%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL042-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 09:37:41 AM UTC 2026
% Result : Unsatisfiable 8.75s 2.28s
% Output : Refutation 8.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 44 unt; 8 def)
% Number of atoms : 48 ( 42 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,axiom,
! [X0,X1] : apply(apply(w1,X0),X1) = apply(apply(X1,X0),X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),b)),b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f5,definition,
sF0 = apply(w1,w1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
apply(w1,w1) = sF0,
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
sF1 = apply(b,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
apply(b,sF0) = sF1,
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
sF2 = apply(b,w1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
apply(b,w1) = sF2,
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
sF3 = apply(sF1,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
apply(sF1,sF2) = sF3,
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
sF4 = apply(b,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
apply(b,sF3) = sF4,
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
sF5 = apply(sF4,b),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f16,plain,
apply(sF4,b) = sF5,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF6 = apply(b,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f18,plain,
apply(b,sF5) = sF6,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF7 = apply(sF6,b),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f20,plain,
apply(sF6,b) = sF7,
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
~ fixed_point(sF7),
inference(definition_folding,[],[f4,f20,f18,f16,f14,f12,f10,f8,f6]) ).
fof(f23,plain,
! [X0,X1] : apply(w1,apply(X0,X1)) = apply(apply(sF2,X0),X1),
inference(superposition,[],[f1,f10]) ).
fof(f25,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(f35,plain,
! [X0,X1] : apply(sF3,apply(X0,X1)) = apply(apply(sF4,X0),X1),
inference(superposition,[],[f1,f14]) ).
fof(f36,plain,
! [X0,X1] : apply(sF5,apply(X0,X1)) = apply(apply(sF6,X0),X1),
inference(superposition,[],[f1,f18]) ).
fof(f37,plain,
! [X0,X1] : apply(sF0,apply(X0,X1)) = apply(apply(sF1,X0),X1),
inference(superposition,[],[f1,f8]) ).
fof(f38,plain,
! [X0] : apply(sF0,apply(sF2,X0)) = apply(sF3,X0),
inference(superposition,[],[f37,f12]) ).
fof(f44,plain,
! [X0] : apply(sF5,apply(b,X0)) = apply(sF7,X0),
inference(superposition,[],[f36,f20]) ).
fof(f54,plain,
! [X0] : apply(sF3,apply(b,X0)) = apply(sF5,X0),
inference(superposition,[],[f35,f16]) ).
fof(f67,plain,
! [X0,X1] : apply(apply(w1,X1),apply(sF2,X0)) = apply(apply(w1,apply(X0,X1)),X1),
inference(superposition,[],[f2,f23]) ).
fof(f110,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,f25]) ).
fof(f147,plain,
! [X2,X0,X1] : apply(X2,apply(apply(w1,X0),X1)) = apply(apply(w1,X0),apply(apply(b,apply(b,X2)),X1)),
inference(superposition,[],[f110,f2]) ).
fof(f238,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,f147]) ).
fof(f248,plain,
! [X0,X1] : apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),w1) = apply(X0,apply(apply(w1,X1),apply(sF2,apply(b,apply(b,X0))))),
inference(forward_demodulation,[],[f238,f67]) ).
fof(f724,plain,
! [X0] : apply(apply(w1,apply(apply(b,apply(b,X0)),w1)),w1) = apply(X0,apply(sF0,apply(sF2,apply(b,apply(b,X0))))),
inference(superposition,[],[f248,f6]) ).
fof(f792,plain,
! [X0] : apply(apply(w1,apply(apply(b,apply(b,X0)),w1)),w1) = apply(X0,apply(sF3,apply(b,apply(b,X0)))),
inference(forward_demodulation,[],[f724,f38]) ).
fof(f795,plain,
! [X0] : apply(apply(w1,apply(apply(b,apply(b,X0)),w1)),w1) = apply(X0,apply(sF5,apply(b,X0))),
inference(forward_demodulation,[],[f792,f54]) ).
fof(f796,plain,
! [X0] : apply(apply(w1,apply(apply(b,apply(b,X0)),w1)),w1) = apply(X0,apply(sF7,X0)),
inference(forward_demodulation,[],[f795,f44]) ).
