%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT168+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 12:37:04 PM UTC 2026
% Result : ContradictoryAxioms 0.16s 2.14s
% Output : Refutation 0.16s
% 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(f385,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(f1942,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(cnf_transformation,[],[f385]) ).
fof(f2131,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f525]) ).
fof(f2133,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(f2135,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(f2396,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,[],[f2135,f2133]) ).
fof(f2428,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,[],[f1942,f2396]) ).
fof(f2438,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,[],[f2428,f2131]) ).
fof(f2454,plain,
$false,
inference(equality_resolution,[],[f2438]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT168+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 23:52:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 6.39/1.95 % (2538631)Detected formulas, will run a generic FOF schedule.
% 6.39/1.95 % (2538641)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2780593575:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.39/1.95 % (2538636)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=1477640201:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.39/1.95 % (2538640)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1394163031:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.39/1.95 % (2538637)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=2339324368:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.39/1.95 % (2538638)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=2968484316:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.39/1.95 % (2538642)dis-21_1_sil=8000:lcm=predicate:random_seed=57419435: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)
% 6.39/1.95 % (2538639)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=735163592:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.39/1.95 % (2538641)Instruction limit reached!
% 6.39/1.95 % (2538641)------------------------------
% 6.39/1.95 % (2538641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.95 % (2538641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.95 % (2538641)CaDiCaL version: 2.1.3
% 6.39/1.95 % (2538641)Termination reason: Instruction limit
% 6.39/1.95 % (2538641)Termination phase: Saturation
% 6.39/1.95 % (2538641)Time elapsed: 0.043 s
% 6.39/1.95 % (2538641)Peak memory usage: 90 MB
% 6.39/1.95 % (2538641)Instructions burned: 142 (million)
% 6.39/1.95 % (2538639)Instruction limit reached!
% 6.39/1.95 % (2538639)------------------------------
% 6.39/1.95 % (2538639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.95 % (2538639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.95 % (2538639)CaDiCaL version: 2.1.3
% 6.39/1.95 % (2538639)Termination reason: Instruction limit
% 6.39/1.95 % (2538639)Termination phase: Saturation
% 6.39/1.95 % (2538639)Time elapsed: 0.052 s
% 6.39/1.95 % (2538639)Peak memory usage: 89 MB
% 6.39/1.95 % (2538639)Instructions burned: 110 (million)
% 6.39/1.95 % (2538642)Instruction limit reached!
% 6.39/1.95 % (2538642)------------------------------
% 6.39/1.95 % (2538642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.95 % (2538642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.95 % (2538642)CaDiCaL version: 2.1.3
% 6.39/1.95 % (2538642)Termination reason: Instruction limit
% 6.39/1.95 % (2538642)Termination phase: Saturation
% 6.39/1.95 % (2538642)Time elapsed: 0.066 s
% 6.39/1.95 % (2538642)Peak memory usage: 89 MB
% 6.39/1.95 % (2538642)Instructions burned: 130 (million)
% 6.39/1.95 % (2538640)Instruction limit reached!
% 6.39/1.95 % (2538640)------------------------------
% 6.39/1.95 % (2538640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.39/1.95 % (2538640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.39/1.95 % (2538640)CaDiCaL version: 2.1.3
% 6.39/1.95 % (2538640)Termination reason: Instruction limit
% 6.39/1.95 % (2538640)Termination phase: Saturation
% 6.39/1.95 % (2538640)Time elapsed: 0.069 s
% 6.39/1.95 % (2538640)Peak memory usage: 89 MB
% 6.39/1.95 % (2538640)Instructions burned: 121 (million)
% 6.39/1.95 % (2538650)lrs+10_1_sil=8000:sp=occurrence:random_seed=2845307098:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.39/1.95 % (2538651)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3116596533:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.39/1.95 % (2538653)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=1109077463:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.39/1.95 % (2538652)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3540000435:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.39/1.95 % (2538650)Instruction limit reached!
% 0.16/2.14 % (2538650)------------------------------
% 0.16/2.14 % (2538650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (2538650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (2538650)CaDiCaL version: 2.1.3
% 0.16/2.14 % (2538650)Termination reason: Instruction limit
% 0.16/2.14 % (2538650)Termination phase: Saturation
% 0.16/2.14 % (2538650)Time elapsed: 0.098 s
% 0.16/2.14 % (2538650)Peak memory usage: 92 MB
% 0.16/2.14 % (2538650)Instructions burned: 287 (million)
% 0.16/2.14 % (2538651)Instruction limit reached!
% 0.16/2.14 % (2538651)------------------------------
% 0.16/2.14 % (2538651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (2538651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (2538651)CaDiCaL version: 2.1.3
% 0.16/2.14 % (2538651)Termination reason: Instruction limit
% 0.16/2.14 % (2538651)Termination phase: Saturation
% 0.16/2.14 % (2538651)Time elapsed: 0.090 s
% 0.16/2.14 % (2538651)Peak memory usage: 90 MB
% 0.16/2.14 % (2538651)Instructions burned: 158 (million)
% 0.16/2.14 % (2538658)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=374227592:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 0.16/2.14 % (2538653)Instruction limit reached!
