 89 MB
% 5.82/1.92 % (1732342)Instructions burned: 119 (million)
% 5.82/1.92 % (1732352)lrs+10_1_sil=8000:sp=occurrence:random_seed=1483760274:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.82/1.92 % (1732353)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1175374517:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.82/1.92 % (1732354)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2792092920:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.82/1.92 % (1732352)Instruction limit reached!
% 5.82/1.92 % (1732352)------------------------------
% 5.82/1.92 % (1732352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.92 % (1732352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.06 % (1732352)CaDiCaL version: 2.1.3
% 9.35/2.06 % (1732352)Termination reason: Instruction limit
% 9.35/2.06 % (1732352)Termination phase: Saturation
% 9.35/2.06 % (1732352)Time elapsed: 0.094 s
% 9.35/2.06 % (1732352)Peak memory usage: 92 MB
% 9.35/2.06 % (1732352)Instructions burned: 286 (million)
% 9.35/2.06 % (1732341)------------------------------
% 9.35/2.06 % (1732341)------------------------------
% 9.35/2.06 % (1732353)Instruction limit reached!
% 9.35/2.06 % (1732353)------------------------------
% 9.35/2.06 % (1732353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.06 % (1732353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.06 % (1732353)CaDiCaL version: 2.1.3
% 9.35/2.06 % (1732353)Termination reason: Instruction limit
% 9.35/2.06 % (1732353)Termination phase: Saturation
% 9.35/2.06 % (1732353)Time elapsed: 0.085 s
% 9.35/2.06 % (1732353)Peak memory usage: 89 MB
% 9.35/2.06 % (1732353)Instructions burned: 158 (million)
% 9.35/2.06 % (1732358)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=3561583367:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 9.35/2.06 % (1732358)Instruction limit reached!
% 9.35/2.06 % (1732358)------------------------------
% 9.35/2.06 % (1732358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.06 % (1732358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.06 % (1732358)CaDiCaL version: 2.1.3
% 9.35/2.06 % (1732358)Termination reason: Instruction limit
% 9.35/2.06 % (1732358)Termination phase: Saturation
% 9.35/2.06 % (1732358)Time elapsed: 0.070 s
% 9.35/2.06 % (1732358)Peak memory usage: 91 MB
% 9.35/2.06 % (1732358)Instructions burned: 251 (million)
% 9.35/2.06 % (1732354)Instruction limit reached!
% 9.35/2.06 % (1732354)------------------------------
% 9.35/2.06 % (1732354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.06 % (1732354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.06 % (1732354)CaDiCaL version: 2.1.3
% 9.35/2.06 % (1732354)Termination reason: Instruction limit
% 9.35/2.06 % (1732354)Termination phase: Saturation
% 9.35/2.06 % (1732354)Time elapsed: 0.190 s
% 9.35/2.06 % (1732354)Peak memory usage: 92 MB
% 9.35/2.06 % (1732354)Instructions burned: 325 (million)
% 9.35/2.06 % (1732359)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1253435487:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.35/2.06 % (1732360)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3666646550:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 9.35/2.06 % (1732362)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3718994489:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.35/2.06 % (1732362)Instruction limit reached!
% 9.35/2.06 % (1732362)------------------------------
% 9.35/2.06 % (1732362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.06 % (1732362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.06 % (1732362)CaDiCaL version: 2.1.3
% 9.35/2.06 % (1732362)Termination reason: Instruction limit
% 9.35/2.06 % (1732362)Termination phase: Saturation
% 9.35/2.06 % (1732362)Time elapsed: 0.029 s
% 9.35/2.06 % (1732362)Peak memory usage: 90 MB
% 9.35/2.06 % (1732362)Instructions burned: 116 (million)
% 9.35/2.06 % (1732364)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3735811046:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 9.35/2.06 % (1732359)Instruction limit reached!
