%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU307+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:52:48 PM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 17 unt; 0 def)
% Number of atoms : 93 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 33 ~; 28 |; 7 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 58 ( 56 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f40,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_intersection2(X0,X1,X2) = subset_intersection2(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
fof(f47,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(f49,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(f56,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f57,axiom,
! [X0] :
( one_sorted_str(X0)
=> cast_as_carrier_subset(X0) = the_carrier(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(f58,conjecture,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_pre_topc) ).
fof(f59,negated_conjecture,
~ ! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f58]) ).
fof(f60,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f109,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = subset_intersection2(X0,X2,X1)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f110,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = subset_intersection2(X0,X2,X1)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f109]) ).
fof(f113,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f114,plain,
! [X0,X1,X2] :
( subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f118,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f119,plain,
? [X0] :
( ? [X1] :
( subset_intersection2(the_carrier(X0),X1,cast_as_carrier_subset(X0)) != X1
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f120,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f126,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f127,plain,
( sK6 != subset_intersection2(the_carrier(sK5),sK6,cast_as_carrier_subset(sK5))
& element(sK6,powerset(the_carrier(sK5)))
& one_sorted_str(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f119]) ).
fof(f207,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f40]) ).
fof(f209,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = subset_intersection2(X0,X2,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f214,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_intersection2(X0,X1,X2) = set_intersection2(X1,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f215,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f218,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f220,plain,
! [X0] :
( ~ one_sorted_str(X0)
| cast_as_carrier_subset(X0) = the_carrier(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f221,plain,
one_sorted_str(sK5),
inference(cnf_transformation,[],[f127]) ).
fof(f222,plain,
element(sK6,powerset(the_carrier(sK5))),
inference(cnf_transformation,[],[f127]) ).
fof(f223,plain,
sK6 != subset_intersection2(the_carrier(sK5),sK6,cast_as_carrier_subset(sK5)),
inference(cnf_transformation,[],[f127]) ).
fof(f224,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f479,plain,
subset(sK6,the_carrier(sK5)),
inference(resolution,[],[f218,f222]) ).
fof(f482,plain,
the_carrier(sK5) = cast_as_carrier_subset(sK5),
inference(resolution,[],[f220,f221]) ).
fof(f485,plain,
sK6 != subset_intersection2(cast_as_carrier_subset(sK5),sK6,cast_as_carrier_subset(sK5)),
inference(superposition,[],[f223,f482]) ).
fof(f690,plain,
( element(cast_as_carrier_subset(sK5),powerset(cast_as_carrier_subset(sK5)))
| ~ one_sorted_str(sK5) ),
inference(superposition,[],[f215,f482]) ).
fof(f693,plain,
element(cast_as_carrier_subset(sK5),powerset(cast_as_carrier_subset(sK5))),
inference(forward_subsumption_resolution,[],[f690,f221]) ).
fof(f698,plain,
sK6 = set_intersection2(sK6,the_carrier(sK5)),
inference(resolution,[],[f224,f479]) ).
fof(f700,plain,
sK6 = set_intersection2(sK6,cast_as_carrier_subset(sK5)),
inference(forward_demodulation,[],[f698,f482]) ).
fof(f829,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK5)))
| subset_intersection2(the_carrier(sK5),X0,sK6) = set_intersection2(X0,sK6) ),
inference(resolution,[],[f214,f222]) ).
fof(f831,plain,
! [X0] :
( ~ element(X0,powerset(cast_as_carrier_subset(sK5)))
| subset_intersection2(the_carrier(sK5),X0,sK6) = set_intersection2(X0,sK6) ),
inference(forward_demodulation,[],[f829,f482]) ).
fof(f834,plain,
! [X0] :
( ~ element(X0,powerset(cast_as_carrier_subset(sK5)))
| set_intersection2(X0,sK6) = subset_intersection2(cast_as_carrier_subset(sK5),X0,sK6) ),
inference(forward_demodulation,[],[f831,f482]) ).
fof(f847,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK5)))
| subset_intersection2(the_carrier(sK5),X0,sK6) = subset_intersection2(the_carrier(sK5),sK6,X0) ),
inference(resolution,[],[f209,f222]) ).
fof(f849,plain,
! [X0] :
( ~ element(X0,powerset(cast_as_carrier_subset(sK5)))
| subset_intersection2(the_carrier(sK5),X0,sK6) = subset_intersection2(the_carrier(sK5),sK6,X0) ),
inference(forward_demodulation,[],[f847,f482]) ).
fof(f851,plain,
! [X0] :
( ~ element(X0,powerset(cast_as_carrier_subset(sK5)))
| subset_intersection2(cast_as_carrier_subset(sK5),X0,sK6) = subset_intersection2(cast_as_carrier_subset(sK5),sK6,X0) ),
inference(forward_demodulation,[],[f849,f482]) ).
fof(f873,plain,
set_intersection2(cast_as_carrier_subset(sK5),sK6) = subset_intersection2(cast_as_carrier_subset(sK5),cast_as_carrier_subset(sK5),sK6),
inference(resolution,[],[f834,f693]) ).
fof(f882,plain,
set_intersection2(sK6,cast_as_carrier_subset(sK5)) = subset_intersection2(cast_as_carrier_subset(sK5),cast_as_carrier_subset(sK5),sK6),
inference(forward_demodulation,[],[f873,f207]) ).
fof(f887,plain,
sK6 = subset_intersection2(cast_as_carrier_subset(sK5),cast_as_carrier_subset(sK5),sK6),
inference(forward_demodulation,[],[f882,f700]) ).
fof(f892,plain,
subset_intersection2(cast_as_carrier_subset(sK5),sK6,cast_as_carrier_subset(sK5)) = subset_intersection2(cast_as_carrier_subset(sK5),cast_as_carrier_subset(sK5),sK6),
inference(resolution,[],[f851,f693]) ).
fof(f1217,plain,
sK6 = subset_intersection2(cast_as_carrier_subset(sK5),sK6,cast_as_carrier_subset(sK5)),
inference(forward_demodulation,[],[f892,f887]) ).
fof(f1218,plain,
$false,
inference(forward_subsumption_resolution,[],[f1217,f485]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU307+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 04:39:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.45 % (1191067)Will run a generic schedule for satisfiability detection.
% 0.09/0.45 % (1191075)dis+10_1_sil=32000:sp=arity:random_seed=4124281878:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.45 % (1191072)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2308462539_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.45 % (1191074)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=373745514:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.45 % (1191076)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1522064493:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.45 % (1191077)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1121397840:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.45 % (1191078)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=307817313:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.45 % (1191075) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1191067-1191075"...
% 0.09/0.45 % TRYING [1]
% 0.09/0.45 % TRYING [2]
% 0.09/0.45 % (1191075)...printing done.
% 0.09/0.45 % TRYING [3]
% 0.09/0.45 % (1191075)Refutation found. Thanks to Tanya!
% 0.09/0.45 % SZS status Theorem for theBenchmark
% 0.09/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.45 % (1191075)------------------------------
% 0.09/0.45 % (1191075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.45 % (1191075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.45 % (1191075)CaDiCaL version: 2.1.3
% 0.09/0.45 % (1191075)Termination reason: Refutation
% 0.09/0.45 % (1191075)Time elapsed: 0.011 s
% 0.09/0.45 % (1191075)Peak memory usage: 12 MB
% 0.09/0.45 % (1191075)Instructions burned: 28 (million)
% 0.09/0.45 % (1191067)Success in time 0.045 s
% 0.09/0.45 % Vampire exiting
%------------------------------------------------------------------------------