%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT166+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 2.31s
% 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(f378,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(f1854,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(cnf_transformation,[],[f378]) ).
fof(f2042,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f525]) ).
fof(f2044,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(f2046,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(f2462,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,[],[f2046,f2044]) ).
fof(f2515,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,[],[f1854,f2462]) ).
fof(f2527,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,[],[f2515,f2042]) ).
fof(f2544,plain,
$false,
inference(equality_resolution,[],[f2527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT166+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n009.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 23:52:15 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 8.62/2.12 % (2538209)Detected formulas, will run a generic FOF schedule.
% 8.62/2.12 % (2538216)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=72397932:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.62/2.12 % (2538215)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=2072922279:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.62/2.12 % (2538220)dis-21_1_sil=8000:lcm=predicate:random_seed=445313895: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)
% 8.62/2.12 % (2538217)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1117383110:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.62/2.12 % (2538218)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1449776962:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.62/2.12 % (2538214)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=3794829495:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.62/2.12 % (2538219)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4117251297:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.62/2.12 % (2538217)Refutation not found, incomplete strategy
% 8.62/2.12 % (2538217)------------------------------
% 8.62/2.12 % (2538217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (2538217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (2538217)CaDiCaL version: 2.1.3
% 8.62/2.12 % (2538217)Termination reason: Refutation not found, incomplete strategy
% 8.62/2.12 % (2538217)Time elapsed: 0.014 s
% 8.62/2.12 % (2538217)Peak memory usage: 89 MB
% 8.62/2.12 % (2538217)Instructions burned: 26 (million)
% 8.62/2.12 % (2538220)Instruction limit reached!
% 8.62/2.12 % (2538220)------------------------------
% 8.62/2.12 % (2538220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (2538220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (2538220)CaDiCaL version: 2.1.3
% 8.62/2.12 % (2538220)Termination reason: Instruction limit
% 8.62/2.12 % (2538220)Termination phase: Saturation
% 8.62/2.12 % (2538220)Time elapsed: 0.066 s
% 8.62/2.12 % (2538220)Peak memory usage: 90 MB
% 8.62/2.12 % (2538220)Instructions burned: 129 (million)
% 8.62/2.12 % (2538218)Instruction limit reached!
% 8.62/2.12 % (2538218)------------------------------
% 8.62/2.12 % (2538218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (2538218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (2538218)CaDiCaL version: 2.1.3
% 8.62/2.12 % (2538218)Termination reason: Instruction limit
% 8.62/2.12 % (2538218)Termination phase: Saturation
% 8.62/2.12 % (2538218)Time elapsed: 0.067 s
% 8.62/2.12 % (2538218)Peak memory usage: 89 MB
% 8.62/2.12 % (2538218)Instructions burned: 121 (million)
% 8.62/2.12 % (2538219)Instruction limit reached!
% 8.62/2.12 % (2538219)------------------------------
% 8.62/2.12 % (2538219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.12 % (2538219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.12 % (2538219)CaDiCaL version: 2.1.3
% 8.62/2.12 % (2538219)Termination reason: Instruction limit
% 8.62/2.12 % (2538219)Termination phase: Saturation
% 8.62/2.12 % (2538219)Time elapsed: 0.075 s
% 8.62/2.12 % (2538219)Peak memory usage: 90 MB
% 8.62/2.12 % (2538219)Instructions burned: 141 (million)
% 8.62/2.12 % (2538229)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1918179894:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.62/2.12 % (2538228)lrs+10_1_sil=8000:sp=occurrence:random_seed=1566200588:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.62/2.12 % (2538230)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1500449091:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.62/2.12 % (2538217)------------------------------
% 8.62/2.12 % (2538217)------------------------------
% 8.62/2.12 % (2538229)Instruction limit reached!
% 8.62/2.12 % (2538229)------------------------------
% 8.62/2.12 % (2538229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.31 % (2538229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.31 % (2538229)CaDiCaL version: 2.1.3
% 9.43/2.31 % (2538229)Termination reason: Instruction limit
% 9.43/2.31 % (2538229)Termination phase: Saturation
% 9.43/2.31 % (2538229)Time elapsed: 0.084 s
% 9.43/2.31 % (2538229)Peak memory usage: 90 MB
% 9.43/2.31 % (2538229)Instructions burned: 158 (million)
% 9.43/2.31 % (2538230)Refutation not found, incomplete strategy
% 9.43/2.31 % (2538230)------------------------------
% 9.43/2.31 % (2538230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.31 % (2538230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.31 % (2538230)CaDiCaL version: 2.1.3
% 9.43/2.31 % (2538230)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.31 % (2538230)Time elapsed: 0.093 s
% 9.43/2.31 % (2538230)Peak memory usage: 90 MB
% 9.43/2.31 % (2538230)Instructions burned: 153 (million)
% 9.43/2.31 % (2538228)Instruction limit reached!
% 9.43/2.31 % (2538228)------------------------------
% 9.43/2.31 % (2538228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.31 % (2538228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.31 % (2538228)CaDiCaL version: 2.1.3
% 9.43/2.31 % (2538228)Termination reason: Instruction limit
% 9.43/2.31 % (2538228)Termination phase: Saturation
% 9.43/2.31 % (2538228)Time elapsed: 0.181 s
% 9.43/2.31 % (2538228)Peak memory usage: 92 MB
% 9.43/2.31 % (2538228)Instructions burned: 285 (million)
% 9.43/2.31 % (2538234)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=359165067:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 9.43/2.31 % (2538235)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1260937723:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.43/2.31 % (2538236)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2088171000:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.43/2.31 % (2538234)Instruction limit reached!
