%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU056+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:47:09 PM UTC 2026
% Result : Theorem 3.55s 1.46s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 13 unt; 0 def)
% Number of atoms : 84 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 77 ( 28 ~; 23 |; 18 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( one_to_one(X2)
=> relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_1) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( disjoint(X0,X1)
& one_to_one(X2) )
=> disjoint(relation_image(X2,X0),relation_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_funct_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( disjoint(X0,X1)
& one_to_one(X2) )
=> disjoint(relation_image(X2,X0),relation_image(X2,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [X0] :
( relation(X0)
=> relation_image(X0,empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).
fof(f31,axiom,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(f53,plain,
! [X0,X1,X2] :
( relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f54,plain,
! [X0,X1,X2] :
( relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1))
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
? [X0,X1,X2] :
( ~ disjoint(relation_image(X2,X0),relation_image(X2,X1))
& disjoint(X0,X1)
& one_to_one(X2)
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f56,plain,
? [X0,X1,X2] :
( ~ disjoint(relation_image(X2,X0),relation_image(X2,X1))
& disjoint(X0,X1)
& one_to_one(X2)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( relation_image(X0,empty_set) = empty_set
| ~ relation(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f68,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f80,plain,
( ~ disjoint(relation_image(sK13,sK11),relation_image(sK13,sK12))
& disjoint(sK11,sK12)
& one_to_one(sK13)
& relation(sK13)
& function(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f56]) ).
fof(f88,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f89,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ one_to_one(X2)
| relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1))
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f121,plain,
function(sK13),
inference(cnf_transformation,[],[f80]) ).
fof(f122,plain,
relation(sK13),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
one_to_one(sK13),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
disjoint(sK11,sK12),
inference(cnf_transformation,[],[f80]) ).
fof(f125,plain,
~ disjoint(relation_image(sK13,sK11),relation_image(sK13,sK12)),
inference(cnf_transformation,[],[f80]) ).
fof(f126,plain,
! [X0] :
( empty_set = relation_image(X0,empty_set)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f128,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f31]) ).
fof(f147,plain,
! [X0,X1] :
( relation_image(sK13,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK13,X0),relation_image(sK13,X1))
| ~ relation(sK13)
| ~ function(sK13) ),
inference(resolution,[],[f120,f123]) ).
fof(f152,plain,
! [X0,X1] :
( relation_image(sK13,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK13,X0),relation_image(sK13,X1))
| ~ function(sK13) ),
inference(forward_subsumption_resolution,[],[f147,f122]) ).
fof(f155,plain,
! [X0,X1] : relation_image(sK13,set_intersection2(X0,X1)) = set_intersection2(relation_image(sK13,X0),relation_image(sK13,X1)),
inference(forward_subsumption_resolution,[],[f152,f121]) ).
fof(f157,plain,
! [X0] :
( relation_image(sK13,set_intersection2(X0,empty_set)) = set_intersection2(relation_image(sK13,X0),empty_set)
| ~ relation(sK13) ),
inference(superposition,[],[f155,f126]) ).
fof(f161,plain,
! [X0,X1] :
( empty_set != relation_image(sK13,set_intersection2(X0,X1))
| disjoint(relation_image(sK13,X0),relation_image(sK13,X1)) ),
inference(superposition,[],[f89,f155]) ).
fof(f164,plain,
! [X0] : relation_image(sK13,set_intersection2(X0,empty_set)) = set_intersection2(relation_image(sK13,X0),empty_set),
inference(forward_subsumption_resolution,[],[f157,f122]) ).
fof(f170,plain,
! [X0] : relation_image(sK13,empty_set) = set_intersection2(relation_image(sK13,X0),empty_set),
inference(superposition,[],[f164,f128]) ).
fof(f174,plain,
empty_set = relation_image(sK13,empty_set),
inference(forward_demodulation,[],[f170,f128]) ).