% 9.35/2.06 % (1732359)------------------------------
% 9.35/2.06 % (1732359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.06 % (1732359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.06 % (1732359)CaDiCaL version: 2.1.3
% 9.35/2.06 % (1732359)Termination reason: Instruction limit
% 9.35/2.06 % (1732359)Termination phase: Saturation
% 9.35/2.06 % (1732359)Time elapsed: 0.153 s
% 9.35/2.06 % (1732359)Peak memory usage: 91 MB
% 9.35/2.06 % (1732359)Instructions burned: 295 (million)
% 9.35/2.06 % (1732364)Instruction limit reached!
% 9.35/2.06 % (1732364)------------------------------
% 9.35/2.06 % (1732364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.06 % (1732364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.06 % (1732364)CaDiCaL version: 2.1.3
% 9.35/2.06 % (1732364)Termination reason: Instruction limit
% 9.35/2.06 % (1732364)Termination phase: Saturation
% 9.35/2.06 % (1732364)Time elapsed: 0.060 s
% 9.35/2.06 % (1732364)Peak memory usage: 89 MB
% 9.35/2.06 % (1732364)Instructions burned: 129 (million)
% 9.35/2.06 % (1732367)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1088794722:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 9.35/2.06 % (1732367)Instruction limit reached!
% 9.35/2.06 % (1732367)------------------------------
% 9.35/2.06 % (1732367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.06 % (1732367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.06 % (1732367)CaDiCaL version: 2.1.3
% 9.35/2.06 % (1732367)Termination reason: Instruction limit
% 9.35/2.06 % (1732367)Termination phase: Saturation
% 9.35/2.06 % (1732367)Time elapsed: 0.032 s
% 9.35/2.06 % (1732367)Peak memory usage: 89 MB
% 9.35/2.06 % (1732367)Instructions burned: 116 (million)
% 9.35/2.06 % (1732369)lrs+10_1_sil=8000:sp=occurrence:random_seed=3139229557:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 9.35/2.06 % (1732371)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4041834213:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 9.35/2.06 % (1732372)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1378721365:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 9.35/2.06 % (1732338)First to succeed.
% 9.35/2.06 % (1732338)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1732333"
% 9.35/2.06 % (1732339)Also succeeded, but the first one will report.
% 9.35/2.06 % (1732371)Instruction limit reached!
% 9.35/2.06 % (1732371)------------------------------
% 9.35/2.06 % (1732371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.06 % (1732371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.06 % (1732371)CaDiCaL version: 2.1.3
% 9.35/2.06 % (1732371)Termination reason: Instruction limit
% 9.35/2.06 % (1732371)Termination phase: Saturation
% 9.35/2.06 % (1732371)Time elapsed: 0.218 s
% 9.35/2.06 % (1732371)Peak memory usage: 92 MB
% 9.35/2.06 % (1732371)Instructions burned: 437 (million)
% 9.35/2.06 % (1732376)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=493352586:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 9.35/2.06 % (1732338)Refutation found. Thanks to Tanya!
% 9.35/2.06 % SZS status ContradictoryAxioms for theBenchmark
% 9.35/2.06 % SZS output start Proof for theBenchmark
% See solution above
% 9.35/2.06 % (1732338)------------------------------
% 9.35/2.06 % (1732338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.35/2.06 % (1732338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.35/2.06 % (1732338)CaDiCaL version: 2.1.3
% 9.35/2.06 % (1732338)Termination reason: Refutation
% 9.35/2.06 % (1732338)Time elapsed: 0.866 s
% 9.35/2.06 % (1732338)Peak memory usage: 137 MB
% 9.35/2.06 % (1732338)Instructions burned: 1417 (million)
% 9.35/2.06 % (1732338)------------------------------
% 9.35/2.06 % (1732338)------------------------------
% 9.35/2.06 % (1732333)Success in time 1.287 s
% 9.35/2.06 % Vampire exiting
%------------------------------------------------------------------------------