fof(f797,plain,
! [X0] : apply(apply(w1,w1),apply(sF2,apply(b,apply(b,X0)))) = apply(X0,apply(sF7,X0)),
inference(forward_demodulation,[],[f796,f67]) ).
fof(f798,plain,
! [X0] : apply(sF0,apply(sF2,apply(b,apply(b,X0)))) = apply(X0,apply(sF7,X0)),
inference(forward_demodulation,[],[f797,f6]) ).
fof(f799,plain,
! [X0] : apply(sF3,apply(b,apply(b,X0))) = apply(X0,apply(sF7,X0)),
inference(forward_demodulation,[],[f798,f38]) ).
fof(f800,plain,
! [X0] : apply(sF5,apply(b,X0)) = apply(X0,apply(sF7,X0)),
inference(forward_demodulation,[],[f799,f54]) ).
fof(f801,plain,
! [X0] : apply(sF7,X0) = apply(X0,apply(sF7,X0)),
inference(forward_demodulation,[],[f800,f44]) ).
fof(f842,plain,
( apply(sF7,fixed_pt) != apply(sF7,fixed_pt)
| fixed_point(sF7) ),
inference(superposition,[],[f3,f801]) ).
fof(f849,plain,
fixed_point(sF7),
inference(trivial_inequality_removal,[],[f842]) ).
fof(f859,plain,
$false,
inference(forward_subsumption_resolution,[],[f849,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n004.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Mon Sep 28 21:30:22 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running first-order theorem proving
% 0.24/0.29 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
% 6.94/2.04 % (808539)Input is clausal, will run a generic CNF schedule.
% 6.94/2.04 % (808554)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=903399130:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.94/2.04 % (808560)dis-21_1_sil=8000:lcm=predicate:random_seed=2246529284: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)
% 6.94/2.04 % (808560)Refutation not found, incomplete strategy
% 6.94/2.04 % (808560)------------------------------
% 6.94/2.04 % (808560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/2.04 % (808560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/2.04 % (808560)CaDiCaL version: 2.1.3
% 6.94/2.04 % (808560)Termination reason: Refutation not found, incomplete strategy
% 6.94/2.04 % (808560)Time elapsed: 0.002 s
% 6.94/2.04 % (808560)Peak memory usage: 88 MB
% 6.94/2.04 % (808558)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=257694698:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.94/2.04 % (808556)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1208182022:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.94/2.04 % (808555)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2989027884:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.94/2.04 % (808557)lrs+10_1_sil=8000:sp=occurrence:random_seed=2828529842:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.94/2.04 % (808559)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=24073107:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.94/2.04 % (808558)Instruction limit reached!
% 6.94/2.04 % (808558)------------------------------
% 6.94/2.04 % (808558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/2.04 % (808557)Instruction limit reached!
% 6.94/2.04 % (808557)------------------------------
% 6.94/2.04 % (808557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/2.04 % (808558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/2.04 % (808557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/2.04 % (808558)CaDiCaL version: 2.1.3
% 6.94/2.04 % (808557)CaDiCaL version: 2.1.3
% 6.94/2.04 % (808557)Termination reason: Instruction limit
% 6.94/2.04 % (808557)Termination phase: Saturation
% 6.94/2.04 % (808558)Termination reason: Instruction limit
% 6.94/2.04 % (808558)Termination phase: Saturation
% 6.94/2.04 % (808557)Time elapsed: 0.114 s
% 6.94/2.04 % (808558)Time elapsed: 0.114 s
% 6.94/2.04 % (808557)Peak memory usage: 89 MB
% 6.94/2.04 % (808558)Peak memory usage: 88 MB
% 6.94/2.04 % (808557)Instructions burned: 107 (million)
% 6.94/2.04 % (808558)Instructions burned: 115 (million)
% 6.94/2.04 % (808559)Instruction limit reached!
