%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 09:37:33 AM UTC 2026
% Result : Unsatisfiable 8.62s 2.07s
% Output : Refutation 8.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 9 ( 7 unt; 0 def)
% Number of atoms : 11 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f3,axiom,
! [X2,X0,X1] : apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_definition) ).
fof(f5,axiom,
! [X0] :
( X0 != apply(fixed_pt,X0)
| fixed_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',weak_fixed_point) ).
fof(f6,plain,
! [X0] :
( apply(fixed_pt,X0) != X0
| fixed_point(X0) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
! [X0] : ~ fixed_point(apply(apply(apply(s,apply(c,apply(b,X0))),apply(s,apply(c,apply(b,X0)))),apply(s,apply(c,apply(b,X0))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
fof(f19,plain,
! [X2,X0,X1] : apply(apply(apply(s,apply(c,X0)),X1),X2) = apply(apply(X0,apply(X1,X2)),X2),
inference(superposition,[],[f1,f3]) ).
fof(f209,plain,
! [X2,X0,X1] : apply(X0,apply(apply(X1,X2),X2)) = apply(apply(apply(s,apply(c,apply(b,X0))),X1),X2),
inference(superposition,[],[f2,f19]) ).
fof(f226,plain,
$false,
inference(unit_resulting_resolution,[],[f6,f7,f209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:31:47 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 8.62/2.06 % (3052731)Input is clausal, will run a generic CNF schedule.
% 8.62/2.06 % (3052782)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=892106664:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 8.62/2.06 % (3052781)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1417373689:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 8.62/2.06 % (3052777)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=1261573623:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 8.62/2.06 % (3052778)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=312766143:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 8.62/2.06 % (3052779)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1859433768:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 8.62/2.06 % (3052780)lrs+10_1_sil=8000:sp=occurrence:random_seed=2551508386:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 8.62/2.06 % (3052783)dis-21_1_sil=8000:lcm=predicate:random_seed=424381857:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 8.62/2.06 % (3052783)Refutation not found, incomplete strategy
% 8.62/2.06 % (3052783)------------------------------
% 8.62/2.06 % (3052783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.06 % (3052783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.06 % (3052783)CaDiCaL version: 2.1.3
% 8.62/2.06 % (3052783)Termination reason: Refutation not found, incomplete strategy
% 8.62/2.06 % (3052783)Time elapsed: 0.002 s
% 8.62/2.06 % (3052783)Peak memory usage: 88 MB
% 8.62/2.06 % (3052782)Instruction limit reached!
% 8.62/2.06 % (3052782)------------------------------
% 8.62/2.06 % (3052782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.06 % (3052782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.06 % (3052782)CaDiCaL version: 2.1.3
% 8.62/2.06 % (3052782)Termination reason: Instruction limit
% 8.62/2.06 % (3052782)Termination phase: Saturation
% 8.62/2.06 % (3052782)Time elapsed: 0.092 s
% 8.62/2.06 % (3052782)Peak memory usage: 90 MB
% 8.62/2.06 % (3052782)Instructions burned: 184 (million)
% 8.62/2.06 % (3052781)Instruction limit reached!
% 8.62/2.06 % (3052781)------------------------------
% 8.62/2.06 % (3052781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.06 % (3052781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.06 % (3052781)CaDiCaL version: 2.1.3
% 8.62/2.06 % (3052781)Termination reason: Instruction limit
% 8.62/2.06 % (3052781)Termination phase: Saturation
% 8.62/2.06 % (3052781)Time elapsed: 0.110 s
% 8.62/2.06 % (3052781)Peak memory usage: 89 MB
% 8.62/2.06 % (3052781)Instructions burned: 114 (million)
% 8.62/2.06 % (3052780)Instruction limit reached!
% 8.62/2.06 % (3052780)------------------------------
% 8.62/2.06 % (3052780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.06 % (3052780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.06 % (3052780)CaDiCaL version: 2.1.3
% 8.62/2.06 % (3052780)Termination reason: Instruction limit
% 8.62/2.06 % (3052780)Termination phase: Saturation
% 8.62/2.06 % (3052780)Time elapsed: 0.112 s
% 8.62/2.06 % (3052780)Peak memory usage: 89 MB
% 8.62/2.06 % (3052780)Instructions burned: 108 (million)
% 8.62/2.06 % (3052796)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2687256685:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 8.62/2.06 % (3052796)Refutation not found, incomplete strategy
% 8.62/2.06 % (3052796)------------------------------
% 8.62/2.06 % (3052796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.06 % (3052796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.06 % (3052796)CaDiCaL version: 2.1.3
% 8.62/2.06 % (3052796)Termination reason: Refutation not found, incomplete strategy
% 8.62/2.06 % (3052796)Time elapsed: 0.001 s
% 8.62/2.06 % (3052796)Peak memory usage: 88 MB
% 8.62/2.06 % (3052798)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3163994207:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 8.62/2.06 % (3052797)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2299746610:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 8.62/2.06 % (3052796)------------------------------
% 8.62/2.06 % (3052796)------------------------------
% 8.62/2.06 % (3052783)------------------------------
% 8.62/2.06 % (3052783)------------------------------
% 8.62/2.06 % (3052797)Instruction limit reached!
% 8.62/2.06 % (3052797)------------------------------
% 8.62/2.06 % (3052797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.06 % (3052797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.06 % (3052797)CaDiCaL version: 2.1.3
% 8.62/2.06 % (3052797)Termination reason: Instruction limit
% 8.62/2.06 % (3052797)Termination phase: Saturation
% 8.62/2.06 % (3052797)Time elapsed: 0.136 s
% 8.62/2.06 % (3052797)Peak memory usage: 91 MB
% 8.62/2.06 % (3052797)Instructions burned: 190 (million)
% 8.62/2.06 % (3052798)Instruction limit reached!
