%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM341+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:12:12 PM UTC 2026
% Result : Theorem 5.13s 1.84s
% Output : Refutation 5.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 4 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 43 ( 17 ~; 14 |; 8 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 45 ( 39 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f296,axiom,
! [X0,X1,X2] :
( sum(X1,X2,X0)
<=> difference(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minus_entry_point) ).
fof(f402,conjecture,
? [X0,X1,X2] :
( sum(X0,X1,X2)
<=> ( difference(X2,X1,X0)
& difference(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_same_as_subtract) ).
fof(f403,negated_conjecture,
~ ? [X0,X1,X2] :
( sum(X0,X1,X2)
<=> ( difference(X2,X1,X0)
& difference(X2,X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f450,plain,
! [X0,X1,X2] :
( sum(X0,X1,X2)
<~> ( difference(X2,X1,X0)
& difference(X2,X0,X1) ) ),
inference(ennf_transformation,[],[f403]) ).
fof(f453,plain,
! [X0,X1,X2] :
( ( sum(X1,X2,X0)
| ~ difference(X0,X1,X2) )
& ( difference(X0,X1,X2)
| ~ sum(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f296]) ).
fof(f454,plain,
! [X0,X1,X2] :
( ( ~ difference(X2,X1,X0)
| ~ difference(X2,X0,X1)
| ~ sum(X0,X1,X2) )
& ( ( difference(X2,X1,X0)
& difference(X2,X0,X1) )
| sum(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f450]) ).
fof(f455,plain,
! [X0,X1,X2] :
( ( ~ difference(X2,X1,X0)
| ~ difference(X2,X0,X1)
| ~ sum(X0,X1,X2) )
& ( ( difference(X2,X1,X0)
& difference(X2,X0,X1) )
| sum(X0,X1,X2) ) ),
inference(flattening,[],[f454]) ).
fof(f753,plain,
! [X2,X0,X1] :
( difference(X0,X1,X2)
| ~ sum(X1,X2,X0) ),
inference(cnf_transformation,[],[f453]) ).
fof(f754,plain,
! [X2,X0,X1] :
( sum(X1,X2,X0)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[],[f453]) ).
fof(f860,plain,
! [X2,X0,X1] :
( difference(X2,X0,X1)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f455]) ).
fof(f862,plain,
! [X2,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ difference(X2,X0,X1)
| ~ difference(X2,X1,X0) ),
inference(cnf_transformation,[],[f455]) ).
fof(f864,plain,
! [X2,X0,X1] : difference(X0,X1,X2),
inference(forward_subsumption_resolution,[],[f753,f860]) ).
fof(f865,plain,
! [X2,X0,X1] : sum(X1,X2,X0),
inference(forward_subsumption_resolution,[],[f754,f860]) ).
fof(f866,plain,
! [X2,X0,X1] :
( ~ difference(X0,X1,X2)
| ~ difference(X0,X2,X1) ),
inference(resolution,[],[f865,f862]) ).
fof(f867,plain,
! [X2,X0,X1] : ~ difference(X0,X2,X1),
inference(forward_subsumption_resolution,[],[f866,f864]) ).
fof(f868,plain,
$false,
inference(forward_subsumption_resolution,[],[f867,f864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM341+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 % Computer : n011.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Sun Sep 27 19:35:46 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.45 Running first-order theorem proving
% 0.11/0.45 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
% 5.13/1.84 % (2707954)Detected formulas, will run a generic FOF schedule.
% 5.13/1.84 % (2707967)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=772501979:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.13/1.84 % (2707971)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=835028530:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.13/1.84 % (2707971)First to succeed.
% 5.13/1.84 % (2707971)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2707954"
% 5.13/1.84 % (2707969)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3179585418:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.13/1.84 % (2707965)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=263774373:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.13/1.84 % (2707970)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3254254863:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.13/1.84 % (2707968)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=2716692089:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.13/1.84 % (2707969)Also succeeded, but the first one will report.
% 5.13/1.84 % (2707970)Also succeeded, but the first one will report.
% 5.13/1.84 % (2707972)dis-21_1_sil=8000:lcm=predicate:random_seed=3463964326: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)
% 5.13/1.84 % (2707972)Also succeeded, but the first one will report.
% 5.13/1.84 [W927 19:35:47.065188480 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.13/1.84 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.13/1.84 [W927 19:35:47.065264893 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 5.13/1.84 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 5.13/1.84 % (2707971)Refutation found. Thanks to Tanya!
% 5.13/1.84 % SZS status Theorem for theBenchmark
% 5.13/1.84 % SZS output start Proof for theBenchmark
% See solution above
% 5.13/1.84 % (2707971)------------------------------
% 5.13/1.84 % (2707971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.13/1.84 % (2707971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.13/1.84 % (2707971)CaDiCaL version: 2.1.3
% 5.13/1.84 % (2707971)Termination reason: Refutation
% 5.13/1.84 % (2707971)Time elapsed: 0.017 s
% 5.13/1.84 % (2707971)Peak memory usage: 89 MB
% 5.13/1.84 % (2707971)Instructions burned: 19 (million)
% 5.13/1.84 % (2707971)------------------------------
% 5.13/1.84 % (2707971)------------------------------
% 5.13/1.84 % (2707954)Success in time 0.628 s
% 5.13/1.84 % Vampire exiting
%------------------------------------------------------------------------------