%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU107+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:47:15 PM UTC 2026
% Result : Theorem 3.48s 1.37s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 13 unt; 0 def)
% Number of atoms : 116 ( 9 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 132 ( 56 ~; 55 |; 15 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 64 ( 61 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( ( ~ empty(X0)
& preboolean(X0)
& element(X1,X0)
& element(X2,X0) )
=> element(prebool_difference(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
fof(f7,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f20,axiom,
! [X0,X1,X2] :
( ( ~ empty(X0)
& preboolean(X0)
& element(X1,X0)
& element(X2,X0) )
=> prebool_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
fof(f21,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f22,conjecture,
! [X0] :
( ( ~ empty(X0)
& preboolean(X0) )
=> in(empty_set,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finsub_1) ).
fof(f23,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& preboolean(X0) )
=> in(empty_set,X0) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f25,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f26,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f35,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f21]) ).
fof(f50,plain,
! [X0,X1,X2] :
( element(prebool_difference(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f51,plain,
! [X0,X1,X2] :
( element(prebool_difference(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f50]) ).
fof(f56,plain,
! [X0,X1,X2] :
( prebool_difference(X0,X1,X2) = set_difference(X1,X2)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f57,plain,
! [X0,X1,X2] :
( prebool_difference(X0,X1,X2) = set_difference(X1,X2)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
? [X0] :
( ~ in(empty_set,X0)
& ~ empty(X0)
& preboolean(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f59,plain,
? [X0] :
( ~ in(empty_set,X0)
& ~ empty(X0)
& preboolean(X0) ),
inference(flattening,[],[f58]) ).
fof(f61,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f62,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f61]) ).
fof(f69,plain,
! [X0] : element(sK0(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f7]) ).
fof(f79,plain,
( ~ in(empty_set,sK10)
& ~ empty(sK10)
& preboolean(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f59]) ).
fof(f80,plain,
! [X0,X1] :
( ( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| set_difference(X0,X1) != empty_set ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f88,plain,
! [X2,X0,X1] :
( element(prebool_difference(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f89,plain,
! [X0] : element(sK0(X0),X0),
inference(cnf_transformation,[],[f69]) ).
fof(f114,plain,
! [X2,X0,X1] :
( prebool_difference(X0,X1,X2) = set_difference(X1,X2)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f115,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f35]) ).
fof(f116,plain,
preboolean(sK10),
inference(cnf_transformation,[],[f79]) ).
fof(f117,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f79]) ).
fof(f118,plain,
~ in(empty_set,sK10),
inference(cnf_transformation,[],[f79]) ).
fof(f120,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f122,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f80]) ).
fof(f153,plain,
( empty(sK10)
| ~ element(empty_set,sK10) ),
inference(resolution,[],[f120,f118]) ).
fof(f157,plain,
~ element(empty_set,sK10),
inference(forward_subsumption_resolution,[],[f153,f117]) ).
fof(f161,plain,
! [X0] : empty_set = set_difference(X0,X0),
inference(resolution,[],[f122,f115]) ).
fof(f171,plain,
! [X2,X0,X1] :
( element(set_difference(X0,X1),X2)
| empty(X2)
| ~ preboolean(X2)
| ~ element(X0,X2)
| ~ element(X1,X2)
| empty(X2)
| ~ preboolean(X2)
| ~ element(X0,X2)
| ~ element(X1,X2) ),
inference(superposition,[],[f88,f114]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ preboolean(X2)
| empty(X2)
| element(set_difference(X0,X1),X2)
| ~ element(X0,X2)
| ~ element(X1,X2) ),
inference(duplicate_literal_removal,[],[f171]) ).
fof(f201,plain,
! [X0,X1] :
( empty(sK10)
| element(set_difference(X0,X1),sK10)
| ~ element(X0,sK10)
| ~ element(X1,sK10) ),
inference(resolution,[],[f172,f116]) ).
fof(f205,plain,
! [X0,X1] :
( element(set_difference(X0,X1),sK10)
| ~ element(X0,sK10)
| ~ element(X1,sK10) ),
inference(forward_subsumption_resolution,[],[f201,f117]) ).
fof(f210,plain,
! [X0] :
( element(empty_set,sK10)
| ~ element(X0,sK10)
| ~ element(X0,sK10) ),
inference(superposition,[],[f205,f161]) ).
fof(f213,plain,
! [X0] :
( element(empty_set,sK10)
| ~ element(X0,sK10) ),
inference(duplicate_literal_removal,[],[f210]) ).
fof(f215,plain,
! [X0] : ~ element(X0,sK10),
inference(forward_subsumption_resolution,[],[f213,f157]) ).
fof(f220,plain,
$false,
inference(resolution,[],[f215,f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU107+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:35:32 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.48/1.37 % (411663)Detected formulas, will run a generic FOF schedule.
