%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL042-5 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 09:37:42 AM UTC 2026
% Result : Unsatisfiable 13.37s 3.27s
% Output : Refutation 13.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 15 unt; 0 def)
% Number of atoms : 19 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 8 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w1,X0),X1) = apply(apply(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w1_definition) ).
fof(f3,axiom,
! [X0] :
( apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt))
| fixed_point(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),apply(apply(b,b),b)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f17,plain,
! [X2,X0,X1] : apply(apply(w1,X2),apply(apply(b,X0),X1)) = apply(apply(X0,apply(X1,X2)),X2),
inference(superposition,[],[f2,f1]) ).
fof(f18,plain,
! [X0,X1] :
( apply(X0,apply(X1,fixed_pt)) != apply(fixed_pt,apply(X0,apply(X1,fixed_pt)))
| fixed_point(apply(apply(b,X0),X1)) ),
inference(superposition,[],[f3,f1]) ).
fof(f34,plain,
! [X2,X0,X1] : apply(apply(w1,X0),apply(apply(b,apply(b,X1)),X2)) = apply(X1,apply(apply(X2,X0),X0)),
inference(superposition,[],[f1,f17]) ).
fof(f46,plain,
! [X2,X3,X0,X1] : apply(X3,apply(apply(X0,apply(X1,X2)),X2)) = apply(apply(w1,X2),apply(apply(b,apply(b,X3)),apply(apply(b,X0),X1))),
inference(superposition,[],[f34,f1]) ).
fof(f52,plain,
! [X2,X0,X1] : apply(X2,apply(apply(w1,X0),X1)) = apply(apply(w1,X0),apply(apply(b,apply(b,X2)),X1)),
inference(superposition,[],[f34,f2]) ).
fof(f83,plain,
! [X2,X3,X0,X1] : apply(X3,apply(apply(w1,X2),apply(apply(b,X0),X1))) = apply(X3,apply(apply(X0,apply(X1,X2)),X2)),
inference(forward_demodulation,[],[f46,f52]) ).
fof(f112,plain,
! [X0,X1] : apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),w1) = apply(X0,apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),X1)),
inference(superposition,[],[f2,f52]) ).
fof(f130,plain,
apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),fixed_pt)) != apply(fixed_pt,apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),apply(apply(b,b),b)),fixed_pt))),
inference(unit_resulting_resolution,[],[f18,f4]) ).
fof(f142,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),fixed_pt))) != apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),fixed_pt)))),
inference(forward_demodulation,[],[f130,f1]) ).
fof(f144,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),fixed_pt))) != apply(fixed_pt,apply(apply(w1,apply(apply(apply(apply(b,b),b),fixed_pt),w1)),w1)),
inference(forward_demodulation,[],[f142,f83]) ).
fof(f145,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)),
inference(forward_demodulation,[],[f144,f1]) ).
fof(f146,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1),
inference(forward_demodulation,[],[f145,f112]) ).
fof(f147,plain,
$false,
inference(forward_subsumption_resolution,[],[f146,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL042-5 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.30 % Computer : n018.cluster.edu
% 0.28/0.30 % Model : x86_64 x86_64
% 0.28/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.28/0.30 % Memory : 8046.5625MB
% 0.28/0.30 % OS : Linux 6.8.0-71-generic
% 0.28/0.30 % CPULimit : 300
% 0.28/0.30 % WCLimit : 300
% 0.28/0.30 % DateTime : Mon Sep 28 21:32:40 UTC 2026
% 0.28/0.31 % CPUTime :
% 0.28/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.37 Running first-order theorem proving
% 0.28/0.37 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
% 11.21/2.89 % (3810163)Input is clausal, will run a generic CNF schedule.
% 11.21/2.89 % (3810172)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=448659042:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 11.21/2.89 % (3810168)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=696271902:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 11.21/2.89 % (3810170)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1973197423:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 11.21/2.89 % (3810169)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1966693565:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 11.21/2.89 % (3810172)Instruction limit reached!
% 11.21/2.89 % (3810172)------------------------------
% 11.21/2.89 % (3810172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/2.89 % (3810172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/2.89 % (3810172)CaDiCaL version: 2.1.3
% 11.21/2.89 % (3810172)Termination reason: Instruction limit
% 11.21/2.89 % (3810172)Termination phase: Saturation
% 11.21/2.89 % (3810172)Time elapsed: 0.059 s
% 11.21/2.89 % (3810172)Peak memory usage: 89 MB
% 11.21/2.89 % (3810172)Instructions burned: 114 (million)
% 11.21/2.89 % (3810174)dis-21_1_sil=8000:lcm=predicate:random_seed=1947430738: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)
% 11.21/2.89 % (3810171)lrs+10_1_sil=8000:sp=occurrence:random_seed=2381233655:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 11.21/2.89 % (3810173)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=528876644:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 11.21/2.89 % (3810174)Refutation not found, incomplete strategy
% 11.21/2.89 % (3810174)------------------------------
% 11.21/2.89 % (3810174)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/2.89 % (3810174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/2.89 % (3810174)CaDiCaL version: 2.1.3
% 11.21/2.89 % (3810174)Termination reason: Refutation not found, incomplete strategy
% 11.21/2.89 % (3810174)Time elapsed: 0.002 s
% 11.21/2.89 % (3810174)Peak memory usage: 88 MB
% 11.21/2.89 % (3810171)Instruction limit reached!
