%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU103+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 3.57s 1.39s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 9 unt; 0 def)
% Number of atoms : 173 ( 12 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 220 ( 91 ~; 93 |; 28 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 92 ( 86 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( ~ empty(X0)
& preboolean(X0)
& element(X1,X0)
& element(X2,X0) )
=> element(prebool_union2(X0,X1,X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_finsub_1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( ( ~ empty(X0)
& preboolean(X0)
& element(X1,X0)
& element(X2,X0) )
=> element(prebool_difference(X0,X1,X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
fof(f31,axiom,
! [X0,X1,X2] :
( ( ~ empty(X0)
& preboolean(X0)
& element(X1,X0)
& element(X2,X0) )
=> prebool_union2(X0,X1,X2) = set_union2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_finsub_1) ).
fof(f32,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/sandbox/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
fof(f34,conjecture,
! [X0,X1,X2] :
( ( ~ empty(X2)
& preboolean(X2) )
=> ( ( element(X0,X2)
& element(X1,X2) )
=> element(symmetric_difference(X0,X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finsub_1) ).
fof(f35,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ~ empty(X2)
& preboolean(X2) )
=> ( ( element(X0,X2)
& element(X1,X2) )
=> element(symmetric_difference(X0,X1),X2) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f67,plain,
! [X0,X1,X2] :
( element(prebool_union2(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f68,plain,
! [X0,X1,X2] :
( element(prebool_union2(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( element(prebool_difference(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(prebool_difference(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f69]) ).
fof(f83,plain,
! [X0,X1,X2] :
( prebool_union2(X0,X1,X2) = set_union2(X1,X2)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f84,plain,
! [X0,X1,X2] :
( prebool_union2(X0,X1,X2) = set_union2(X1,X2)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(flattening,[],[f83]) ).
fof(f85,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,[],[f32]) ).
fof(f86,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,[],[f85]) ).
fof(f87,plain,
? [X0,X1,X2] :
( ~ element(symmetric_difference(X0,X1),X2)
& element(X0,X2)
& element(X1,X2)
& ~ empty(X2)
& preboolean(X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f88,plain,
? [X0,X1,X2] :
( ~ element(symmetric_difference(X0,X1),X2)
& element(X0,X2)
& element(X1,X2)
& ~ empty(X2)
& preboolean(X2) ),
inference(flattening,[],[f87]) ).
fof(f109,plain,
( ~ element(symmetric_difference(sK10,sK11),sK12)
& element(sK10,sK12)
& element(sK11,sK12)
& ~ empty(sK12)
& preboolean(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f88]) ).
fof(f119,plain,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f120,plain,
! [X2,X0,X1] :
( element(prebool_union2(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f121,plain,
! [X2,X0,X1] :
( element(prebool_difference(X0,X1,X2),X0)
| empty(X0)
| ~ preboolean(X0)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ preboolean(X0)
| empty(X0)
| prebool_union2(X0,X1,X2) = set_union2(X1,X2)
| ~ element(X1,X0)
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f154,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,[],[f86]) ).
fof(f156,plain,
preboolean(sK12),
inference(cnf_transformation,[],[f109]) ).
fof(f157,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f109]) ).
fof(f158,plain,
element(sK11,sK12),
inference(cnf_transformation,[],[f109]) ).
fof(f159,plain,
element(sK10,sK12),
inference(cnf_transformation,[],[f109]) ).
fof(f160,plain,
~ element(symmetric_difference(sK10,sK11),sK12),
inference(cnf_transformation,[],[f109]) ).
fof(f240,plain,
! [X0,X1] :
( empty(sK12)
| set_union2(X0,X1) = prebool_union2(sK12,X0,X1)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(resolution,[],[f153,f156]) ).
fof(f244,plain,
! [X0,X1] :
( set_union2(X0,X1) = prebool_union2(sK12,X0,X1)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(forward_subsumption_resolution,[],[f240,f157]) ).
fof(f246,plain,
! [X0,X1] :
( element(set_union2(X0,X1),sK12)
| empty(sK12)
| ~ preboolean(sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(superposition,[],[f120,f244]) ).
fof(f249,plain,
! [X0,X1] :
( element(set_union2(X0,X1),sK12)
| empty(sK12)
| ~ preboolean(sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(duplicate_literal_removal,[],[f246]) ).
fof(f251,plain,
! [X0,X1] :
( element(set_union2(X0,X1),sK12)
| ~ preboolean(sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(forward_subsumption_resolution,[],[f249,f157]) ).
fof(f252,plain,
! [X0,X1] :
( element(set_union2(X0,X1),sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(forward_subsumption_resolution,[],[f251,f156]) ).
fof(f253,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,[],[f121,f154]) ).
fof(f254,plain,
! [X2,X0,X1] :
( ~ preboolean(X2)
| empty(X2)
| element(set_difference(X0,X1),X2)
| ~ element(X0,X2)
| ~ element(X1,X2) ),
inference(duplicate_literal_removal,[],[f253]) ).
