%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:39:28 PM UTC 2026
% Result : Unsatisfiable 2.82s 1.28s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 78 ( 12 unt; 6 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 172 ( 79 ~; 87 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X0)
| member(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
fof(f10,axiom,
! [X2,X0,X1] :
( intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2)
| member(h(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom1) ).
fof(f11,axiom,
! [X2,X0,X1] :
( intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2)
| member(h(X0,X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom2) ).
fof(f12,axiom,
! [X2,X0,X1] :
( intersection(X0,X1,X2)
| ~ member(h(X0,X1,X2),X1)
| ~ member(h(X0,X1,X2),X0)
| ~ member(h(X0,X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom3) ).
fof(f13,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_b) ).
fof(f14,axiom,
intersection(b,c,bIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_intersection_c) ).
fof(f15,axiom,
intersection(a,bIc,aIbIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_bIc) ).
fof(f16,negated_conjecture,
~ intersection(aIb,c,aIbIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aIb_intersection_c_is_aIbIc) ).
fof(f21,plain,
! [X0] :
( ~ member(X0,aIb)
| member(X0,a) ),
inference(resolution,[],[f7,f13]) ).
fof(f22,plain,
! [X0] :
( ~ member(X0,aIbIc)
| member(X0,a) ),
inference(resolution,[],[f7,f15]) ).
fof(f23,plain,
! [X0] :
( ~ member(X0,bIc)
| member(X0,b) ),
inference(resolution,[],[f7,f14]) ).
fof(f24,plain,
! [X0] :
( ~ member(X0,aIb)
| member(X0,b) ),
inference(resolution,[],[f8,f13]) ).
fof(f25,plain,
! [X0] :
( ~ member(X0,aIbIc)
| member(X0,bIc) ),
inference(resolution,[],[f8,f15]) ).
fof(f26,plain,
! [X0] :
( ~ member(X0,bIc)
| member(X0,c) ),
inference(resolution,[],[f8,f14]) ).
fof(f27,plain,
! [X0] :
( member(X0,aIb)
| ~ member(X0,a)
| ~ member(X0,b) ),
inference(resolution,[],[f9,f13]) ).
fof(f28,plain,
! [X0] :
( member(X0,aIbIc)
| ~ member(X0,a)
| ~ member(X0,bIc) ),
inference(resolution,[],[f9,f15]) ).
fof(f29,plain,
! [X0] :
( member(X0,bIc)
| ~ member(X0,b)
| ~ member(X0,c) ),
inference(resolution,[],[f9,f14]) ).
fof(f30,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| member(h(aIb,c,aIbIc),aIb) ),
inference(resolution,[],[f10,f16]) ).
fof(f35,definition,
( spl0_1
<=> member(h(aIb,c,aIbIc),aIb) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f36,plain,
( member(h(aIb,c,aIbIc),aIb)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f38,definition,
( spl0_2
<=> member(h(aIb,c,aIbIc),aIbIc) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f39,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f40,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f30,f38,f35]) ).
fof(f41,plain,
( member(h(aIb,c,aIbIc),a)
| ~ spl0_2 ),
inference(resolution,[],[f39,f22]) ).
fof(f42,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| member(h(aIb,c,aIbIc),c) ),
inference(resolution,[],[f11,f16]) ).
fof(f46,plain,
( ~ member(h(aIb,c,aIbIc),c)
| ~ member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolution,[],[f12,f16]) ).
fof(f50,plain,
( ~ member(h(aIb,c,aIbIc),aIbIc)
| spl0_2 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f51,plain,
( ~ member(h(aIb,c,aIbIc),aIb)
| spl0_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f53,definition,
( spl0_3
<=> member(h(aIb,c,aIbIc),c) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f55,plain,
( ~ spl0_2
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f46,f53,f35,f38]) ).
fof(f56,plain,
( member(h(aIb,c,aIbIc),bIc)
| ~ spl0_2 ),
inference(resolution,[],[f25,f39]) ).
fof(f57,plain,
( member(h(aIb,c,aIbIc),b)
| ~ spl0_2 ),
inference(resolution,[],[f56,f23]) ).
fof(f58,plain,
( member(h(aIb,c,aIbIc),c)
| ~ spl0_2 ),
inference(resolution,[],[f26,f56]) ).
fof(f61,plain,
( ~ member(h(aIb,c,aIbIc),a)
| ~ member(h(aIb,c,aIbIc),b)
| spl0_1 ),
inference(resolution,[],[f27,f51]) ).
fof(f63,definition,
( spl0_4
<=> member(h(aIb,c,aIbIc),b) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f64,plain,
( ~ member(h(aIb,c,aIbIc),b)
| spl0_4 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f66,definition,
( spl0_5
<=> member(h(aIb,c,aIbIc),a) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f67,plain,
( ~ member(h(aIb,c,aIbIc),a)
| spl0_5 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f68,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_1 ),
inference(avatar_split_clause,[],[f61,f35,f66,f63]) ).
fof(f69,plain,
( $false
| ~ spl0_2
| spl0_4 ),
inference(resolution,[],[f64,f57]) ).
fof(f70,plain,
( ~ spl0_2
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f69]) ).
fof(f71,plain,
( $false
| ~ spl0_2
| spl0_5 ),
inference(resolution,[],[f67,f41]) ).
fof(f72,plain,
( ~ spl0_2
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f71]) ).
fof(f74,plain,
( spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f42,f38,f53]) ).
fof(f75,plain,
( member(h(aIb,c,aIbIc),b)
| ~ spl0_1 ),
inference(resolution,[],[f36,f24]) ).