% 11.21/2.89 % (3810171)------------------------------
% 11.21/2.89 % (3810171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/2.89 % (3810171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/2.89 % (3810171)CaDiCaL version: 2.1.3
% 11.21/2.89 % (3810171)Termination reason: Instruction limit
% 11.21/2.89 % (3810171)Termination phase: Saturation
% 11.21/2.89 % (3810171)Time elapsed: 0.114 s
% 11.21/2.89 % (3810171)Peak memory usage: 89 MB
% 11.21/2.89 % (3810171)Instructions burned: 107 (million)
% 11.21/2.89 % (3810173)Instruction limit reached!
% 11.21/2.89 % (3810173)------------------------------
% 11.21/2.89 % (3810173)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/2.89 % (3810173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/2.89 % (3810173)CaDiCaL version: 2.1.3
% 11.21/2.89 % (3810173)Termination reason: Instruction limit
% 11.21/2.89 % (3810173)Termination phase: Saturation
% 11.21/2.89 % (3810173)Time elapsed: 0.170 s
% 11.21/2.89 % (3810173)Peak memory usage: 89 MB
% 11.21/2.89 % (3810173)Instructions burned: 180 (million)
% 11.21/2.89 % (3810179)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=2669736168:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 11.21/2.89 % (3810179)Refutation not found, incomplete strategy
% 11.21/2.89 % (3810179)------------------------------
% 11.21/2.89 % (3810179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/2.89 % (3810179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/2.89 % (3810179)CaDiCaL version: 2.1.3
% 11.21/2.89 % (3810179)Termination reason: Refutation not found, incomplete strategy
% 11.21/2.89 % (3810179)Time elapsed: 0.001 s
% 11.21/2.89 % (3810179)Peak memory usage: 88 MB
% 11.21/2.89 % (3810174)------------------------------
% 11.21/2.89 % (3810174)------------------------------
% 11.21/2.89 % (3810179)------------------------------
% 13.37/3.27 % (3810179)------------------------------
% 13.37/3.27 % (3810183)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2370906704:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 13.37/3.27 % (3810183)Refutation not found, incomplete strategy
% 13.37/3.27 % (3810183)------------------------------
% 13.37/3.27 % (3810183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.37/3.27 % (3810183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.37/3.27 % (3810183)CaDiCaL version: 2.1.3
% 13.37/3.27 % (3810183)Termination reason: Refutation not found, incomplete strategy
% 13.37/3.27 % (3810183)Time elapsed: 0.003 s
% 13.37/3.27 % (3810183)Peak memory usage: 88 MB
% 13.37/3.27 % (3810183)Instructions burned: 1 (million)
% 13.37/3.27 % (3810184)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=432372396:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 13.37/3.27 % (3810184)Refutation not found, incomplete strategy
% 13.37/3.27 % (3810184)------------------------------
% 13.37/3.27 % (3810184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.37/3.27 % (3810184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.37/3.27 % (3810184)CaDiCaL version: 2.1.3
% 13.37/3.27 % (3810184)Termination reason: Refutation not found, incomplete strategy
% 13.37/3.27 % (3810184)Time elapsed: 0.002 s
% 13.37/3.27 % (3810184)Peak memory usage: 88 MB
% 13.37/3.27 % (3810188)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1513932390:avsq=on:i=194:fgj=on:bd=preordered_2992 on theBenchmark for (2992ds/194Mi)
% 13.37/3.27 % (3810186)lrs+10_64_to=lpo:sil=8000:random_seed=2185329953:i=126:bd=preordered_2993 on theBenchmark for (2993ds/126Mi)
% 13.37/3.27 % (3810188)Instruction limit reached!
% 13.37/3.27 % (3810188)------------------------------
% 13.37/3.27 % (3810188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.37/3.27 % (3810188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.37/3.27 % (3810188)CaDiCaL version: 2.1.3
% 13.37/3.27 % (3810188)Termination reason: Instruction limit
% 13.37/3.27 % (3810188)Termination phase: Saturation
% 13.37/3.27 % (3810188)Time elapsed: 0.113 s
% 13.37/3.27 % (3810188)Peak memory usage: 91 MB
% 13.37/3.27 % (3810188)Instructions burned: 195 (million)
% 13.37/3.27 % (3810186)Instruction limit reached!
