%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU131+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:47:20 PM UTC 2026
% Result : Theorem 2.71s 1.33s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 10 unt; 0 def)
% Number of atoms : 198 ( 36 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 232 ( 93 ~; 100 |; 30 &)
% ( 6 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 113 ( 103 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f6,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f7,conjecture,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f14,axiom,
! [X0] : set_difference(empty_set,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(f15,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f16,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f19,plain,
? [X0,X1] :
( set_difference(X0,X1) = empty_set
<~> subset(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f20,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f22,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f26,plain,
? [X0,X1] :
( ( ~ subset(X0,X1)
| set_difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f27,plain,
( ( ~ subset(sK0,sK1)
| empty_set != set_difference(sK0,sK1) )
& ( subset(sK0,sK1)
| empty_set = set_difference(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X2) )
& ( ( in(sK2(X0,X1,X2),X0)
& ~ in(sK2(X0,X1,X2),X1) )
| in(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f33,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f33]) ).
fof(f38,plain,
empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f9]) ).
fof(f39,plain,
( empty_set = set_difference(sK0,sK1)
| subset(sK0,sK1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f40,plain,
( empty_set != set_difference(sK0,sK1)
| ~ subset(sK0,sK1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f41,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f43,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f31]) ).
fof(f45,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f31]) ).
fof(f46,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f31]) ).
fof(f47,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X2)
| in(sK2(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f50,plain,
empty(empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f52,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f54,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f55,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f61,plain,
empty(sK6),
inference(cnf_transformation,[],[f38]) ).
fof(f62,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f45]) ).
fof(f64,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f43]) ).
fof(f86,plain,
! [X0,X1] :
( ~ in(X0,empty_set)
| ~ in(X0,X1) ),
inference(superposition,[],[f64,f41]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ empty(set_difference(X1,X2))
| in(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[],[f62,f55]) ).
fof(f101,plain,
! [X0] :
( in(X0,empty_set)
| ~ in(X0,sK0)
| in(X0,sK1)
| subset(sK0,sK1) ),
inference(superposition,[],[f62,f39]) ).
fof(f105,plain,
! [X0] :
( in(X0,sK1)
| ~ in(X0,sK0)
| in(X0,empty_set) ),
inference(forward_subsumption_resolution,[],[f101,f52]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ in(sK2(X0,X1,X2),X1)
| set_difference(X0,X1) = X2
| ~ empty(X2) ),
inference(resolution,[],[f46,f55]) ).
fof(f133,plain,
! [X2,X0,X1] :
( in(sK2(X0,X1,X2),X0)
| set_difference(X0,X1) = X2
| ~ empty(X2) ),
inference(resolution,[],[f47,f55]) ).
fof(f208,plain,
! [X0] :
( ~ empty(empty_set)
| in(X0,sK1)
| ~ in(X0,sK0)
| subset(sK0,sK1) ),
inference(superposition,[],[f98,f39]) ).
fof(f214,plain,
! [X0] :
( ~ empty(empty_set)
| in(X0,sK1)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f208,f52]) ).
fof(f215,plain,
! [X0] :
( in(X0,sK1)
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f214,f50]) ).
fof(f220,plain,
! [X0] :
( ~ in(sK3(X0,sK1),sK0)
| subset(X0,sK1) ),
inference(resolution,[],[f215,f54]) ).
fof(f272,plain,
( subset(sK0,sK1)
| subset(sK0,sK1) ),
inference(resolution,[],[f220,f53]) ).
fof(f275,plain,
subset(sK0,sK1),
inference(duplicate_literal_removal,[],[f272]) ).
fof(f380,plain,
! [X0,X1] :
( set_difference(X0,sK1) = X1
| ~ empty(X1)
| ~ in(sK2(X0,sK1,X1),sK0)
| in(sK2(X0,sK1,X1),empty_set) ),
inference(resolution,[],[f127,f105]) ).
