%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT163+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 : n009.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 12:37:03 PM UTC 2026
% Result : ContradictoryAxioms 9.43s 2.23s
% Output : Refutation 9.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-5 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f392,axiom,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(f525,axiom,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f527,axiom,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(c_COMBB(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(f529,axiom,
! [X0,X1,X2,X3,X4,X5] : 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(f1808,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(cnf_transformation,[],[f392]) ).
fof(f1978,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f525]) ).
fof(f1980,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(c_COMBB(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
inference(cnf_transformation,[],[f527]) ).
fof(f1982,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(c_COMBS(X5,X4,X3,X2,X1),X0) = hAPP(hAPP(X2,X0),hAPP(X1,X0)),
inference(cnf_transformation,[],[f529]) ).
fof(f2263,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(X0,hAPP(X1,hAPP(X2,X1))) = hAPP(c_COMBS(X3,X4,X5,c_COMBB(X6,X7,X8,X0),X2),X1),
inference(superposition,[],[f1982,f1980]) ).
fof(f2316,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(X7,hAPP(X6,X7)) != hAPP(c_COMBS(X0,X1,X2,c_COMBB(X3,X4,X5,c_Nat_OSuc),X6),X7),
inference(superposition,[],[f1808,f2263]) ).
fof(f2328,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(X0,X0) != hAPP(c_COMBS(X2,X3,X4,c_COMBB(X5,X6,X7,c_Nat_OSuc),c_COMBI(X1)),X0),
inference(superposition,[],[f2316,f1978]) ).
fof(f2345,plain,
$false,
inference(equality_resolution,[],[f2328]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT163+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 23:51:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 7.21/2.04 % (2537355)Detected formulas, will run a generic FOF schedule.
% 7.21/2.04 % (2537363)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2373852956:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.21/2.04 % (2537366)dis-21_1_sil=8000:lcm=predicate:random_seed=1393192130: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)
% 7.21/2.04 % (2537362)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=4037303884:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.21/2.04 % (2537365)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3935042676:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.21/2.04 % (2537364)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1885375215:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.21/2.04 % (2537360)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=4267494999:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.21/2.04 % (2537361)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=1085574825:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.21/2.04 % (2537363)Refutation not found, incomplete strategy
% 7.21/2.04 % (2537363)------------------------------
% 7.21/2.04 % (2537363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.21/2.04 % (2537363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.21/2.04 % (2537363)CaDiCaL version: 2.1.3
% 7.21/2.04 % (2537363)Termination reason: Refutation not found, incomplete strategy
% 7.21/2.04 % (2537363)Time elapsed: 0.011 s
% 7.21/2.04 % (2537363)Peak memory usage: 89 MB
% 7.21/2.04 % (2537363)Instructions burned: 18 (million)
% 7.21/2.04 % (2537364)Instruction limit reached!
% 7.21/2.04 % (2537364)------------------------------
% 7.21/2.04 % (2537364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.21/2.04 % (2537364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.21/2.04 % (2537364)CaDiCaL version: 2.1.3
% 7.21/2.04 % (2537364)Termination reason: Instruction limit
% 7.21/2.04 % (2537364)Termination phase: Saturation
% 7.21/2.04 % (2537364)Time elapsed: 0.067 s
% 7.21/2.04 % (2537364)Peak memory usage: 89 MB
% 7.21/2.04 % (2537364)Instructions burned: 120 (million)
% 7.21/2.04 % (2537366)Instruction limit reached!
% 7.21/2.04 % (2537366)------------------------------
% 7.21/2.04 % (2537366)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.21/2.04 % (2537366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.21/2.04 % (2537366)CaDiCaL version: 2.1.3
% 7.21/2.04 % (2537366)Termination reason: Instruction limit
% 7.21/2.04 % (2537366)Termination phase: Saturation
% 7.21/2.04 % (2537366)Time elapsed: 0.069 s
% 7.21/2.04 % (2537366)Peak memory usage: 89 MB
% 7.21/2.04 % (2537366)Instructions burned: 130 (million)
% 7.21/2.04 % (2537365)Instruction limit reached!