% 8.62/2.06 % (3052798)------------------------------
% 8.62/2.06 % (3052798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.06 % (3052798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.06 % (3052798)CaDiCaL version: 2.1.3
% 8.62/2.06 % (3052798)Termination reason: Instruction limit
% 8.62/2.06 % (3052798)Termination phase: Saturation
% 8.62/2.06 % (3052798)Time elapsed: 0.165 s
% 8.62/2.06 % (3052798)Peak memory usage: 90 MB
% 8.62/2.06 % (3052798)Instructions burned: 219 (million)
% 8.62/2.06 % (3052805)lrs+10_64_to=lpo:sil=8000:random_seed=565239999:i=126:bd=preordered_2993 on theBenchmark for (2993ds/126Mi)
% 8.62/2.06 % (3052805)Instruction limit reached!
% 8.62/2.06 % (3052805)------------------------------
% 8.62/2.06 % (3052805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.06 % (3052805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.06 % (3052805)CaDiCaL version: 2.1.3
% 8.62/2.06 % (3052805)Termination reason: Instruction limit
% 8.62/2.06 % (3052805)Termination phase: Saturation
% 8.62/2.06 % (3052805)Time elapsed: 0.036 s
% 8.62/2.06 % (3052805)Peak memory usage: 88 MB
% 8.62/2.07 % (3052805)Instructions burned: 128 (million)
% 8.62/2.07 % (3052806)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2548164248:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 8.62/2.07 % (3052808)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1149236196:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 8.62/2.07 % (3052807)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2646221780:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 8.62/2.07 % (3052810)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=3867548435:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2992 on theBenchmark for (2992ds/106Mi)
% 8.62/2.07 % (3052810)Instruction limit reached!
% 8.62/2.07 % (3052810)------------------------------
% 8.62/2.07 % (3052810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.07 % (3052810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.07 % (3052810)CaDiCaL version: 2.1.3
% 8.62/2.07 % (3052810)Termination reason: Instruction limit
% 8.62/2.07 % (3052810)Termination phase: Saturation
% 8.62/2.07 % (3052810)Time elapsed: 0.034 s
% 8.62/2.07 % (3052810)Peak memory usage: 89 MB
% 8.62/2.07 % (3052810)Instructions burned: 106 (million)
% 8.62/2.07 % (3052806)Instruction limit reached!
% 8.62/2.07 % (3052806)------------------------------
% 8.62/2.07 % (3052806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.07 % (3052806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.07 % (3052806)CaDiCaL version: 2.1.3
% 8.62/2.07 % (3052806)Termination reason: Instruction limit
% 8.62/2.07 % (3052806)Termination phase: Saturation
% 8.62/2.07 % (3052806)Time elapsed: 0.112 s
% 8.62/2.07 % (3052806)Peak memory usage: 89 MB
% 8.62/2.07 % (3052806)Instructions burned: 195 (million)
% 8.62/2.07 % (3052807)Instruction limit reached!
% 8.62/2.07 % (3052807)------------------------------
% 8.62/2.07 % (3052807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.07 % (3052807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.07 % (3052807)CaDiCaL version: 2.1.3
% 8.62/2.07 % (3052807)Termination reason: Instruction limit
% 8.62/2.07 % (3052807)Termination phase: Saturation
% 8.62/2.07 % (3052807)Time elapsed: 0.099 s
% 8.62/2.07 % (3052807)Peak memory usage: 90 MB
% 8.62/2.07 % (3052807)Instructions burned: 158 (million)
% 8.62/2.07 % (3052778)First to succeed.
% 8.62/2.07 % (3052778)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3052731"
% 8.62/2.07 % (3052837)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=2268617823:i=107_2991 on theBenchmark for (2991ds/107Mi)
% 8.62/2.07 % (3052837)Refutation not found, incomplete strategy
% 8.62/2.07 % (3052837)------------------------------
% 8.62/2.07 % (3052837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.07 % (3052837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.07 % (3052837)CaDiCaL version: 2.1.3
% 8.62/2.07 % (3052837)Termination reason: Refutation not found, incomplete strategy
% 8.62/2.07 % (3052837)Time elapsed: 0.001 s
% 8.62/2.07 % (3052837)Peak memory usage: 87 MB
% 8.62/2.07 % (3052777)Also succeeded, but the first one will report.
% 8.62/2.07 % (3052839)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=1765054911:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2991 on theBenchmark for (2991ds/242Mi)
% 8.62/2.07 % (3052848)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=848597117:cond=fast:i=5208:av=off_2990 on theBenchmark for (2990ds/5208Mi)
% 8.62/2.07 % (3052778)Refutation found. Thanks to Tanya!
% 8.62/2.07 % SZS status Unsatisfiable for theBenchmark
% 8.62/2.07 % SZS output start Proof for theBenchmark
% See solution above
% 8.62/2.07 % (3052778)------------------------------
% 8.62/2.07 % (3052778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.62/2.07 % (3052778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.62/2.07 % (3052778)CaDiCaL version: 2.1.3
% 8.62/2.07 % (3052778)Termination reason: Refutation
% 8.62/2.07 % (3052778)Time elapsed: 0.739 s
% 8.62/2.07 % (3052778)Peak memory usage: 128 MB
% 8.62/2.07 % (3052778)Instructions burned: 998 (million)
% 8.62/2.07 % (3052778)------------------------------
% 8.62/2.07 % (3052778)------------------------------
% 8.62/2.07 % (3052731)Success in time 1.118 s
% 8.62/2.07 % Vampire exiting
%------------------------------------------------------------------------------