% 9.43/2.31 % (2538234)------------------------------
% 9.43/2.31 % (2538234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.31 % (2538234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.31 % (2538234)CaDiCaL version: 2.1.3
% 9.43/2.31 % (2538234)Termination reason: Instruction limit
% 9.43/2.31 % (2538234)Termination phase: Saturation
% 9.43/2.31 % (2538234)Time elapsed: 0.147 s
% 9.43/2.31 % (2538234)Peak memory usage: 92 MB
% 9.43/2.31 % (2538234)Instructions burned: 278 (million)
% 9.43/2.31 % (2538230)------------------------------
% 9.43/2.31 % (2538230)------------------------------
% 9.43/2.31 % (2538235)Instruction limit reached!
% 9.43/2.31 % (2538235)------------------------------
% 9.43/2.31 % (2538235)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.31 % (2538235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.31 % (2538235)CaDiCaL version: 2.1.3
% 9.43/2.31 % (2538235)Termination reason: Instruction limit
% 9.43/2.31 % (2538235)Termination phase: Saturation
% 9.43/2.31 % (2538235)Time elapsed: 0.173 s
% 9.43/2.31 % (2538235)Peak memory usage: 91 MB
% 9.43/2.31 % (2538235)Instructions burned: 295 (million)
% 9.43/2.31 % (2538240)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=660361575:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 9.43/2.31 % (2538241)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=263768616:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 9.43/2.31 % (2538242)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1322333097:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 9.43/2.31 % (2538240)Instruction limit reached!
% 9.43/2.31 % (2538240)------------------------------
% 9.43/2.31 % (2538240)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.31 % (2538240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.31 % (2538240)CaDiCaL version: 2.1.3
% 9.43/2.31 % (2538240)Termination reason: Instruction limit
% 9.43/2.31 % (2538240)Termination phase: Saturation
% 9.43/2.31 % (2538240)Time elapsed: 0.059 s
% 9.43/2.31 % (2538240)Peak memory usage: 90 MB
% 9.43/2.31 % (2538240)Instructions burned: 114 (million)
% 9.43/2.31 % (2538241)Instruction limit reached!
% 9.43/2.31 % (2538241)------------------------------
% 9.43/2.31 % (2538241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.31 % (2538241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.31 % (2538241)CaDiCaL version: 2.1.3
% 9.43/2.31 % (2538241)Termination reason: Instruction limit
% 9.43/2.31 % (2538241)Termination phase: Saturation
% 9.43/2.31 % (2538241)Time elapsed: 0.058 s
% 9.43/2.31 % (2538241)Peak memory usage: 89 MB
% 9.43/2.31 % (2538241)Instructions burned: 129 (million)
% 9.43/2.31 % (2538242)Instruction limit reached!
% 9.43/2.31 % (2538242)------------------------------
% 9.43/2.31 % (2538242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.31 % (2538242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.31 % (2538242)CaDiCaL version: 2.1.3
% 9.43/2.31 % (2538242)Termination reason: Instruction limit
% 9.43/2.31 % (2538242)Termination phase: Saturation
% 9.43/2.31 % (2538242)Time elapsed: 0.050 s
% 9.43/2.31 % (2538242)Peak memory usage: 89 MB
% 9.43/2.31 % (2538242)Instructions burned: 116 (million)
% 9.43/2.31 % (2538214)First to succeed.
% 9.43/2.31 % (2538214)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2538209"
% 9.43/2.31 % (2538246)lrs+10_1_sil=8000:sp=occurrence:random_seed=2426403593:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 9.43/2.31 % (2538215)Also succeeded, but the first one will report.
% 9.43/2.31 % (2538247)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2587662929:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 9.43/2.31 % (2538248)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1073476800:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 9.43/2.31 % (2538247)Refutation not found, incomplete strategy
% 9.43/2.31 % (2538247)------------------------------
% 9.43/2.31 % (2538247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.31 % (2538247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.31 % (2538247)CaDiCaL version: 2.1.3
% 9.43/2.31 % (2538247)Termination reason: Refutation not found, incomplete strategy
% 9.43/2.31 % (2538247)Time elapsed: 0.046 s
% 9.43/2.31 % (2538247)Peak memory usage: 90 MB
% 9.43/2.31 % (2538247)Instructions burned: 92 (million)
% 9.43/2.31 % (2538214)Refutation found. Thanks to Tanya!
% 9.43/2.31 % SZS status ContradictoryAxioms for theBenchmark
% 9.43/2.31 % SZS output start Proof for theBenchmark
% See solution above
% 9.43/2.31 % (2538214)------------------------------
% 9.43/2.31 % (2538214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.43/2.31 % (2538214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.43/2.31 % (2538214)CaDiCaL version: 2.1.3
% 9.43/2.31 % (2538214)Termination reason: Refutation
% 9.43/2.31 % (2538214)Time elapsed: 0.832 s
% 9.43/2.31 % (2538214)Peak memory usage: 136 MB
% 9.43/2.31 % (2538214)Instructions burned: 1335 (million)
% 9.43/2.31 % (2538214)------------------------------
% 9.43/2.31 % (2538214)------------------------------
% 9.43/2.31 % (2538209)Success in time 1.281 s
% 9.43/2.31 % Vampire exiting
%------------------------------------------------------------------------------