%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET617+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 : n026.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 12:41:23 PM UTC 2026
% Result : Theorem 2.54s 1.32s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 19 ~; 8 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 17 ( 16 !; 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,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(f3,axiom,
! [X0] : difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).
fof(f4,axiom,
! [X0] : difference(empty_set,X0) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).
fof(f7,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f13,conjecture,
! [X0] :
( symmetric_difference(X0,empty_set) = X0
& symmetric_difference(empty_set,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th92) ).
fof(f14,negated_conjecture,
~ ! [X0] :
( symmetric_difference(X0,empty_set) = X0
& symmetric_difference(empty_set,X0) = X0 ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0] :
( symmetric_difference(X0,empty_set) != X0
| symmetric_difference(empty_set,X0) != X0 ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,plain,
( sK0 != symmetric_difference(sK0,empty_set)
| sK0 != symmetric_difference(empty_set,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f15]) ).
fof(f17,plain,
( sK0 != symmetric_difference(sK0,empty_set)
| sK0 != symmetric_difference(empty_set,sK0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f19,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
! [X0] : empty_set = difference(empty_set,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f21,plain,
! [X0] : difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f23,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f24,plain,
( sK0 != union(difference(sK0,empty_set),difference(empty_set,sK0))
| sK0 != union(difference(empty_set,sK0),difference(sK0,empty_set)) ),
inference(definition_unfolding,[],[f17,f19,f19]) ).
fof(f28,plain,
( sK0 != union(sK0,difference(empty_set,sK0))
| sK0 != union(difference(empty_set,sK0),sK0) ),
inference(superposition,[],[f24,f21]) ).
fof(f29,plain,
( sK0 != union(sK0,empty_set)
| sK0 != union(difference(empty_set,sK0),sK0) ),
inference(forward_demodulation,[],[f28,f20]) ).
fof(f30,plain,
( sK0 != union(sK0,empty_set)
| sK0 != union(empty_set,sK0) ),
inference(forward_demodulation,[],[f29,f20]) ).
fof(f31,plain,
( sK0 != sK0
| sK0 != union(empty_set,sK0) ),
inference(superposition,[],[f30,f23]) ).
fof(f32,plain,
sK0 != union(empty_set,sK0),
inference(trivial_inequality_removal,[],[f31]) ).
fof(f38,plain,
sK0 != union(sK0,empty_set),
inference(superposition,[],[f32,f22]) ).
fof(f39,plain,
$false,
inference(forward_subsumption_resolution,[],[f38,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET617+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 02:21:56 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.54/1.32 % (3410863)Detected formulas, will run a generic FOF schedule.
% 2.54/1.32 % (3410872)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=494899854:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/1.32 % (3410872)First to succeed.
% 2.54/1.32 % (3410872)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3410863"
% 2.54/1.32 % (3410871)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1799886718:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/1.32 % (3410871)Refutation not found, incomplete strategy
% 2.54/1.32 % (3410871)------------------------------
% 2.54/1.32 % (3410871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.32 % (3410871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.32 % (3410871)CaDiCaL version: 2.1.3
% 2.54/1.32 % (3410871)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.32 % (3410871)Time elapsed: 0.002 s
% 2.54/1.32 % (3410871)Peak memory usage: 88 MB
% 2.54/1.32 % (3410868)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=4196965510:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/1.32 % (3410869)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=1583864:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/1.32 % (3410874)dis-21_1_sil=8000:lcm=predicate:random_seed=1868164244: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)
% 2.54/1.32 % (3410870)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=1439203921:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/1.32 % (3410873)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=840670208:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/1.32 % (3410873)Also succeeded, but the first one will report.
% 2.54/1.32 % (3410874)Instruction limit reached!
% 2.54/1.32 % (3410874)------------------------------
% 2.54/1.32 % (3410874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.32 % (3410874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.32 % (3410874)CaDiCaL version: 2.1.3
% 2.54/1.32 % (3410874)Termination reason: Instruction limit
% 2.54/1.32 % (3410874)Termination phase: Saturation
% 2.54/1.32 % (3410874)Time elapsed: 0.071 s
% 2.54/1.32 % (3410874)Peak memory usage: 88 MB
% 2.54/1.32 % (3410874)Instructions burned: 130 (million)
% 2.54/1.32 % (3410872)Refutation found. Thanks to Tanya!
% 2.54/1.32 % SZS status Theorem for theBenchmark
% 2.54/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/1.32 % (3410872)------------------------------
% 2.54/1.32 % (3410872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.32 % (3410872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.32 % (3410872)CaDiCaL version: 2.1.3
% 2.54/1.32 % (3410872)Termination reason: Refutation
% 2.54/1.32 % (3410872)Time elapsed: 0.001 s
% 2.54/1.32 % (3410872)Peak memory usage: 88 MB
% 2.54/1.32 % (3410872)Instructions burned: 1 (million)
% 2.54/1.32 % (3410872)------------------------------
% 2.54/1.32 % (3410872)------------------------------
% 2.54/1.32 % (3410863)Success in time 0.268 s
% 2.54/1.32 % Vampire exiting
%------------------------------------------------------------------------------