%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL080-2 : 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 : n020.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 09:37:53 AM UTC 2026
% Result : Unsatisfiable 8.14s 1.92s
% Output : Refutation 8.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 9 unt; 0 def)
% Number of atoms : 11 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 4 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstraction) ).
fof(f3,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
fof(f5,negated_conjecture,
k(b) != apply(abstraction,apply(abstraction,k(b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_TRC2b) ).
fof(f8,plain,
apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))) != apply(k(b),n(apply(abstraction,apply(abstraction,k(b))),k(b))),
inference(unit_resulting_resolution,[],[f3,f5]) ).
fof(f11,plain,
b != apply(apply(abstraction,apply(abstraction,k(b))),n(apply(abstraction,apply(abstraction,k(b))),k(b))),
inference(forward_demodulation,[],[f8,f1]) ).
fof(f16,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f31,plain,
! [X2,X0,X1] : apply(X0,apply(k(X1),apply(X2,X1))) = apply(apply(apply(abstraction,apply(abstraction,k(X0))),X2),X1),
inference(superposition,[],[f2,f16]) ).
fof(f37,plain,
! [X2,X0,X1] : apply(X0,X1) = apply(apply(apply(abstraction,apply(abstraction,k(X0))),X2),X1),
inference(forward_demodulation,[],[f31,f1]) ).
fof(f45,plain,
$false,
inference(unit_resulting_resolution,[],[f3,f11,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL080-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:35:34 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 8.14/1.92 % (595235)Input is clausal, will run a generic CNF schedule.
% 8.14/1.92 % (595246)dis-21_1_sil=8000:lcm=predicate:random_seed=3147112961: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)
% 8.14/1.92 % (595246)Refutation not found, incomplete strategy
% 8.14/1.92 % (595246)------------------------------
% 8.14/1.92 % (595246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595246)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595246)Termination reason: Refutation not found, incomplete strategy
% 8.14/1.92 % (595246)Time elapsed: 0.001 s
% 8.14/1.92 % (595246)Peak memory usage: 88 MB
% 8.14/1.92 % (595245)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3628651265:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 8.14/1.92 % (595241)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2152241052:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 8.14/1.92 % (595243)lrs+10_1_sil=8000:sp=occurrence:random_seed=1558262289:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 8.14/1.92 % (595244)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3731165361:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 8.14/1.92 % (595240)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=3120811028:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 8.14/1.92 % (595242)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=943859476:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 8.14/1.92 % (595243)Instruction limit reached!
% 8.14/1.92 % (595243)------------------------------
% 8.14/1.92 % (595243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595243)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595243)Termination reason: Instruction limit
% 8.14/1.92 % (595243)Termination phase: Saturation
% 8.14/1.92 % (595243)Time elapsed: 0.067 s
% 8.14/1.92 % (595243)Peak memory usage: 89 MB
% 8.14/1.92 % (595243)Instructions burned: 107 (million)
% 8.14/1.92 % (595244)Instruction limit reached!
% 8.14/1.92 % (595244)------------------------------
% 8.14/1.92 % (595244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595244)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595244)Termination reason: Instruction limit
% 8.14/1.92 % (595244)Termination phase: Saturation
% 8.14/1.92 % (595244)Time elapsed: 0.072 s
% 8.14/1.92 % (595244)Peak memory usage: 88 MB
% 8.14/1.92 % (595244)Instructions burned: 115 (million)
% 8.14/1.92 % (595246)------------------------------
% 8.14/1.92 % (595246)------------------------------
% 8.14/1.92 % (595245)Instruction limit reached!
% 8.14/1.92 % (595245)------------------------------
% 8.14/1.92 % (595245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595245)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595245)Termination reason: Instruction limit
% 8.14/1.92 % (595245)Termination phase: Saturation
% 8.14/1.92 % (595245)Time elapsed: 0.102 s
% 8.14/1.92 % (595245)Peak memory usage: 90 MB
% 8.14/1.92 % (595245)Instructions burned: 181 (million)
% 8.14/1.92 % (595256)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=360476696:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 8.14/1.92 % (595256)Refutation not found, incomplete strategy
% 8.14/1.92 % (595256)------------------------------
% 8.14/1.92 % (595256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595256)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595256)Termination reason: Refutation not found, incomplete strategy
% 8.14/1.92 % (595256)Time elapsed: 0.001 s
% 8.14/1.92 % (595256)Peak memory usage: 87 MB
% 8.14/1.92 % (595254)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=2768521120:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 8.14/1.92 % (595255)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1502110166:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 8.14/1.92 % (595254)Refutation not found, incomplete strategy
% 8.14/1.92 % (595254)------------------------------
% 8.14/1.92 % (595254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595254)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595254)Termination reason: Refutation not found, incomplete strategy
% 8.14/1.92 % (595254)Time elapsed: 0.001 s
% 8.14/1.92 % (595254)Peak memory usage: 87 MB
% 8.14/1.92 % (595257)lrs+10_64_to=lpo:sil=8000:random_seed=2640206016:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 8.14/1.92 % (595255)Instruction limit reached!