% 6.94/2.04 % (808559)------------------------------
% 6.94/2.04 % (808559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/2.04 % (808559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/2.04 % (808559)CaDiCaL version: 2.1.3
% 6.94/2.04 % (808559)Termination reason: Instruction limit
% 6.94/2.04 % (808559)Termination phase: Saturation
% 6.94/2.04 % (808559)Time elapsed: 0.162 s
% 6.94/2.04 % (808559)Peak memory usage: 89 MB
% 6.94/2.04 % (808559)Instructions burned: 180 (million)
% 6.94/2.04 % (808571)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=1248092032:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 6.94/2.04 % (808571)Refutation not found, incomplete strategy
% 6.94/2.04 % (808571)------------------------------
% 6.94/2.04 % (808571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.94/2.04 % (808571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.94/2.04 % (808571)CaDiCaL version: 2.1.3
% 6.94/2.04 % (808571)Termination reason: Refutation not found, incomplete strategy
% 6.94/2.04 % (808571)Time elapsed: 0.002 s
% 6.94/2.04 % (808571)Peak memory usage: 88 MB
% 6.94/2.04 % (808572)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1843808440: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)
% 8.75/2.28 % (808572)Refutation not found, incomplete strategy
% 8.75/2.28 % (808572)------------------------------
% 8.75/2.28 % (808572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.28 % (808572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.28 % (808572)CaDiCaL version: 2.1.3
% 8.75/2.28 % (808572)Termination reason: Refutation not found, incomplete strategy
% 8.75/2.28 % (808572)Time elapsed: 0.002 s
% 8.75/2.28 % (808572)Peak memory usage: 88 MB
% 8.75/2.28 % (808572)Instructions burned: 1 (million)
% 8.75/2.28 % (808560)------------------------------
% 8.75/2.28 % (808560)------------------------------
% 8.75/2.28 % (808574)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2257578762:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 8.75/2.28 % (808574)Refutation not found, incomplete strategy
% 8.75/2.28 % (808574)------------------------------
% 8.75/2.28 % (808574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.28 % (808574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.28 % (808574)CaDiCaL version: 2.1.3
% 8.75/2.28 % (808574)Termination reason: Refutation not found, incomplete strategy
% 8.75/2.28 % (808574)Time elapsed: 0.002 s
% 8.75/2.28 % (808574)Peak memory usage: 88 MB
% 8.75/2.28 % (808577)lrs+10_64_to=lpo:sil=8000:random_seed=4249046457:i=126:bd=preordered_2994 on theBenchmark for (2994ds/126Mi)
% 8.75/2.28 % (808554)First to succeed.
% 8.75/2.28 % (808554)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-808539"
% 8.75/2.28 % (808571)------------------------------
% 8.75/2.28 % (808571)------------------------------
% 8.75/2.28 % (808577)Instruction limit reached!
% 8.75/2.28 % (808577)------------------------------
% 8.75/2.28 % (808577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.28 % (808577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.28 % (808577)CaDiCaL version: 2.1.3
% 8.75/2.28 % (808577)Termination reason: Instruction limit
% 8.75/2.28 % (808577)Termination phase: Saturation
% 8.75/2.28 % (808577)Time elapsed: 0.131 s
% 8.75/2.28 % (808577)Peak memory usage: 89 MB
% 8.75/2.28 % (808577)Instructions burned: 126 (million)
% 8.75/2.28 % (808572)------------------------------
% 8.75/2.28 % (808572)------------------------------
% 8.75/2.28 % (808574)------------------------------
% 8.75/2.28 % (808574)------------------------------
% 8.75/2.28 % (808554)Refutation found. Thanks to Tanya!
% 8.75/2.28 % SZS status Unsatisfiable for theBenchmark
% 8.75/2.28 % SZS output start Proof for theBenchmark
% See solution above
% 8.75/2.28 % (808554)------------------------------
% 8.75/2.28 % (808554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.28 % (808554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.28 % (808554)CaDiCaL version: 2.1.3
% 8.75/2.28 % (808554)Termination reason: Refutation
% 8.75/2.28 % (808554)Time elapsed: 0.718 s
% 8.75/2.28 % (808554)Peak memory usage: 131 MB
% 8.75/2.28 % (808554)Instructions burned: 1150 (million)
% 8.75/2.28 % (808554)------------------------------
% 8.75/2.28 % (808554)------------------------------
% 8.75/2.28 % (808539)Success in time 1.112 s
% 8.75/2.28 % Vampire exiting
%------------------------------------------------------------------------------