% 13.37/3.27 % (3810186)------------------------------
% 13.37/3.27 % (3810186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.37/3.27 % (3810186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.37/3.27 % (3810186)CaDiCaL version: 2.1.3
% 13.37/3.27 % (3810186)Termination reason: Instruction limit
% 13.37/3.27 % (3810186)Termination phase: Saturation
% 13.37/3.27 % (3810186)Time elapsed: 0.138 s
% 13.37/3.27 % (3810186)Peak memory usage: 89 MB
% 13.37/3.27 % (3810186)Instructions burned: 126 (million)
% 13.37/3.27 % (3810184)------------------------------
% 13.37/3.27 % (3810184)------------------------------
% 13.37/3.27 % (3810183)------------------------------
% 13.37/3.27 % (3810183)------------------------------
% 13.37/3.27 % (3810192)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3906965160:i=157:gtg=all_2989 on theBenchmark for (2989ds/157Mi)
% 13.37/3.27 % (3810169)First to succeed.
% 13.37/3.27 % (3810169)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3810163"
% 13.37/3.27 % (3810168)Also succeeded, but the first one will report.
% 13.37/3.27 % (3810192)Instruction limit reached!
% 13.37/3.27 % (3810192)------------------------------
% 13.37/3.27 % (3810192)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.37/3.27 % (3810192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.37/3.27 % (3810192)CaDiCaL version: 2.1.3
% 13.37/3.27 % (3810192)Termination reason: Instruction limit
% 13.37/3.27 % (3810192)Termination phase: Saturation
% 13.37/3.27 % (3810192)Time elapsed: 0.092 s
% 13.37/3.27 % (3810192)Peak memory usage: 91 MB
% 13.37/3.27 % (3810192)Instructions burned: 157 (million)
% 13.37/3.27 % (3810193)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2610350644:i=3394:sd=4:ss=included:sgt=64_2988 on theBenchmark for (2988ds/3394Mi)
% 13.37/3.27 % (3810194)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=287967257:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2988 on theBenchmark for (2988ds/106Mi)
% 13.37/3.27 % (3810195)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=373215799:i=107_2988 on theBenchmark for (2988ds/107Mi)
% 13.37/3.27 % (3810195)Refutation not found, incomplete strategy
% 13.37/3.27 % (3810195)------------------------------
% 13.37/3.27 % (3810195)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.37/3.27 % (3810195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.37/3.27 % (3810195)CaDiCaL version: 2.1.3
% 13.37/3.27 % (3810195)Termination reason: Refutation not found, incomplete strategy
% 13.37/3.27 % (3810195)Time elapsed: 0.002 s
% 13.37/3.27 % (3810195)Peak memory usage: 87 MB
% 13.37/3.27 % (3810170)Also succeeded, but the first one will report.
% 13.37/3.27 % (3810194)Instruction limit reached!
% 13.37/3.27 % (3810194)------------------------------
% 13.37/3.27 % (3810194)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.37/3.27 % (3810194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.37/3.27 % (3810194)CaDiCaL version: 2.1.3
% 13.37/3.27 % (3810194)Termination reason: Instruction limit
% 13.37/3.27 % (3810194)Termination phase: Saturation
% 13.37/3.27 % (3810194)Time elapsed: 0.112 s
% 13.37/3.27 % (3810194)Peak memory usage: 89 MB
% 13.37/3.27 % (3810194)Instructions burned: 106 (million)
% 13.37/3.27 % (3810198)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=1494658160:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2986 on theBenchmark for (2986ds/242Mi)
% 13.37/3.27 % (3810169)Refutation found. Thanks to Tanya!
% 13.37/3.27 % SZS status Unsatisfiable for theBenchmark
% 13.37/3.27 % SZS output start Proof for theBenchmark
% See solution above
% 13.37/3.27 % (3810169)------------------------------
% 13.37/3.27 % (3810169)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.37/3.27 % (3810169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.37/3.27 % (3810169)CaDiCaL version: 2.1.3
% 13.37/3.27 % (3810169)Termination reason: Refutation
% 13.37/3.27 % (3810169)Time elapsed: 1.038 s
% 13.37/3.27 % (3810169)Peak memory usage: 126 MB
% 13.37/3.27 % (3810169)Instructions burned: 945 (million)
% 13.37/3.27 % (3810169)------------------------------
% 13.37/3.27 % (3810169)------------------------------
% 13.37/3.27 % (3810163)Success in time 1.746 s
% 13.37/3.27 % Vampire exiting
%------------------------------------------------------------------------------