%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET754+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:41:50 PM UTC 2026
% Result : Theorem 0.59s 0.82s
% Output : Refutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 8 unt; 0 def)
% Number of atoms : 177 ( 6 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 204 ( 71 ~; 65 |; 49 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 140 ( 119 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X2)
& member(X6,X2) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X6) )
=> X5 = X6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
fof(f22,axiom,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X0,X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image2) ).
fof(f24,axiom,
! [X0,X1,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X0,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_image2) ).
fof(f29,conjecture,
! [X0,X1,X2,X3] :
( ( maps(X0,X1,X2)
& subset(X3,X1) )
=> subset(X3,inverse_image2(X0,image2(X0,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa04) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( maps(X0,X1,X2)
& subset(X3,X1) )
=> subset(X3,inverse_image2(X0,image2(X0,X3))) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f32,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X3] :
( member(X3,X1)
=> ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X2)
& member(X7,X2) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X5,X7) )
=> X6 = X7 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ? [X4] :
( member(X4,X2)
& apply(X0,X3,X4) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f41,plain,
? [X0,X1,X2,X3] :
( ~ subset(X3,inverse_image2(X0,image2(X0,X3)))
& maps(X0,X1,X2)
& subset(X3,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f42,plain,
? [X0,X1,X2,X3] :
( ~ subset(X3,inverse_image2(X0,image2(X0,X3)))
& maps(X0,X1,X2)
& subset(X3,X1) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f44,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f44]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(sK3(X0,X2,X3),X2)
& apply(X0,X3,sK3(X0,X2,X3)) )
| ~ member(X3,X1) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X0,X5,X6)
| ~ apply(X0,X5,X7)
| ~ member(X5,X1)
| ~ member(X6,X2)
| ~ member(X7,X2) ) )
| ~ maps(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X2,X3))],[f36]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& apply(X0,X3,X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ( member(sK5(X0,X1,X2),X1)
& apply(X0,sK5(X0,X1,X2),X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X1,X2))],[f68]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ? [X3] :
( member(X3,X1)
& apply(X0,X2,X3) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ? [X4] :
( member(X4,X1)
& apply(X0,X2,X4) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X2,X3) ) )
& ( ( member(sK7(X0,X1,X2),X1)
& apply(X0,X2,sK7(X0,X1,X2)) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X4,sK7(X0,X1,X2))],[f75]) ).
fof(f81,plain,
( ~ subset(sK12,inverse_image2(sK9,image2(sK9,sK12)))
& maps(sK9,sK10,sK11)
& subset(sK12,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f42]) ).
fof(f82,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f83,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f84,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f126,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f131,plain,
subset(sK12,sK10),
inference(cnf_transformation,[],[f81]) ).
fof(f132,plain,
maps(sK9,sK10,sK11),
inference(cnf_transformation,[],[f81]) ).
fof(f133,plain,
~ subset(sK12,inverse_image2(sK9,image2(sK9,sK12))),
inference(cnf_transformation,[],[f81]) ).
fof(f138,plain,
member(sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),sK12),
inference(resolution,[],[f83,f133]) ).
fof(f140,plain,
! [X0] :
( member(X0,sK10)
| ~ member(X0,sK12) ),
inference(resolution,[],[f82,f131]) ).
fof(f146,plain,
! [X0] :
( ~ member(X0,sK10)
| apply(sK9,X0,sK3(sK9,sK11,X0)) ),
inference(resolution,[],[f109,f132]) ).
fof(f147,plain,
! [X0] :
( ~ member(X0,sK12)
| apply(sK9,X0,sK3(sK9,sK11,X0)) ),
inference(resolution,[],[f146,f140]) ).
fof(f150,plain,
apply(sK9,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),sK3(sK9,sK11,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))))),
inference(resolution,[],[f147,f138]) ).
fof(f153,plain,
! [X0] :
( member(sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),inverse_image2(sK9,X0))
| ~ member(sK3(sK9,sK11,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12)))),X0) ),
inference(resolution,[],[f150,f126]) ).
fof(f154,plain,
! [X0] :
( member(sK3(sK9,sK11,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12)))),image2(sK9,X0))
| ~ member(sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),X0) ),
inference(resolution,[],[f150,f119]) ).