% 7.21/2.04 % (2537365)------------------------------
% 7.21/2.04 % (2537365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.21/2.04 % (2537365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.21/2.04 % (2537365)CaDiCaL version: 2.1.3
% 7.21/2.04 % (2537365)Termination reason: Instruction limit
% 7.21/2.04 % (2537365)Termination phase: Saturation
% 7.21/2.04 % (2537365)Time elapsed: 0.082 s
% 7.21/2.04 % (2537365)Peak memory usage: 89 MB
% 7.21/2.04 % (2537365)Instructions burned: 140 (million)
% 7.21/2.04 % (2537376)lrs+1011_1_sil=32000:sp=occurrence:random_seed=72250484:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.21/2.04 % (2537374)lrs+10_1_sil=8000:sp=occurrence:random_seed=2106761693:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 7.21/2.04 % (2537375)lrs+10_1_sil=32000:urr=on:br=off:random_seed=955949303:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.21/2.04 % (2537363)------------------------------
% 7.21/2.04 % (2537363)------------------------------
% 7.21/2.04 % (2537376)Instruction limit reached!
% 7.21/2.04 % (2537376)------------------------------
% 7.21/2.04 % (2537376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.23 % (2537376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.23 % (2537376)CaDiCaL version: 2.1.3
% 9.43/2.23 % (2537376)Termination reason: Instruction limit
% 9.43/2.23 % (2537376)Termination phase: Saturation
% 9.43/2.23 % (2537376)Time elapsed: 0.088 s
% 9.43/2.23 % (2537376)Peak memory usage: 91 MB
% 9.43/2.23 % (2537376)Instructions burned: 329 (million)
% 9.43/2.23 % (2537375)Instruction limit reached!
% 9.43/2.23 % (2537375)------------------------------
% 9.43/2.23 % (2537375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.23 % (2537375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.23 % (2537375)CaDiCaL version: 2.1.3
% 9.43/2.23 % (2537375)Termination reason: Instruction limit
% 9.43/2.23 % (2537375)Termination phase: Saturation
% 9.43/2.23 % (2537375)Time elapsed: 0.088 s
% 9.43/2.23 % (2537375)Peak memory usage: 90 MB
% 9.43/2.23 % (2537375)Instructions burned: 158 (million)
% 9.43/2.23 % (2537374)Instruction limit reached!
% 9.43/2.23 % (2537374)------------------------------
% 9.43/2.23 % (2537374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.23 % (2537374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.23 % (2537374)CaDiCaL version: 2.1.3
% 9.43/2.23 % (2537374)Termination reason: Instruction limit
% 9.43/2.23 % (2537374)Termination phase: Saturation
% 9.43/2.23 % (2537374)Time elapsed: 0.183 s
% 9.43/2.23 % (2537374)Peak memory usage: 91 MB
% 9.43/2.23 % (2537374)Instructions burned: 285 (million)
% 9.43/2.23 % (2537380)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=991473266:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 9.43/2.23 % (2537382)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2918001799:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 9.43/2.23 % (2537381)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=417267965:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.43/2.23 % (2537380)Instruction limit reached!
% 9.43/2.23 % (2537380)------------------------------
% 9.43/2.23 % (2537380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.23 % (2537380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.23 % (2537380)CaDiCaL version: 2.1.3
% 9.43/2.23 % (2537380)Termination reason: Instruction limit
% 9.43/2.23 % (2537380)Termination phase: Saturation
% 9.43/2.23 % (2537380)Time elapsed: 0.137 s
% 9.43/2.23 % (2537380)Peak memory usage: 91 MB
% 9.43/2.23 % (2537380)Instructions burned: 248 (million)
% 9.43/2.23 % (2537383)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1632961414:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.43/2.23 % (2537383)Instruction limit reached!
% 9.43/2.23 % (2537383)------------------------------
% 9.43/2.23 % (2537383)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.23 % (2537383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.23 % (2537383)CaDiCaL version: 2.1.3
% 9.43/2.23 % (2537383)Termination reason: Instruction limit
% 9.43/2.23 % (2537383)Termination phase: Saturation
% 9.43/2.23 % (2537383)Time elapsed: 0.061 s
% 9.43/2.23 % (2537383)Peak memory usage: 90 MB
% 9.43/2.23 % (2537383)Instructions burned: 114 (million)
% 9.43/2.23 % (2537381)Instruction limit reached!