fof(f257,plain,
! [X0,X1] :
( ~ element(set_difference(X0,X1),sK12)
| element(symmetric_difference(X0,X1),sK12)
| ~ element(set_difference(X1,X0),sK12) ),
inference(superposition,[],[f252,f119]) ).
fof(f357,plain,
! [X0,X1] :
( empty(sK12)
| element(set_difference(X0,X1),sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(resolution,[],[f254,f156]) ).
fof(f361,plain,
! [X0,X1] :
( element(set_difference(X0,X1),sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(forward_subsumption_resolution,[],[f357,f157]) ).
fof(f428,plain,
! [X0,X1] :
( element(symmetric_difference(X0,X1),sK12)
| ~ element(set_difference(X1,X0),sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(resolution,[],[f257,f361]) ).
fof(f435,plain,
! [X0,X1] :
( element(symmetric_difference(X0,X1),sK12)
| ~ element(X0,sK12)
| ~ element(X1,sK12) ),
inference(forward_subsumption_resolution,[],[f428,f361]) ).
fof(f527,plain,
( ~ element(sK10,sK12)
| ~ element(sK11,sK12) ),
inference(resolution,[],[f435,f160]) ).
fof(f541,plain,
~ element(sK11,sK12),
inference(forward_subsumption_resolution,[],[f527,f159]) ).
fof(f543,plain,
$false,
inference(forward_subsumption_resolution,[],[f541,f158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU103+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n009.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 03:34:15 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
% 3.57/1.39 % (2638555)Detected formulas, will run a generic FOF schedule.
% 3.57/1.39 % (2638562)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=1150088578:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.57/1.39 % (2638563)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1961925424:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.57/1.39 % (2638564)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2614268986:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.57/1.39 % (2638560)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=1165482862:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.57/1.39 % (2638566)dis-21_1_sil=8000:lcm=predicate:random_seed=1026594798: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)
% 3.57/1.39 % (2638565)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1809033082:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.57/1.39 % (2638561)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=2862749569:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.57/1.39 % (2638563)Refutation not found, incomplete strategy
% 3.57/1.39 % (2638563)------------------------------
% 3.57/1.39 % (2638563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.39 % (2638563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.39 % (2638563)CaDiCaL version: 2.1.3
% 3.57/1.39 % (2638563)Termination reason: Refutation not found, incomplete strategy
% 3.57/1.39 % (2638563)Time elapsed: 0.002 s
% 3.57/1.39 % (2638563)Peak memory usage: 88 MB
% 3.57/1.39 % (2638564)Refutation not found, incomplete strategy
% 3.57/1.39 % (2638564)------------------------------
% 3.57/1.39 % (2638564)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.39 % (2638564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.39 % (2638564)CaDiCaL version: 2.1.3
% 3.57/1.39 % (2638564)Termination reason: Refutation not found, incomplete strategy
% 3.57/1.39 % (2638564)Time elapsed: 0.006 s
% 3.57/1.39 % (2638564)Peak memory usage: 88 MB
% 3.57/1.39 % (2638564)Instructions burned: 7 (million)
% 3.57/1.39 % (2638565)First to succeed.
% 3.57/1.39 % (2638565)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2638555"
% 3.57/1.39 % (2638566)Instruction limit reached!
% 3.57/1.39 % (2638566)------------------------------
% 3.57/1.39 % (2638566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.39 % (2638566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.39 % (2638566)CaDiCaL version: 2.1.3
% 3.57/1.39 % (2638566)Termination reason: Instruction limit
% 3.57/1.39 % (2638566)Termination phase: Saturation
% 3.57/1.39 % (2638566)Time elapsed: 0.074 s
% 3.57/1.39 % (2638566)Peak memory usage: 91 MB
% 3.57/1.39 % (2638566)Instructions burned: 129 (million)
% 3.57/1.39 % (2638564)------------------------------
% 3.57/1.39 % (2638564)------------------------------
% 3.57/1.39 % (2638563)------------------------------
% 3.57/1.39 % (2638563)------------------------------
% 3.57/1.39 % (2638574)lrs+10_1_sil=8000:sp=occurrence:random_seed=612550203:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.57/1.39 % (2638565)Refutation found. Thanks to Tanya!
% 3.57/1.39 % SZS status Theorem for theBenchmark
% 3.57/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.39 % (2638565)------------------------------
% 3.57/1.39 % (2638565)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.39 % (2638565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.39 % (2638565)CaDiCaL version: 2.1.3
% 3.57/1.39 % (2638565)Termination reason: Refutation
% 3.57/1.39 % (2638565)Time elapsed: 0.016 s
% 3.57/1.39 % (2638565)Peak memory usage: 89 MB
% 3.57/1.39 % (2638565)Instructions burned: 21 (million)
% 3.57/1.39 % (2638565)------------------------------
% 3.57/1.39 % (2638565)------------------------------
% 3.57/1.39 % (2638555)Success in time 0.438 s
% 3.57/1.39 % Vampire exiting
%------------------------------------------------------------------------------