fof(f155,plain,
( ~ member(sK3(sK9,sK11,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12)))),image2(sK9,sK12))
| subset(sK12,inverse_image2(sK9,image2(sK9,sK12))) ),
inference(resolution,[],[f153,f84]) ).
fof(f158,plain,
~ member(sK3(sK9,sK11,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12)))),image2(sK9,sK12)),
inference(forward_subsumption_resolution,[],[f155,f133]) ).
fof(f159,plain,
~ member(sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),sK12),
inference(resolution,[],[f154,f158]) ).
fof(f162,plain,
$false,
inference(forward_subsumption_resolution,[],[f159,f138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET754+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 28 02:43:19 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 0.59/0.82 % (2960824)Detected formulas, will run a generic FOF schedule.
% 0.59/0.82 % (2960829)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=342869496:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.59/0.82 % (2960830)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=3689242901:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.59/0.82 % (2960831)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=3037699000:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.59/0.82 % (2960835)dis-21_1_sil=8000:lcm=predicate:random_seed=2367539821: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)
% 0.59/0.82 % (2960833)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4015947967:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.59/0.82 % (2960834)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3620605476:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.59/0.82 % (2960832)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2124960868:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.59/0.82 % (2960832)Refutation not found, incomplete strategy
% 0.59/0.82 % (2960832)------------------------------
% 0.59/0.82 % (2960832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.82 % (2960834)First to succeed.
% 0.59/0.82 % (2960832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.82 % (2960832)CaDiCaL version: 2.1.3
% 0.59/0.82 % (2960832)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.82 % (2960832)Time elapsed: 0.002 s
% 0.59/0.82 % (2960832)Peak memory usage: 88 MB
% 0.59/0.82 % (2960832)Instructions burned: 4 (million)
% 0.59/0.82 % (2960834)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2960824"
% 0.59/0.82 % (2960833)Instruction limit reached!
% 0.59/0.82 % (2960833)------------------------------
% 0.59/0.82 % (2960833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.82 % (2960833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.82 % (2960833)CaDiCaL version: 2.1.3
% 0.59/0.82 % (2960833)Termination reason: Instruction limit
% 0.59/0.82 % (2960833)Termination phase: Saturation
% 0.59/0.82 % (2960833)Time elapsed: 0.025 s
% 0.59/0.82 % (2960833)Peak memory usage: 87 MB
% 0.59/0.82 % (2960833)Instructions burned: 121 (million)
% 0.59/0.82 % (2960835)Instruction limit reached!
% 0.59/0.82 % (2960835)------------------------------
% 0.59/0.82 % (2960835)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.59/0.82 % (2960835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.82 % (2960835)CaDiCaL version: 2.1.3
% 0.59/0.82 % (2960835)Termination reason: Instruction limit
% 0.59/0.82 % (2960835)Termination phase: Saturation
% 0.59/0.82 % (2960835)Time elapsed: 0.043 s
% 0.59/0.82 % (2960835)Peak memory usage: 89 MB
% 0.59/0.82 % (2960835)Instructions burned: 130 (million)
% 0.59/0.82 % (2960843)lrs+10_1_sil=8000:sp=occurrence:random_seed=910558572:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.59/0.82 % (2960832)------------------------------
% 0.59/0.82 % (2960832)------------------------------
% 0.59/0.82 % (2960834)Refutation found. Thanks to Tanya!
% 0.59/0.82 % SZS status Theorem for theBenchmark
% 0.59/0.82 % SZS output start Proof for theBenchmark
% See solution above
% 2.32/0.92 % (2960834)------------------------------
% 2.32/0.92 % (2960834)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.92 % (2960834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.92 % (2960834)CaDiCaL version: 2.1.3
% 2.32/0.92 % (2960834)Termination reason: Refutation
% 2.32/0.92 % (2960834)Time elapsed: 0.003 s
% 2.32/0.92 % (2960834)Peak memory usage: 88 MB
% 2.32/0.92 % (2960834)Instructions burned: 6 (million)
% 2.32/0.92 % (2960834)------------------------------
% 2.32/0.92 % (2960834)------------------------------
% 2.32/0.92 % (2960824)Success in time 0.292 s
% 2.32/0.92 % Vampire exiting
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