%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PLA013-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:27:42 PM UTC 2026
% Result : Unsatisfiable 4.32s 1.92s
% Output : Refutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 23
% Syntax : Number of formulae : 64 ( 18 unt; 3 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 195 ( 104 ~; 88 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( holds(and(X0,X1),X2)
| ~ holds(X0,X2)
| ~ holds(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition) ).
fof(f2,axiom,
! [X0,X1] :
( ~ differ(X0,table)
| ~ holds(empty,X1)
| ~ holds(clear(X0),X1)
| holds(holding(X0),do(pickup(X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pickup_1) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ differ(X0,X2)
| ~ holds(on(X0,X1),X3)
| holds(on(X0,X1),do(pickup(X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pickup_3) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ differ(X0,X1)
| ~ holds(clear(X0),X2)
| holds(clear(X0),do(pickup(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pickup_4) ).
fof(f6,axiom,
! [X2,X0,X1] :
( holds(empty,do(putdown(X0,X1),X2))
| ~ holds(holding(X0),X2)
| ~ holds(clear(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',putdown_1) ).
fof(f7,axiom,
! [X2,X0,X1] :
( holds(on(X0,X1),do(putdown(X0,X1),X2))
| ~ holds(holding(X0),X2)
| ~ holds(clear(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',putdown_2) ).
fof(f8,axiom,
! [X2,X0,X1] :
( holds(clear(X0),do(putdown(X0,X1),X2))
| ~ holds(holding(X0),X2)
| ~ holds(clear(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',putdown_3) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( holds(on(X0,X1),do(putdown(X2,X3),X4))
| ~ holds(on(X0,X1),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',putdown_4) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( ~ differ(X0,X2)
| ~ holds(clear(X0),X3)
| holds(clear(X0),do(putdown(X1,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',putdown_5) ).
fof(f11,axiom,
! [X0,X1] :
( differ(X0,X1)
| ~ differ(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_differ) ).
fof(f12,axiom,
differ(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',differ_a_b) ).
fof(f13,axiom,
differ(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',differ_a_c) ).
fof(f15,axiom,
differ(a,table),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',differ_a_table) ).
fof(f16,axiom,
differ(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',differ_b_c) ).
fof(f20,axiom,
differ(c,table),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',differ_c_table) ).
fof(f26,axiom,
holds(clear(a),s0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_state5) ).
fof(f27,axiom,
holds(clear(b),s0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_state6) ).
fof(f28,axiom,
holds(clear(c),s0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_state7) ).
fof(f29,axiom,
holds(empty,s0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_state8) ).
fof(f31,negated_conjecture,
! [X0] : ~ holds(and(on(a,c),on(c,b)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ACB) ).
fof(f32,plain,
! [X0] :
( ~ holds(on(a,c),X0)
| ~ holds(on(c,b),X0) ),
inference(resolution,[],[f1,f31]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ differ(X2,X0)
| holds(clear(X0),do(pickup(X2),X1))
| ~ holds(clear(X0),X1) ),
inference(resolution,[],[f5,f11]) ).
fof(f36,plain,
! [X0] :
( holds(clear(a),do(pickup(c),X0))
| ~ holds(clear(a),X0) ),
inference(resolution,[],[f5,f13]) ).
fof(f38,plain,
! [X0] :
( holds(clear(b),do(pickup(c),X0))
| ~ holds(clear(b),X0) ),
inference(resolution,[],[f5,f16]) ).
fof(f48,plain,
! [X0,X1] :
( holds(clear(a),do(putdown(X1,b),X0))
| ~ holds(clear(a),X0) ),
inference(resolution,[],[f10,f12]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( ~ differ(X3,X0)
| holds(on(X0,X1),do(pickup(X3),X2))
| ~ holds(on(X0,X1),X2) ),
inference(resolution,[],[f4,f11]) ).
fof(f69,plain,
! [X0] :
( holds(holding(a),do(pickup(a),X0))
| ~ holds(clear(a),X0)
| ~ holds(empty,X0) ),
inference(resolution,[],[f2,f15]) ).
fof(f71,plain,
! [X0] :
( holds(holding(c),do(pickup(c),X0))
| ~ holds(clear(c),X0)
| ~ holds(empty,X0) ),
inference(resolution,[],[f2,f20]) ).
