%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET618+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:41:24 PM UTC 2026
% Result : Theorem 3.53s 1.43s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 12 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2,axiom,
! [X0] : union(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotency_of_union) ).
fof(f3,axiom,
! [X0] : difference(X0,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_difference_is_empty_set) ).
fof(f12,conjecture,
! [X0] : symmetric_difference(X0,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th93) ).
fof(f13,negated_conjecture,
~ ! [X0] : symmetric_difference(X0,X0) = empty_set,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f15,plain,
? [X0] : empty_set != symmetric_difference(X0,X0),
inference(ennf_transformation,[],[f13]) ).
fof(f24,plain,
empty_set != symmetric_difference(sK2,sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f15]) ).
fof(f25,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0] : union(X0,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0] : difference(X0,X0) = empty_set,
inference(cnf_transformation,[],[f3]) ).
fof(f42,plain,
empty_set != symmetric_difference(sK2,sK2),
inference(cnf_transformation,[],[f24]) ).
fof(f55,plain,
! [X0] : difference(X0,X0) = symmetric_difference(X0,X0),
inference(superposition,[],[f26,f25]) ).
fof(f58,plain,
! [X0] : empty_set = symmetric_difference(X0,X0),
inference(forward_demodulation,[],[f55,f27]) ).
fof(f64,plain,
empty_set != empty_set,
inference(superposition,[],[f42,f58]) ).
fof(f65,plain,
$false,
inference(trivial_inequality_removal,[],[f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET618+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:17:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.53/1.43 % (1966394)Detected formulas, will run a generic FOF schedule.
% 3.53/1.43 % (1966405)dis-21_1_sil=8000:lcm=predicate:random_seed=466751436: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)
% 3.53/1.43 % (1966405)Refutation not found, incomplete strategy
% 3.53/1.43 % (1966405)------------------------------
% 3.53/1.43 % (1966405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.43 % (1966405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.43 % (1966405)CaDiCaL version: 2.1.3
% 3.53/1.43 % (1966405)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.43 % (1966405)Time elapsed: 0.001 s
% 3.53/1.43 % (1966405)Peak memory usage: 88 MB
% 3.53/1.43 % (1966405)Instructions burned: 1 (million)
% 3.53/1.43 % (1966404)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3285004599:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.43 % (1966402)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=631320378:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.43 % (1966403)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3805592145:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.43 % (1966399)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=3600805293:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.43 % (1966400)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=4001257309:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.43 % (1966401)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=2301500532:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.43 % (1966402)Refutation not found, incomplete strategy
% 3.53/1.43 % (1966402)------------------------------
% 3.53/1.43 % (1966402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.43 % (1966402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.43 % (1966402)CaDiCaL version: 2.1.3
% 3.53/1.43 % (1966402)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.43 % (1966402)Time elapsed: 0.001 s
% 3.53/1.43 % (1966402)Peak memory usage: 88 MB
% 3.53/1.43 % (1966403)Refutation not found, incomplete strategy
% 3.53/1.43 % (1966403)------------------------------
% 3.53/1.43 % (1966403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.43 % (1966403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.43 % (1966403)CaDiCaL version: 2.1.3
% 3.53/1.43 % (1966403)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.43 % (1966403)Time elapsed: 0.001 s
% 3.53/1.43 % (1966403)Peak memory usage: 88 MB
% 3.53/1.43 % (1966404)First to succeed.
% 3.53/1.43 % (1966404)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1966394"
% 3.53/1.43 % (1966405)------------------------------
% 3.53/1.43 % (1966405)------------------------------
% 3.53/1.43 % (1966413)lrs+10_1_sil=8000:sp=occurrence:random_seed=850529554:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.53/1.43 % (1966413)Also succeeded, but the first one will report.
% 3.53/1.43 % (1966402)------------------------------
% 3.53/1.43 % (1966402)------------------------------
% 3.53/1.43 % (1966403)------------------------------
% 3.53/1.43 % (1966403)------------------------------
% 3.53/1.43 % (1966404)Refutation found. Thanks to Tanya!
% 3.53/1.43 % SZS status Theorem for theBenchmark
% 3.53/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.43 % (1966404)------------------------------
% 3.53/1.43 % (1966404)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.43 % (1966404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.43 % (1966404)CaDiCaL version: 2.1.3
% 3.53/1.43 % (1966404)Termination reason: Refutation
% 3.53/1.43 % (1966404)Time elapsed: 0.003 s
% 3.53/1.43 % (1966404)Peak memory usage: 89 MB
% 3.53/1.43 % (1966404)Instructions burned: 2 (million)
% 3.53/1.43 % (1966404)------------------------------
% 3.53/1.43 % (1966404)------------------------------
% 3.53/1.43 % (1966394)Success in time 0.414 s
% 3.53/1.43 % Vampire exiting
%------------------------------------------------------------------------------