% 3.48/1.37 % (411672)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2585014216:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.37 % (411671)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2767679608:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.37 % (411671)Refutation not found, incomplete strategy
% 3.48/1.37 % (411671)------------------------------
% 3.48/1.37 % (411671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.37 % (411671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.37 % (411671)CaDiCaL version: 2.1.3
% 3.48/1.37 % (411671)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.37 % (411671)Time elapsed: 0.001 s
% 3.48/1.37 % (411671)Peak memory usage: 88 MB
% 3.48/1.37 % (411672)Instruction limit reached!
% 3.48/1.37 % (411672)------------------------------
% 3.48/1.37 % (411672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.37 % (411672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.37 % (411672)CaDiCaL version: 2.1.3
% 3.48/1.37 % (411672)Termination reason: Instruction limit
% 3.48/1.37 % (411672)Termination phase: Saturation
% 3.48/1.37 % (411672)Time elapsed: 0.039 s
% 3.48/1.37 % (411672)Peak memory usage: 88 MB
% 3.48/1.37 % (411672)Instructions burned: 130 (million)
% 3.48/1.37 % (411669)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=381454789:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.37 % (411670)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=948824238:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.37 % (411668)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=1597002536:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.37 % (411674)dis-21_1_sil=8000:lcm=predicate:random_seed=1670309778: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)
% 3.48/1.37 % (411673)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2802309418:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.37 % (411673)First to succeed.
% 3.48/1.37 % (411673)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-411663"
% 3.48/1.37 % (411680)lrs+10_1_sil=8000:sp=occurrence:random_seed=1078533308:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.48/1.37 % (411674)Instruction limit reached!
% 3.48/1.37 % (411674)------------------------------
% 3.48/1.37 % (411674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.37 % (411674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.37 % (411674)CaDiCaL version: 2.1.3
% 3.48/1.37 % (411674)Termination reason: Instruction limit
% 3.48/1.37 % (411674)Termination phase: Saturation
% 3.48/1.37 % (411674)Time elapsed: 0.079 s
% 3.48/1.37 % (411674)Peak memory usage: 92 MB
% 3.48/1.37 % (411674)Instructions burned: 130 (million)
% 3.48/1.37 % (411680)Also succeeded, but the first one will report.
% 3.48/1.37 % (411684)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4107187855:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.48/1.37 % (411684)Refutation not found, incomplete strategy
% 3.48/1.37 % (411684)------------------------------
% 3.48/1.37 % (411684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.37 % (411684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.37 % (411684)CaDiCaL version: 2.1.3
% 3.48/1.37 % (411684)Termination reason: Refutation not found, incomplete strategy
% 3.48/1.37 % (411684)Time elapsed: 0.002 s
% 3.48/1.37 % (411684)Peak memory usage: 88 MB
% 3.48/1.37 % (411684)Instructions burned: 2 (million)
% 3.48/1.37 % (411671)------------------------------
% 3.48/1.37 % (411671)------------------------------
% 3.48/1.37 % (411673)Refutation found. Thanks to Tanya!
% 3.48/1.37 % SZS status Theorem for theBenchmark
% 3.48/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.37 % (411673)------------------------------
% 3.48/1.37 % (411673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.37 % (411673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.37 % (411673)CaDiCaL version: 2.1.3
% 3.48/1.37 % (411673)Termination reason: Refutation
% 3.48/1.37 % (411673)Time elapsed: 0.006 s
% 3.48/1.37 % (411673)Peak memory usage: 88 MB
% 3.48/1.37 % (411673)Instructions burned: 6 (million)
% 3.48/1.37 % (411673)------------------------------
% 3.48/1.37 % (411673)------------------------------
% 3.48/1.37 % (411663)Success in time 0.42 s
% 3.48/1.37 % Vampire exiting
%------------------------------------------------------------------------------