% 0.16/2.14 % (2538653)------------------------------
% 0.16/2.14 % (2538653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (2538653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (2538653)CaDiCaL version: 2.1.3
% 0.16/2.14 % (2538653)Termination reason: Instruction limit
% 0.16/2.14 % (2538653)Termination phase: Saturation
% 0.16/2.14 % (2538653)Time elapsed: 0.138 s
% 0.16/2.14 % (2538653)Peak memory usage: 91 MB
% 0.16/2.14 % (2538653)Instructions burned: 249 (million)
% 0.16/2.14 % (2538652)Instruction limit reached!
% 0.16/2.14 % (2538652)------------------------------
% 0.16/2.14 % (2538652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (2538652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (2538652)CaDiCaL version: 2.1.3
% 0.16/2.14 % (2538652)Termination reason: Instruction limit
% 0.16/2.14 % (2538652)Termination phase: Saturation
% 0.16/2.14 % (2538652)Time elapsed: 0.200 s
% 0.16/2.14 % (2538652)Peak memory usage: 92 MB
% 0.16/2.14 % (2538652)Instructions burned: 325 (million)
% 0.16/2.14 % (2538658)Instruction limit reached!
% 0.16/2.14 % (2538658)------------------------------
% 0.16/2.14 % (2538658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (2538658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (2538658)CaDiCaL version: 2.1.3
% 0.16/2.14 % (2538658)Termination reason: Instruction limit
% 0.16/2.14 % (2538658)Termination phase: Saturation
% 0.16/2.14 % (2538658)Time elapsed: 0.078 s
% 0.16/2.14 % (2538658)Peak memory usage: 90 MB
% 0.16/2.14 % (2538658)Instructions burned: 294 (million)
% 0.16/2.14 % (2538659)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=236362551:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 0.16/2.14 % (2538661)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2538405553:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 0.16/2.14 % (2538663)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=70421319:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 0.16/2.14 % (2538663)Instruction limit reached!
% 0.16/2.14 % (2538663)------------------------------
% 0.16/2.14 % (2538663)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (2538663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (2538663)CaDiCaL version: 2.1.3
% 0.16/2.14 % (2538663)Termination reason: Instruction limit
% 0.16/2.14 % (2538663)Termination phase: Saturation
% 0.16/2.14 % (2538663)Time elapsed: 0.028 s
% 0.16/2.14 % (2538663)Peak memory usage: 89 MB
% 0.16/2.14 % (2538663)Instructions burned: 116 (million)
% 0.16/2.14 % (2538662)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=798613842:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 0.16/2.14 % (2538661)Instruction limit reached!
% 0.16/2.14 % (2538661)------------------------------
% 0.16/2.14 % (2538661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (2538661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (2538661)CaDiCaL version: 2.1.3
% 0.16/2.14 % (2538661)Termination reason: Instruction limit
% 0.16/2.14 % (2538661)Termination phase: Saturation
% 0.16/2.14 % (2538661)Time elapsed: 0.061 s
% 0.16/2.14 % (2538661)Peak memory usage: 90 MB
% 0.16/2.14 % (2538661)Instructions burned: 114 (million)
% 0.16/2.14 % (2538662)Instruction limit reached!
% 0.16/2.14 % (2538662)------------------------------
% 0.16/2.14 % (2538662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (2538662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (2538662)CaDiCaL version: 2.1.3
% 0.16/2.14 % (2538662)Termination reason: Instruction limit
% 0.16/2.14 % (2538662)Termination phase: Saturation
% 0.16/2.14 % (2538662)Time elapsed: 0.058 s
% 0.16/2.14 % (2538662)Peak memory usage: 89 MB
% 0.16/2.14 % (2538662)Instructions burned: 128 (million)
% 0.16/2.14 % (2538667)lrs+10_1_sil=8000:sp=occurrence:random_seed=637027121:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 0.16/2.14 % (2538637)First to succeed.
% 0.16/2.14 % (2538637)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2538631"
% 0.16/2.14 % (2538669)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4041581059:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 0.16/2.14 % (2538670)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1261845406:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 0.16/2.14 % (2538669)Refutation not found, incomplete strategy
% 0.16/2.14 % (2538669)------------------------------
% 0.16/2.14 % (2538669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (2538669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (2538669)CaDiCaL version: 2.1.3
% 0.16/2.14 % (2538669)Termination reason: Refutation not found, incomplete strategy
% 0.16/2.14 % (2538669)Time elapsed: 0.055 s
% 0.16/2.14 % (2538669)Peak memory usage: 90 MB
% 0.16/2.14 % (2538669)Instructions burned: 109 (million)
% 0.16/2.14 % (2538636)Also succeeded, but the first one will report.
% 0.16/2.14 % (2538637)Refutation found. Thanks to Tanya!
% 0.16/2.14 % SZS status ContradictoryAxioms for theBenchmark
% 0.16/2.14 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/2.14 % (2538637)------------------------------
% 0.16/2.14 % (2538637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (2538637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (2538637)CaDiCaL version: 2.1.3
% 0.16/2.14 % (2538637)Termination reason: Refutation
% 0.16/2.14 % (2538637)Time elapsed: 0.728 s
% 0.16/2.14 % (2538637)Peak memory usage: 140 MB
% 0.16/2.14 % (2538637)Instructions burned: 1366 (million)
% 0.16/2.14 % (2538637)------------------------------
% 0.16/2.14 % (2538637)------------------------------
% 0.16/2.14 % (2538631)Success in time 1.109 s
% 0.16/2.14 % Vampire exiting
%------------------------------------------------------------------------------