%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU119+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:47:17 PM UTC 2026
% Result : Theorem 3.17s 1.19s
% Output : Refutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 9 unt; 0 def)
% Number of atoms : 187 ( 37 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 235 ( 101 ~; 83 |; 46 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 111 ( 100 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f12,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f13,conjecture,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X2] :
( in(X2,X0)
& in(X2,X1) )
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X2] :
( in(X2,X0)
& in(X2,X1) )
& disjoint(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
~ ! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X3] :
( in(X3,X0)
& in(X3,X1) )
& disjoint(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f17,plain,
? [X0,X1] :
( ( ~ disjoint(X0,X1)
& ! [X2] :
( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| ( ? [X3] :
( in(X3,X0)
& in(X3,X1) )
& disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f19,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,plain,
( ( ~ disjoint(sK0,sK1)
& ! [X2] :
( ~ in(X2,sK0)
| ~ in(X2,sK1) ) )
| ( in(sK2,sK0)
& in(sK2,sK1)
& disjoint(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2)],[f17]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X1) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0] :
( ( X0 = empty_set
| in(sK4(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f27]) ).
fof(f31,plain,
! [X2] :
( disjoint(sK0,sK1)
| ~ in(X2,sK1)
| ~ in(X2,sK0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
( in(sK2,sK1)
| ~ disjoint(sK0,sK1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
( in(sK2,sK0)
| ~ disjoint(sK0,sK1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f45,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f50,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X0] :
( in(sK4(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f39]) ).
fof(f55,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f38]) ).
fof(f56,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f37]) ).
fof(f57,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f50]) ).
fof(f79,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X1,X0) ),
inference(superposition,[],[f46,f48]) ).
fof(f81,plain,
! [X0,X1] :
( in(sK4(set_intersection2(X0,X1)),X0)
| set_intersection2(X0,X1) = empty_set ),
inference(resolution,[],[f55,f51]) ).
fof(f86,plain,
! [X0,X1] :
( in(sK4(set_intersection2(X0,X1)),X1)
| set_intersection2(X0,X1) = empty_set ),
inference(resolution,[],[f56,f51]) ).
fof(f97,plain,
! [X2,X0,X1] :
( in(X0,empty_set)
| ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X1,X2) ),
inference(superposition,[],[f54,f45]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f97,f57]) ).
fof(f137,plain,
! [X0,X1] :
( ~ in(X1,sK1)
| ~ in(X0,sK0)
| ~ in(X0,sK1)
| ~ in(X1,sK0) ),
inference(resolution,[],[f101,f31]) ).
fof(f146,plain,
! [X0] :
( ~ in(X0,sK1)
| ~ in(X0,sK0)
| ~ in(X0,sK0) ),
inference(factoring,[],[f137]) ).
fof(f147,plain,
! [X0] :
( ~ in(X0,sK1)
| ~ in(X0,sK0) ),
inference(duplicate_literal_removal,[],[f146]) ).
fof(f159,plain,
( ~ in(sK2,sK0)
| ~ disjoint(sK0,sK1) ),
inference(resolution,[],[f147,f35]) ).
fof(f163,plain,
! [X0] :
( ~ in(sK4(set_intersection2(sK1,X0)),sK0)
| empty_set = set_intersection2(sK1,X0) ),
inference(resolution,[],[f147,f81]) ).
fof(f164,plain,
~ disjoint(sK0,sK1),
inference(forward_subsumption_resolution,[],[f159,f36]) ).
fof(f175,plain,
~ disjoint(sK1,sK0),
inference(resolution,[],[f164,f44]) ).
fof(f193,plain,
( empty_set = set_intersection2(sK1,sK0)
| empty_set = set_intersection2(sK1,sK0) ),
inference(resolution,[],[f163,f86]) ).
fof(f197,plain,
empty_set = set_intersection2(sK1,sK0),
inference(duplicate_literal_removal,[],[f193]) ).
fof(f198,plain,
empty_set = set_intersection2(sK0,sK1),
inference(forward_demodulation,[],[f197,f48]) ).
fof(f213,plain,
( empty_set != empty_set
| disjoint(sK1,sK0) ),
inference(superposition,[],[f79,f198]) ).
fof(f215,plain,
disjoint(sK1,sK0),
inference(trivial_inequality_removal,[],[f213]) ).
fof(f217,plain,
$false,
inference(forward_subsumption_resolution,[],[f215,f175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU119+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:36:01 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.17/1.19 % (2993018)Detected formulas, will run a generic FOF schedule.
% 3.17/1.19 % (2993058)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3973186370:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 3.17/1.19 % (2993054)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=4160915158:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 3.17/1.19 % (2993056)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=43320163:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 3.17/1.19 % (2993059)dis-21_1_sil=8000:lcm=predicate:random_seed=2686600141:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 3.17/1.19 % (2993057)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=833099045:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 3.17/1.19 % (2993055)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=3030255054:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 3.17/1.19 % (2993053)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=2722731581:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 3.17/1.19 % (2993056)Refutation not found, incomplete strategy
% 3.17/1.19 % (2993056)------------------------------
% 3.17/1.19 % (2993056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.19 % (2993056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.19 % (2993056)CaDiCaL version: 2.1.3
% 3.17/1.19 % (2993056)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.19 % (2993056)Time elapsed: 0.002 s
% 3.17/1.19 % (2993056)Peak memory usage: 88 MB
% 3.17/1.19 % (2993056)Instructions burned: 1 (million)
% 3.17/1.19 % (2993057)First to succeed.
% 3.17/1.19 % (2993058)Also succeeded, but the first one will report.
% 3.17/1.19 % (2993057)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2993018"
% 3.17/1.19 % (2993059)Instruction limit reached!
% 3.17/1.19 % (2993059)------------------------------
% 3.17/1.19 % (2993059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.19 % (2993059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.19 % (2993059)CaDiCaL version: 2.1.3
% 3.17/1.19 % (2993059)Termination reason: Instruction limit
% 3.17/1.19 % (2993059)Termination phase: Saturation
% 3.17/1.19 % (2993059)Time elapsed: 0.068 s
% 3.17/1.19 % (2993059)Peak memory usage: 88 MB
% 3.17/1.19 % (2993059)Instructions burned: 131 (million)
% 3.17/1.19 % (2993109)lrs+10_1_sil=8000:sp=occurrence:random_seed=688134208:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.17/1.19 % (2993109)Also succeeded, but the first one will report.
% 3.17/1.19 % (2993056)------------------------------
% 3.17/1.19 % (2993056)------------------------------
% 3.17/1.19 % (2993057)Refutation found. Thanks to Tanya!
% 3.17/1.19 % SZS status Theorem for theBenchmark
% 3.17/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.17/1.20 % (2993057)------------------------------
% 3.17/1.20 % (2993057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.20 % (2993057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.20 % (2993057)CaDiCaL version: 2.1.3
% 3.17/1.20 % (2993057)Termination reason: Refutation
% 3.17/1.20 % (2993057)Time elapsed: 0.006 s
% 3.17/1.20 % (2993057)Peak memory usage: 88 MB
% 3.17/1.20 % (2993057)Instructions burned: 8 (million)
% 3.17/1.20 % (2993057)------------------------------
% 3.17/1.20 % (2993057)------------------------------
% 3.17/1.20 % (2993018)Success in time 0.387 s
% 3.17/1.20 % Vampire exiting
%------------------------------------------------------------------------------