fof(f76,plain,
( member(h(aIb,c,aIbIc),a)
| ~ spl0_1 ),
inference(resolution,[],[f36,f21]) ).
fof(f80,plain,
( $false
| ~ spl0_1
| spl0_5 ),
inference(resolution,[],[f76,f67]) ).
fof(f81,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f82,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f58,f38,f53]) ).
fof(f83,plain,
( ~ member(h(aIb,c,aIbIc),a)
| ~ member(h(aIb,c,aIbIc),bIc)
| spl0_2 ),
inference(resolution,[],[f50,f28]) ).
fof(f85,definition,
( spl0_6
<=> member(h(aIb,c,aIbIc),bIc) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( ~ member(h(aIb,c,aIbIc),bIc)
| spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( ~ spl0_6
| ~ spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f83,f38,f66,f85]) ).
fof(f90,plain,
( ~ member(h(aIb,c,aIbIc),b)
| ~ member(h(aIb,c,aIbIc),c)
| spl0_6 ),
inference(resolution,[],[f29,f86]) ).
fof(f91,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6 ),
inference(avatar_split_clause,[],[f90,f85,f63,f53]) ).
fof(f92,plain,
( $false
| ~ spl0_1
| spl0_4 ),
inference(resolution,[],[f64,f75]) ).
fof(f93,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f92]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f68]) ).
cnf(s4,plain,
( ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f70]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f72]) ).
cnf(s6,plain,
( spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f74]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f81]) ).
cnf(s8,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f82]) ).
cnf(s9,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f87]) ).
cnf(s10,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f91]) ).
cnf(s11,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f93]) ).
cnf(s12,plain,
spl0_1,
inference(rat,[],[s3,s4,s5,s1]) ).
cnf(s13,plain,
spl0_4,
inference(rat,[],[s11,s12]) ).
cnf(s14,plain,
spl0_5,
inference(rat,[],[s7,s12]) ).
cnf(s15,plain,
~ spl0_2,
inference(rat,[],[s2,s8,s12]) ).
cnf(s16,plain,
~ spl0_6,
inference(rat,[],[s9,s14,s15]) ).
cnf(s17,plain,
spl0_3,
inference(rat,[],[s6,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s10,s13,s16,s17]) ).
fof(f94,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n003.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 00:04:43 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 2.82/1.28 % (1064685)Input is clausal, will run a generic CNF schedule.
% 2.82/1.28 % (1064694)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3629525787:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.82/1.28 % (1064694)Refutation not found, incomplete strategy
% 2.82/1.28 % (1064694)------------------------------
% 2.82/1.28 % (1064694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.28 % (1064694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.28 % (1064694)CaDiCaL version: 2.1.3
% 2.82/1.28 % (1064694)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.28 % (1064694)Time elapsed: 0.001 s
% 2.82/1.28 % (1064694)Peak memory usage: 87 MB
% 2.82/1.28 % (1064691)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2053332692:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.82/1.28 % (1064692)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1205171560:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.82/1.28 % (1064693)lrs+10_1_sil=8000:sp=occurrence:random_seed=296803840:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.82/1.28 % (1064690)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=4224841054:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.82/1.28 % (1064696)dis-21_1_sil=8000:lcm=predicate:random_seed=1348484245: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)
% 2.82/1.28 % (1064695)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2812455579:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.82/1.28 % (1064693)Refutation not found, incomplete strategy
% 2.82/1.28 % (1064693)------------------------------
% 2.82/1.28 % (1064693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.28 % (1064693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.28 % (1064693)CaDiCaL version: 2.1.3
% 2.82/1.28 % (1064693)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.28 % (1064693)Time elapsed: 0.001 s
% 2.82/1.28 % (1064693)Peak memory usage: 87 MB
% 2.82/1.28 % (1064696)First to succeed.
% 2.82/1.28 % (1064696)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1064685"
% 2.82/1.28 % (1064695)Also succeeded, but the first one will report.
% 2.82/1.28 % (1064694)------------------------------
% 2.82/1.28 % (1064694)------------------------------
% 2.82/1.28 % (1064704)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=3317983199:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.82/1.28 % (1064704)Refutation not found, incomplete strategy
% 2.82/1.28 % (1064704)------------------------------
% 2.82/1.28 % (1064704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.28 % (1064704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.28 % (1064704)CaDiCaL version: 2.1.3
% 2.82/1.28 % (1064704)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.28 % (1064704)Time elapsed: 0.0000 s
% 2.82/1.28 % (1064704)Peak memory usage: 87 MB
% 2.82/1.28 % (1064693)------------------------------
% 2.82/1.28 % (1064693)------------------------------
% 2.82/1.28 % (1064696)Refutation found. Thanks to Tanya!
% 2.82/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.82/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.49 % (1064696)------------------------------
% 3.63/1.49 % (1064696)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.49 % (1064696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.49 % (1064696)CaDiCaL version: 2.1.3
% 3.63/1.49 % (1064696)Termination reason: Refutation
% 3.63/1.49 % (1064696)Time elapsed: 0.004 s
% 3.63/1.49 % (1064696)Peak memory usage: 89 MB
% 3.63/1.49 % (1064696)Instructions burned: 3 (million)
% 3.63/1.49 % (1064696)------------------------------
% 3.63/1.49 % (1064696)------------------------------
% 3.63/1.49 % (1064685)Success in time 0.433 s
% 3.63/1.49 % Vampire exiting
%------------------------------------------------------------------------------