fof(f406,plain,
! [X0,X1] :
( empty_set != relation_image(sK13,empty_set)
| disjoint(relation_image(sK13,X0),relation_image(sK13,X1))
| ~ disjoint(X0,X1) ),
inference(superposition,[],[f161,f88]) ).
fof(f425,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(relation_image(sK13,X0),relation_image(sK13,X1)) ),
inference(forward_subsumption_resolution,[],[f406,f174]) ).
fof(f513,plain,
disjoint(relation_image(sK13,sK11),relation_image(sK13,sK12)),
inference(resolution,[],[f425,f124]) ).
fof(f514,plain,
$false,
inference(forward_subsumption_resolution,[],[f513,f125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU056+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n017.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 03:23:36 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.55/1.46 % (3179470)Detected formulas, will run a generic FOF schedule.
% 3.55/1.46 % (3179478)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2490224903:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.55/1.46 % (3179478)Refutation not found, incomplete strategy
% 3.55/1.46 % (3179478)------------------------------
% 3.55/1.46 % (3179478)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.46 % (3179478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.46 % (3179478)CaDiCaL version: 2.1.3
% 3.55/1.46 % (3179478)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.46 % (3179478)Time elapsed: 0.001 s
% 3.55/1.46 % (3179478)Peak memory usage: 88 MB
% 3.55/1.46 % (3179478)Instructions burned: 1 (million)
% 3.55/1.46 % (3179481)dis-21_1_sil=8000:lcm=predicate:random_seed=232601815: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)
% 3.55/1.46 % (3179480)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=844807649:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.55/1.46 % (3179475)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=2366673447:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.55/1.46 % (3179476)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=1294041166:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.55/1.46 % (3179477)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=3829255404:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.55/1.46 % (3179479)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4077016935:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.55/1.46 % (3179480)First to succeed.
% 3.55/1.46 % (3179479)Also succeeded, but the first one will report.
% 3.55/1.46 % (3179480)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3179470"
% 3.55/1.46 % (3179481)Instruction limit reached!
% 3.55/1.46 % (3179481)------------------------------
% 3.55/1.46 % (3179481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.46 % (3179481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.46 % (3179481)CaDiCaL version: 2.1.3
% 3.55/1.46 % (3179481)Termination reason: Instruction limit
% 3.55/1.46 % (3179481)Termination phase: Saturation
% 3.55/1.46 % (3179481)Time elapsed: 0.078 s
% 3.55/1.46 % (3179481)Peak memory usage: 90 MB
% 3.55/1.46 % (3179481)Instructions burned: 130 (million)
% 3.55/1.46 % (3179478)------------------------------
% 3.55/1.46 % (3179478)------------------------------
% 3.55/1.46 % (3179489)lrs+10_1_sil=8000:sp=occurrence:random_seed=3824130838:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.55/1.46 % (3179489)Also succeeded, but the first one will report.
% 3.55/1.46 % (3179490)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2250428922:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.55/1.46 % (3179490)Also succeeded, but the first one will report.
% 3.55/1.46 % (3179480)Refutation found. Thanks to Tanya!
% 3.55/1.46 % SZS status Theorem for theBenchmark
% 3.55/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.46 % (3179480)------------------------------
% 3.55/1.46 % (3179480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.46 % (3179480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.46 % (3179480)CaDiCaL version: 2.1.3
% 3.55/1.46 % (3179480)Termination reason: Refutation
% 3.55/1.46 % (3179480)Time elapsed: 0.012 s
% 3.55/1.46 % (3179480)Peak memory usage: 89 MB
% 3.55/1.46 % (3179480)Instructions burned: 14 (million)
% 3.55/1.46 % (3179480)------------------------------
% 3.55/1.46 % (3179480)------------------------------
% 3.55/1.46 % (3179470)Success in time 0.421 s
% 3.55/1.46 % Vampire exiting
%------------------------------------------------------------------------------