%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU308+2 : 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 : n006.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 12:48:16 PM UTC 2026
% Result : Theorem 3.91s 1.57s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 61 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 58 ( 27 ~; 17 |; 6 &)
% ( 1 <=>; 7 =>; 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 : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 37 ( 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f291,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f296,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f337,axiom,
! [X0] :
( one_sorted_str(X0)
=> cast_as_carrier_subset(X0) = the_carrier(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
fof(f361,conjecture,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(f362,negated_conjecture,
~ ! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
inference(negated_conjecture,[status(cth)],[f361]) ).
fof(f424,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f502,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f296]) ).
fof(f636,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f94]) ).
fof(f783,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f291]) ).
fof(f784,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f783]) ).
fof(f848,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f337]) ).
fof(f882,plain,
? [X0] :
( ? [X1] :
( subset_complement(the_carrier(X0),X1) != subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)
& element(X1,powerset(the_carrier(X0))) )
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f362]) ).
fof(f1510,plain,
( subset_complement(the_carrier(sK332),sK333) != subset_difference(the_carrier(sK332),cast_as_carrier_subset(sK332),sK333)
& element(sK333,powerset(the_carrier(sK332)))
& one_sorted_str(sK332) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK332,sK333]),skolemize(X0,sK332),skolemize(X1,sK333)],[f882]) ).
fof(f1537,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f424]) ).
fof(f1878,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f636]) ).
fof(f2252,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f784]) ).
fof(f2260,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f502]) ).
fof(f2591,plain,
! [X0] :
( the_carrier(X0) = cast_as_carrier_subset(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f848]) ).
fof(f2627,plain,
one_sorted_str(sK332),
inference(cnf_transformation,[],[f1510]) ).
fof(f2628,plain,
element(sK333,powerset(the_carrier(sK332))),
inference(cnf_transformation,[],[f1510]) ).
fof(f2629,plain,
subset_complement(the_carrier(sK332),sK333) != subset_difference(the_carrier(sK332),cast_as_carrier_subset(sK332),sK333),
inference(cnf_transformation,[],[f1510]) ).
fof(f2727,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1537]) ).
fof(f3303,plain,
( subset_complement(the_carrier(sK332),sK333) != subset_difference(the_carrier(sK332),the_carrier(sK332),sK333)
| ~ one_sorted_str(sK332) ),
inference(superposition,[],[f2629,f2591]) ).
fof(f3304,plain,
subset_complement(the_carrier(sK332),sK333) != subset_difference(the_carrier(sK332),the_carrier(sK332),sK333),
inference(forward_subsumption_resolution,[],[f3303,f2627]) ).
fof(f3378,plain,
( subset_complement(the_carrier(sK332),sK333) != set_difference(the_carrier(sK332),sK333)
| ~ element(the_carrier(sK332),powerset(the_carrier(sK332)))
| ~ element(sK333,powerset(the_carrier(sK332))) ),
inference(superposition,[],[f3304,f2252]) ).
fof(f3381,plain,
( ~ element(the_carrier(sK332),powerset(the_carrier(sK332)))
| ~ element(sK333,powerset(the_carrier(sK332))) ),
inference(forward_subsumption_resolution,[],[f3378,f1878]) ).
fof(f3383,plain,
~ element(the_carrier(sK332),powerset(the_carrier(sK332))),
inference(forward_subsumption_resolution,[],[f3381,f2628]) ).
fof(f3425,plain,
~ subset(the_carrier(sK332),the_carrier(sK332)),
inference(resolution,[],[f3383,f2727]) ).
fof(f3428,plain,
$false,
inference(forward_subsumption_resolution,[],[f3425,f2260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU308+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n006.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 04:37:55 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 3.91/1.57 % (3584739)Detected formulas, will run a generic FOF schedule.
% 3.91/1.57 % (3584745)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=3423726368:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.91/1.57 % (3584746)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=2911038531:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.91/1.57 % (3584747)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2887395138:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.91/1.57 % (3584748)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=935177623:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.91/1.57 % (3584744)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=2643547296:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.91/1.57 % (3584749)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2044948436:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.91/1.57 % (3584750)dis-21_1_sil=8000:lcm=predicate:random_seed=2913662835: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)
% 3.91/1.57 % (3584749)First to succeed.
% 3.91/1.57 % (3584749)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3584739"
% 3.91/1.57 % (3584747)Instruction limit reached!
% 3.91/1.57 % (3584747)------------------------------
% 3.91/1.57 % (3584747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.57 % (3584747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.57 % (3584747)CaDiCaL version: 2.1.3
% 3.91/1.57 % (3584747)Termination reason: Instruction limit
% 3.91/1.57 % (3584747)Termination phase: Saturation
% 3.91/1.57 % (3584747)Time elapsed: 0.062 s
% 3.91/1.57 % (3584747)Peak memory usage: 91 MB
% 3.91/1.57 % (3584747)Instructions burned: 111 (million)
% 3.91/1.57 % (3584748)Instruction limit reached!
% 3.91/1.57 % (3584748)------------------------------
% 3.91/1.57 % (3584748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.57 % (3584748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.57 % (3584748)CaDiCaL version: 2.1.3
% 3.91/1.57 % (3584748)Termination reason: Instruction limit
% 3.91/1.57 % (3584748)Termination phase: Saturation
% 3.91/1.57 % (3584748)Time elapsed: 0.077 s
% 3.91/1.57 % (3584748)Peak memory usage: 90 MB
% 3.91/1.57 % (3584748)Instructions burned: 119 (million)
% 3.91/1.57 % (3584750)Instruction limit reached!
% 3.91/1.57 % (3584750)------------------------------
% 3.91/1.57 % (3584750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.57 % (3584750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.57 % (3584750)CaDiCaL version: 2.1.3
% 3.91/1.57 % (3584750)Termination reason: Instruction limit
% 3.91/1.57 % (3584750)Termination phase: Saturation
% 3.91/1.57 % (3584750)Time elapsed: 0.064 s
% 3.91/1.57 % (3584750)Peak memory usage: 91 MB
% 3.91/1.57 % (3584750)Instructions burned: 129 (million)
% 3.91/1.57 % (3584758)lrs+10_1_sil=8000:sp=occurrence:random_seed=614203585:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.91/1.57 % (3584759)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3732619871:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.91/1.57 % (3584760)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4049527016:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.91/1.57 % (3584759)Also succeeded, but the first one will report.
% 3.91/1.57 % (3584749)Refutation found. Thanks to Tanya!
% 3.91/1.57 % SZS status Theorem for theBenchmark
% 3.91/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.57 % (3584749)------------------------------
% 3.91/1.57 % (3584749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.57 % (3584749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.57 % (3584749)CaDiCaL version: 2.1.3
% 3.91/1.57 % (3584749)Termination reason: Refutation
% 3.91/1.57 % (3584749)Time elapsed: 0.039 s
% 3.91/1.57 % (3584749)Peak memory usage: 91 MB
% 3.91/1.57 % (3584749)Instructions burned: 65 (million)
% 3.91/1.57 % (3584749)------------------------------
% 3.91/1.57 % (3584749)------------------------------
% 3.91/1.57 % (3584739)Success in time 0.478 s
% 3.91/1.57 % Vampire exiting
%------------------------------------------------------------------------------