% 8.14/1.92 % (595255)------------------------------
% 8.14/1.92 % (595255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595255)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595255)Termination reason: Instruction limit
% 8.14/1.92 % (595255)Termination phase: Saturation
% 8.14/1.92 % (595255)Time elapsed: 0.087 s
% 8.14/1.92 % (595255)Peak memory usage: 93 MB
% 8.14/1.92 % (595255)Instructions burned: 190 (million)
% 8.14/1.92 % (595257)Instruction limit reached!
% 8.14/1.92 % (595257)------------------------------
% 8.14/1.92 % (595257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595257)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595257)Termination reason: Instruction limit
% 8.14/1.92 % (595257)Termination phase: Saturation
% 8.14/1.92 % (595257)Time elapsed: 0.078 s
% 8.14/1.92 % (595257)Peak memory usage: 89 MB
% 8.14/1.92 % (595257)Instructions burned: 128 (million)
% 8.14/1.92 % (595256)------------------------------
% 8.14/1.92 % (595256)------------------------------
% 8.14/1.92 % (595254)------------------------------
% 8.14/1.92 % (595254)------------------------------
% 8.14/1.92 % (595262)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1985908432:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 8.14/1.92 % (595264)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=4024298829:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 8.14/1.92 % (595263)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3194275124:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 8.14/1.92 % (595263)Instruction limit reached!
% 8.14/1.92 % (595263)------------------------------
% 8.14/1.92 % (595263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595263)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595263)Termination reason: Instruction limit
% 8.14/1.92 % (595263)Termination phase: Saturation
% 8.14/1.92 % (595263)Time elapsed: 0.097 s
% 8.14/1.92 % (595263)Peak memory usage: 90 MB
% 8.14/1.92 % (595263)Instructions burned: 157 (million)
% 8.14/1.92 % (595262)Instruction limit reached!
% 8.14/1.92 % (595262)------------------------------
% 8.14/1.92 % (595262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595262)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595262)Termination reason: Instruction limit
% 8.14/1.92 % (595262)Termination phase: Saturation
% 8.14/1.92 % (595262)Time elapsed: 0.123 s
% 8.14/1.92 % (595262)Peak memory usage: 91 MB
% 8.14/1.92 % (595262)Instructions burned: 195 (million)
% 8.14/1.92 % (595241)First to succeed.
% 8.14/1.92 % (595240)Also succeeded, but the first one will report.
% 8.14/1.92 % (595241)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-595235"
% 8.14/1.92 % (595242)Also succeeded, but the first one will report.
% 8.14/1.92 % (595266)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=1642861617:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 8.14/1.92 % (595266)Instruction limit reached!
% 8.14/1.92 % (595266)------------------------------
% 8.14/1.92 % (595266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595266)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595266)Termination reason: Instruction limit
% 8.14/1.92 % (595266)Termination phase: Saturation
% 8.14/1.92 % (595266)Time elapsed: 0.051 s
% 8.14/1.92 % (595266)Peak memory usage: 89 MB
% 8.14/1.92 % (595266)Instructions burned: 106 (million)
% 8.14/1.92 % (595269)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=2543134688:i=107_2992 on theBenchmark for (2992ds/107Mi)
% 8.14/1.92 % (595269)Refutation not found, incomplete strategy
% 8.14/1.92 % (595269)------------------------------
% 8.14/1.92 % (595269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595269)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595269)Termination reason: Refutation not found, incomplete strategy
% 8.14/1.92 % (595269)Time elapsed: 0.001 s
% 8.14/1.92 % (595269)Peak memory usage: 87 MB
% 8.14/1.92 % (595270)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3107038660:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 8.14/1.92 % (595272)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=1403585663:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 8.14/1.92 % (595264)Also succeeded, but the first one will report.
% 8.14/1.92 % (595241)Refutation found. Thanks to Tanya!
% 8.14/1.92 % SZS status Unsatisfiable for theBenchmark
% 8.14/1.92 % SZS output start Proof for theBenchmark
% See solution above
% 8.14/1.92 % (595241)------------------------------
% 8.14/1.92 % (595241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.14/1.92 % (595241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.14/1.92 % (595241)CaDiCaL version: 2.1.3
% 8.14/1.92 % (595241)Termination reason: Refutation
% 8.14/1.92 % (595241)Time elapsed: 0.619 s
% 8.14/1.92 % (595241)Peak memory usage: 125 MB
% 8.14/1.92 % (595241)Instructions burned: 919 (million)
% 8.14/1.92 % (595241)------------------------------
% 8.14/1.92 % (595241)------------------------------
% 8.14/1.92 % (595235)Success in time 1.06 s
% 8.14/1.92 % Vampire exiting
%------------------------------------------------------------------------------