fof(f384,plain,
! [X0,X1] :
( ~ in(sK2(X0,sK1,X1),sK0)
| ~ empty(X1)
| set_difference(X0,sK1) = X1 ),
inference(forward_subsumption_resolution,[],[f380,f86]) ).
fof(f979,plain,
! [X0] :
( ~ empty(X0)
| set_difference(sK0,sK1) = X0
| set_difference(sK0,sK1) = X0
| ~ empty(X0) ),
inference(resolution,[],[f384,f133]) ).
fof(f989,plain,
! [X0] :
( set_difference(sK0,sK1) = X0
| ~ empty(X0) ),
inference(duplicate_literal_removal,[],[f979]) ).
fof(f1001,plain,
! [X0] :
( empty_set != X0
| ~ subset(sK0,sK1)
| ~ empty(X0) ),
inference(superposition,[],[f40,f989]) ).
fof(f1040,plain,
! [X0] :
( empty_set != X0
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f1001,f275]) ).
fof(f1041,plain,
! [X0] : ~ empty(X0),
inference(forward_subsumption_resolution,[],[f1040,f49]) ).
fof(f1062,plain,
$false,
inference(resolution,[],[f1041,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU131+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n015.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:43:16 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.71/1.33 % (2236095)Detected formulas, will run a generic FOF schedule.
% 2.71/1.33 % (2236104)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1718629747:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.33 % (2236104)First to succeed.
% 2.71/1.33 % (2236104)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2236095"
% 2.71/1.33 % (2236100)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=1833725242:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.33 % (2236106)dis-21_1_sil=8000:lcm=predicate:random_seed=2124204232: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)
% 2.71/1.33 % (2236103)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=662979984:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.33 % (2236102)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=422919161:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.33 % (2236101)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=1200142612:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.33 % (2236105)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1123612363:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.33 % (2236103)Refutation not found, incomplete strategy
% 2.71/1.33 % (2236103)------------------------------
% 2.71/1.33 % (2236103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.33 % (2236103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.33 % (2236103)CaDiCaL version: 2.1.3
% 2.71/1.33 % (2236103)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.33 % (2236103)Time elapsed: 0.006 s
% 2.71/1.33 % (2236103)Peak memory usage: 89 MB
% 2.71/1.33 % (2236103)Instructions burned: 6 (million)
% 2.71/1.33 % (2236105)Also succeeded, but the first one will report.
% 2.71/1.33 % (2236106)Instruction limit reached!
% 2.71/1.33 % (2236106)------------------------------
% 2.71/1.33 % (2236106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.33 % (2236106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.33 % (2236106)CaDiCaL version: 2.1.3
% 2.71/1.33 % (2236106)Termination reason: Instruction limit
% 2.71/1.33 % (2236106)Termination phase: Saturation
% 2.71/1.33 % (2236106)Time elapsed: 0.078 s
% 2.71/1.33 % (2236106)Peak memory usage: 89 MB
% 2.71/1.33 % (2236106)Instructions burned: 129 (million)
% 2.71/1.33 % (2236104)Refutation found. Thanks to Tanya!
% 2.71/1.33 % SZS status Theorem for theBenchmark
% 2.71/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.33 % (2236104)------------------------------
% 2.71/1.33 % (2236104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.33 % (2236104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.33 % (2236104)CaDiCaL version: 2.1.3
% 2.71/1.33 % (2236104)Termination reason: Refutation
% 2.71/1.33 % (2236104)Time elapsed: 0.013 s
% 2.71/1.33 % (2236104)Peak memory usage: 89 MB
% 2.71/1.33 % (2236104)Instructions burned: 36 (million)
% 2.71/1.33 % (2236104)------------------------------
% 2.71/1.33 % (2236104)------------------------------
% 2.71/1.33 % (2236095)Success in time 0.3 s
% 2.71/1.33 % Vampire exiting
%------------------------------------------------------------------------------