fof(f74,plain,
! [X0] :
( ~ holds(on(c,b),do(putdown(a,c),X0))
| ~ holds(clear(c),X0)
| ~ holds(holding(a),X0) ),
inference(resolution,[],[f7,f32]) ).
fof(f77,plain,
! [X0] :
( ~ holds(on(c,b),X0)
| ~ holds(holding(a),X0)
| ~ holds(clear(c),X0) ),
inference(resolution,[],[f74,f9]) ).
fof(f95,plain,
! [X0] :
( holds(clear(c),do(pickup(a),X0))
| ~ holds(clear(c),X0) ),
inference(resolution,[],[f33,f13]) ).
fof(f129,plain,
! [X0,X1] :
( holds(on(c,X0),do(pickup(a),X1))
| ~ holds(on(c,X0),X1) ),
inference(resolution,[],[f57,f13]) ).
fof(f162,plain,
! [X0] :
( ~ holds(holding(a),do(pickup(a),X0))
| ~ holds(on(c,b),X0)
| ~ holds(clear(c),do(pickup(a),X0)) ),
inference(resolution,[],[f129,f77]) ).
fof(f163,plain,
! [X0] :
( ~ holds(clear(c),do(pickup(a),X0))
| ~ holds(on(c,b),X0)
| ~ holds(clear(a),X0)
| ~ holds(empty,X0) ),
inference(resolution,[],[f162,f69]) ).
fof(f164,plain,
! [X0] :
( ~ holds(on(c,b),X0)
| ~ holds(clear(a),X0)
| ~ holds(empty,X0)
| ~ holds(clear(c),X0) ),
inference(resolution,[],[f163,f95]) ).
fof(f170,plain,
! [X0] :
( ~ holds(clear(a),do(putdown(c,b),X0))
| ~ holds(empty,do(putdown(c,b),X0))
| ~ holds(clear(c),do(putdown(c,b),X0))
| ~ holds(holding(c),X0)
| ~ holds(clear(b),X0) ),
inference(resolution,[],[f164,f7]) ).
fof(f204,plain,
! [X0] :
( ~ holds(clear(c),do(putdown(c,b),X0))
| ~ holds(empty,do(putdown(c,b),X0))
| ~ holds(holding(c),X0)
| ~ holds(clear(b),X0)
| ~ holds(clear(a),X0) ),
inference(resolution,[],[f170,f48]) ).
fof(f224,plain,
! [X0] :
( ~ holds(empty,do(putdown(c,b),X0))
| ~ holds(holding(c),X0)
| ~ holds(clear(b),X0)
| ~ holds(clear(a),X0)
| ~ holds(holding(c),X0)
| ~ holds(clear(b),X0) ),
inference(resolution,[],[f204,f8]) ).
fof(f226,plain,
! [X0] :
( ~ holds(empty,do(putdown(c,b),X0))
| ~ holds(holding(c),X0)
| ~ holds(clear(b),X0)
| ~ holds(clear(a),X0) ),
inference(duplicate_literal_removal,[],[f224]) ).
fof(f227,plain,
! [X0] :
( ~ holds(holding(c),X0)
| ~ holds(clear(b),X0)
| ~ holds(clear(a),X0)
| ~ holds(holding(c),X0)
| ~ holds(clear(b),X0) ),
inference(resolution,[],[f226,f6]) ).
fof(f228,plain,
! [X0] :
( ~ holds(holding(c),X0)
| ~ holds(clear(b),X0)
| ~ holds(clear(a),X0) ),
inference(duplicate_literal_removal,[],[f227]) ).
fof(f233,plain,
! [X0] :
( ~ holds(clear(b),do(pickup(c),X0))
| ~ holds(clear(a),do(pickup(c),X0))
| ~ holds(clear(c),X0)
| ~ holds(empty,X0) ),
inference(resolution,[],[f228,f71]) ).
fof(f265,plain,
! [X0] :
( ~ holds(clear(a),do(pickup(c),X0))
| ~ holds(clear(c),X0)
| ~ holds(empty,X0)
| ~ holds(clear(b),X0) ),
inference(resolution,[],[f233,f38]) ).
fof(f271,plain,
! [X0] :
( ~ holds(clear(b),X0)
| ~ holds(empty,X0)
| ~ holds(clear(c),X0)
| ~ holds(clear(a),X0) ),
inference(resolution,[],[f265,f36]) ).