% 9.43/2.23 % (2537381)------------------------------
% 9.43/2.23 % (2537381)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.23 % (2537381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.23 % (2537381)CaDiCaL version: 2.1.3
% 9.43/2.23 % (2537381)Termination reason: Instruction limit
% 9.43/2.23 % (2537381)Termination phase: Saturation
% 9.43/2.23 % (2537381)Time elapsed: 0.170 s
% 9.43/2.23 % (2537381)Peak memory usage: 90 MB
% 9.43/2.23 % (2537381)Instructions burned: 294 (million)
% 9.43/2.23 % (2537388)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1866849171:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 9.43/2.23 % (2537389)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4230088944:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 9.43/2.23 % (2537388)Instruction limit reached!
% 9.43/2.23 % (2537388)------------------------------
% 9.43/2.23 % (2537388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.23 % (2537388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.23 % (2537388)CaDiCaL version: 2.1.3
% 9.43/2.23 % (2537388)Termination reason: Instruction limit
% 9.43/2.23 % (2537388)Termination phase: Saturation
% 9.43/2.23 % (2537388)Time elapsed: 0.057 s
% 9.43/2.23 % (2537388)Peak memory usage: 89 MB
% 9.43/2.23 % (2537388)Instructions burned: 127 (million)
% 9.43/2.23 % (2537390)lrs+10_1_sil=8000:sp=occurrence:random_seed=638080475:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 9.43/2.23 % (2537389)Instruction limit reached!
% 9.43/2.23 % (2537389)------------------------------
% 9.43/2.23 % (2537389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.23 % (2537389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.23 % (2537389)CaDiCaL version: 2.1.3
% 9.43/2.23 % (2537389)Termination reason: Instruction limit
% 9.43/2.23 % (2537389)Termination phase: Saturation
% 9.43/2.23 % (2537389)Time elapsed: 0.050 s
% 9.43/2.23 % (2537389)Peak memory usage: 89 MB
% 9.43/2.23 % (2537389)Instructions burned: 114 (million)
% 9.43/2.23 % (2537360)First to succeed.
% 9.43/2.23 % (2537360)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2537355"
% 9.43/2.23 % (2537361)Also succeeded, but the first one will report.
% 9.43/2.23 % (2537393)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1358699741:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 9.43/2.23 % (2537395)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1315287995:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 9.43/2.23 % (2537382)Also succeeded, but the first one will report.
% 9.43/2.23 % (2537393)Instruction limit reached!
% 9.43/2.23 % (2537393)------------------------------
% 9.43/2.23 % (2537393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.23 % (2537393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.23 % (2537393)CaDiCaL version: 2.1.3
% 9.43/2.23 % (2537393)Termination reason: Instruction limit
% 9.43/2.23 % (2537393)Termination phase: Saturation
% 9.43/2.23 % (2537393)Time elapsed: 0.128 s
% 9.43/2.23 % (2537393)Peak memory usage: 92 MB
% 9.43/2.23 % (2537393)Instructions burned: 441 (million)
% 9.43/2.23 % (2537360)Refutation found. Thanks to Tanya!
% 9.43/2.23 % SZS status ContradictoryAxioms for theBenchmark
% 9.43/2.23 % SZS output start Proof for theBenchmark
% See solution above
% 9.43/2.23 % (2537360)------------------------------
% 9.43/2.23 % (2537360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.23 % (2537360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.23 % (2537360)CaDiCaL version: 2.1.3
% 9.43/2.23 % (2537360)Termination reason: Refutation
% 9.43/2.23 % (2537360)Time elapsed: 0.825 s
% 9.43/2.23 % (2537360)Peak memory usage: 134 MB
% 9.43/2.23 % (2537360)Instructions burned: 1312 (million)
% 9.43/2.23 % (2537360)------------------------------
% 9.43/2.23 % (2537360)------------------------------
% 9.43/2.23 % (2537355)Success in time 1.276 s
% 9.43/2.23 % Vampire exiting
%------------------------------------------------------------------------------