fof(f287,plain,
( ~ holds(empty,s0)
| ~ holds(clear(c),s0)
| ~ holds(clear(a),s0) ),
inference(resolution,[],[f271,f27]) ).
fof(f289,definition,
( spl0_1
<=> holds(clear(a),s0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f290,plain,
( ~ holds(clear(a),s0)
| spl0_1 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f292,definition,
( spl0_2
<=> holds(clear(c),s0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f293,plain,
( ~ holds(clear(c),s0)
| spl0_2 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f295,definition,
( spl0_3
<=> holds(empty,s0) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f296,plain,
( ~ holds(empty,s0)
| spl0_3 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f297,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f287,f295,f292,f289]) ).
fof(f298,plain,
( $false
| spl0_1 ),
inference(resolution,[],[f290,f26]) ).
fof(f299,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f298]) ).
fof(f300,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f293,f28]) ).
fof(f301,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f300]) ).
fof(f302,plain,
( $false
| spl0_3 ),
inference(resolution,[],[f296,f29]) ).
fof(f303,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f302]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f297]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f299]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f301]) ).
cnf(s4,plain,
spl0_3,
inference(sat_conversion,[],[f303]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3,s2]) ).
fof(f304,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : PLA013-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.47 % Computer : n006.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Sun Sep 27 22:09:10 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.47 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 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
% 4.32/1.92 % (3372418)Input is clausal, will run a generic CNF schedule.
% 4.32/1.92 % (3372429)dis-21_1_sil=8000:lcm=predicate:random_seed=3243672024: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)
% 4.32/1.92 % (3372429)First to succeed.
% 4.32/1.92 % (3372429)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3372418"
% 4.32/1.92 % (3372426)lrs+10_1_sil=8000:sp=occurrence:random_seed=3954824597:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.32/1.92 % (3372425)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3426292342:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.32/1.92 % (3372424)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1984098445:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.32/1.92 % (3372423)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=3148022858:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.32/1.92 % (3372427)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1540516982:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.32/1.92 % (3372427)Refutation not found, incomplete strategy
% 4.32/1.92 % (3372427)------------------------------
% 4.32/1.92 % (3372427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.92 % (3372427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.92 % (3372427)CaDiCaL version: 2.1.3
% 4.32/1.92 % (3372427)Termination reason: Refutation not found, incomplete strategy
% 4.32/1.92 % (3372427)Time elapsed: 0.002 s
% 4.32/1.92 % (3372427)Peak memory usage: 87 MB
% 4.32/1.92 % (3372426)Refutation not found, incomplete strategy
% 4.32/1.92 % (3372426)------------------------------
% 4.32/1.92 % (3372426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.92 % (3372426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.92 % (3372426)CaDiCaL version: 2.1.3
% 4.32/1.92 % (3372426)Termination reason: Refutation not found, incomplete strategy
% 4.32/1.92 % (3372426)Time elapsed: 0.002 s
% 4.32/1.92 % (3372426)Peak memory usage: 87 MB
% 4.32/1.92 % (3372426)Instructions burned: 1 (million)
% 4.32/1.92 % (3372428)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3364523943:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.32/1.92 % (3372428)Also succeeded, but the first one will report.
% 4.32/1.92 % (3372429)Refutation found. Thanks to Tanya!
% 4.32/1.92 % SZS status Unsatisfiable for theBenchmark
% 4.32/1.92 % SZS output start Proof for theBenchmark
% See solution above
% 4.32/1.92 % (3372429)------------------------------
% 4.32/1.92 % (3372429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.92 % (3372429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.92 % (3372429)CaDiCaL version: 2.1.3
% 4.32/1.92 % (3372429)Termination reason: Refutation
% 4.32/1.92 % (3372429)Time elapsed: 0.009 s
% 4.32/1.92 % (3372429)Peak memory usage: 89 MB
% 4.32/1.92 % (3372429)Instructions burned: 16 (million)
% 4.32/1.92 % (3372429)------------------------------
% 4.32/1.92 % (3372429)------------------------------
% 4.32/1.92 % (3372418)Success in time 0.489 s
% 4.32/1.92 % Vampire exiting
%------------------------------------------------------------------------------